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Hong Kong Philharmonic Orchestra

The Hong Kong Philharmonic Orchestra (Cantonese: 香港管弦樂團), commonly abbreviated as HKPO or HKPhil (Cantonese: 港樂), is a symphony orchestra based in Hong Kong. First established in 1947 as an amateur orchestra under the name Sino-British Orchestra (中英管弦樂團), it was renamed the Hong Kong Philharmonic Orchestra in 1957 and became a professional orchestra in 1974 under the funding of the government.

Sino-British Orchestra
The Sino-British Club was an organisation founded in 1946, aimed at promoting harmony among different groups in Hong Kong (especially British and native Hongkongese) through cultural activities. Various groups were found under the club, including drama, literature, film, and music.

In 1947, Anthony Braga, one of the leaders of the music group of the Sino-British Club, suggested to form a symphony orchestra to gather instrumentalists in the city and provide musical performance to the citizens, as the society was still recovering from the World War II. About 20 amateur musicians were found, and a chamber orchestra was formed quickly. Weekly rehearsal started in the summer.

Solomon Bard, a violinist who just finished his medical degree in the UK, returned to Hong Kong in the autumn of 1947, and was invited by Braga to be the conductor of the orchestra. Bard took over the orchestra, and conducted its debut performance on 30 April 1948 in St. Stephen's Girls' College.

Arrigo Foa
Bard continued his directorship of the orchestra after the debut. In 1953, Bard invited the Italian violinist and conductor Arrigo Foa to take over the orchestra, and Bard worked as the concertmaster and deputy conductor of the Orchestra.

Foa was a professional musician who joined Shanghai Municipal Orchestra as concertmaster in 1919. He succeeded Mario Paci as the conductor of the Shanghai orchestra in 1942, under the Japanese occupation. Foa migrated to Hong Kong in 1953 and led the orchestra immediately. He led the orchestra to play a critically acclaimed concert with pianist Louis Kentner.

Under the professional training of Foa, the orchestra improved rapidly, and gained a higher reputation in the city. Collaborating artists included pianist Julius Katchen and violinist Ruggiero Ricci.

Hong Kong Philharmonic Orchestra
In 1957, members of the orchestra decided to separate the group from Sino-British Club. As an independent organisation, the orchestra was renamed to the Hong Kong Philharmonic Orchestra, and registered as the Hong Kong Philharmonic Society. Most of the musicians remained, and Foa and Bard stayed on the same positions in the new ensemble.

In 1974, Hong Kong Philharmonic Orchestra became the first professional orchestra in Hong Kong, while the Sino-British Club dismissed in the same year. Kek-tjiang Lim was the orchestra's first music director with the ensemble in professional status, from 1974 to 1975. In February 1986, the HKPO made its debut tour of several cities in the People's Republic of China, with conductor Kenneth Schermerhorn and soloists Stephanie Chase (violin) and Li Jian (piano). In the autumn of 1995, the HKPO travelled to nine cities in the United States and Canada in its North American début under conductor David Atherton. In 2003, the orchestra made its European début with performances in London's Barbican Hall, Belfast, Dublin and Paris (Théâtre des Champs-Élysées).

The orchestra's most recent and longest-serving music director was Jaap van Zweden, from 2012 to 2024. In June 2023, Tarmo Peltokoski first guest-conducted the orchestra. In July 2024, the orchestra announced the appointment of Peltokoski as its next music director, effective with the 2026-2027 season, with an initial contract of four years. He is to hold the title of music director-designate for the 2025-2026 season.

In addition to classical performances, the orchestra occasionally appears backing local pop stars such as Hacken Lee, Jacky Cheung, Frances Yip, Teresa Carpio, Leehom Wang and Hins Cheung.

Recording history
The orchestra made its debut recording under the label Philips in 1978. Its repertoire includes Butterfly Lovers' Violin Concerto and selected Chinese orchestral works, under the baton of Hans Gunther Mommer. In the 1980s, the orchestra made a serious recording for HK Records. Recordings were also made for the label Marco Polo after Klaus Heymann founded Naxos.

Under the directorship of David Atherton, several recordings were released on Virgin Classics and GMN. In 1997, the orchestra was featured in Tan Dun's album Heaven Earth Mankind: Symphony 1997 (Sony Classical Records), as a celebration for the handover of Hong Kong.

The orchestra started a four-year project in 2015, making it the first Hong Kong and mainland Chinese orchestra to perform Wagner's The Ring of the Nibelung. The four operas were performed, one per year, in concert and recorded live for the Naxos label.

Each year the orchestra holds a crossover concert with selected cantopop singers. Live recordings are made after each production. Since the concert of Michael Kwan (conducted by Joseph Koo) in 1982, the most successful one has been the live recording of the concert with Jacky Cheung (conducted by Yip Wing-sie) in 1996.

Performance venues
After the reorganization from the Sino-British Orchestra into the Hong Kong Philharmonic Orchestra in 1957, the orchestra played the first concert in Loke Yew Hall, the University of Hong Kong. Hong Kong City Hall Concert Hall was the performance venue of the orchestra in its early years. The orchestra was the first to perform in the Hong Kong Cultural Centre after the venue's opening in 1989, participating in the International Celebration of the Arts, which was a festival to open the centre. Since then, Hong Kong Philharmonic has been the most frequent orchestra to perform in the venue. The orchestra officially became the venue partner of Hong Kong Cultural Centre in 2009.

The orchestra also gives an annual outdoor performance, Symphony Under the Stars, Hong Kong's largest outdoor symphonic concert, which attracts thousands of participants every year. Venues include the Happy Valley Racecourse and the New central Harbourfront.

Sino-British Orchestra (1947–1957)

 * Solomon Bard (1947–1953)
 * Arrigo Foa (1953–1957)

Music Directors (amateur era)

 * Arrigo Foa (1957–1969)
 * Kek-tjiang Lim (1969–1974)

Music Directors (professional era)

 * Kek-tjiang Lim (1974–1975)
 * Hans-Gunther Mommer (1975–1978)
 * Ling Tung (1979–1981)
 * Kenneth Schermerhorn (1984–1989)
 * David Atherton (1989–2000)
 * Samuel Wong (2000–2003 Music Director; 2003–2005 Principal Conductor)
 * Edo de Waart (2004–2012 Artistic Director & Chief Conductor)
 * Jaap van Zweden (2012–2024)
 * Tarmo Peltokoski (2025-26 Music Director Designate; 2026–30 Music Director)

Conductor Laureate

 * David Atherton (2000–2009)

Principal Guest Conductors

 * Maxim Shostakovich (1982–1985)
 * Kenneth Jean (1984–1993)
 * Yu Long (2015–present)

Resident Conductors

 * John-Szicheng Lau (1984–1986)
 * Wing-sie Yip (1986–2000)
 * Harmen Cnossen (2005–2006)
 * Lio Kuokman (2020-present)

Assistant Conductors

 * Perry So (2008–2010)
 * Vivian Ip (2016–2018)
 * Gerard Salonga (2016–2018)

Associate Conductors

 * Perry So (2010–2012)

title: Hong Kong Philharmonic Orchestra


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Unionville

Unionville is the name of some places in North America:

Canada

 * Unionville, Ontario
 * Unionville GO Station, a station in the GO Transit network located in the community
 * South Unionville, a community in Markham, Ontario

United States

 * Unionville, Connecticut
 * Unionville, Georgia
 * Unionville, Illinois (disambiguation)
 * Unionville, Indiana
 * Unionville, Iowa
 * Unionville, Frederick County, Maryland
 * Unionville, Michigan
 * Unionville, Missouri
 * Unionville, Nevada
 * Unionville, New Jersey
 * Unionville Vineyards, a winery in Unionville.
 * Unionville, New York (disambiguation) (multiple)
 * Unionville, North Carolina
 * Unionville, Ashtabula County, Ohio; on the border with Lake County
 * Unionville, Columbiana County, Ohio
 * Unionville, Holmes County, Ohio
 * Unionville, Morgan County, Ohio
 * Unionville, Washington County, Ohio
 * Unionville Center, Ohio
 * Unionville, Pennsylvania (disambiguation) (multiple)
 * Unionville, South Carolina, historic settlement now named Union, South Carolina
 * Unionville, Tennessee
 * Unionville, Utah, historic settlement now renamed Hoytsville, Utah

license: Creative Commons - Attribution Share-Alike - https://creativecommons.org/licenses/by-sa/4.0/

title: Unionville


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Class (philosophy)

A class is a collection whose members either fall under a predicate or are classified by a rule. Hence, while a set can be extensionally defined only by its elements, a class has also an intensional dimension that unites its members. When the term 'class' is applied so that it includes those sets whose elements are intended to be collected without a common predicate or rule, the distinction can be indicated by calling such sets "improper class."

Philosophers sometimes distinguish classes from types and kinds. We can talk about the class of human beings, just as we can talk about the type (or natural kind), human being, or humanity. How, then, might classes differ from types? One might well think they are not actually different categories of being, but typically, while both are treated as abstract objects, classes are not usually treated as universals, whereas types usually are. Whether natural kinds ought to be considered universals is vexed; see natural kind.

There is, in any case, a difference in how we talk about types or kinds. We say that Socrates is a token of a type, or an instance of the natural kind, human being. But notice that we say instead that Socrates is a member of the class of human beings. We would not say that Socrates is a "member" of the type or kind, human beings. Nor would we say he is a type (or kind) of a class. He is a token (instance) of the type (kind). So the linguistic difference is: types (or kinds) have tokens (or instances); classes, on the other hand, have members.

The concept of a class is similar to the concept of a set defined by its members. Here, the class is extensional. If, however, a set is defined intensionally, then it is a set of things that meet some requirement to be a member. Thus, such a set can be seen as creating a type. Note that it also creates a class from the extension of the intensional set. A type always has a corresponding class (though that class might have no members), but a class does not necessarily have a corresponding type.

title: Class (philosophy)


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Cayley graph

In mathematics, a Cayley graph, also known as a Cayley color graph, Cayley diagram, group diagram, or color group, is a graph that encodes the abstract structure of a group. Its definition is suggested by Cayley's theorem (named after Arthur Cayley), and uses a specified set of generators for the group. It is a central tool in combinatorial and geometric group theory. The structure and symmetry of Cayley graphs makes them particularly good candidates for constructing expander graphs.

Definition
Let $$G$$ be a group and $$S$$ be a generating set of $$G$$. The Cayley graph $$\Gamma = \Gamma(G,S)$$ is an edge-colored directed graph constructed as follows:

 * Each element $$g$$ of $$G$$ is assigned a vertex: the vertex set of $$\Gamma$$ is identified with $$G.$$
 * Each element $$s$$ of $$S$$ is assigned a color $$c_s$$.
 * For every $$g \in G$$ and $$s \in S$$, there is a directed edge of color $$c_s$$ from the vertex corresponding to $$g$$ to the one corresponding to $$gs$$.

Not every convention requires that $$S$$ generate the group. If $$S$$ is not a generating set for $$G$$, then $$\Gamma$$ is disconnected and each connected component represents a coset of the subgroup generated by $$S$$.

If an element $$s$$ of $$S$$ is its own inverse, $$s = s^{-1},$$ then it is typically represented by an undirected edge.

The set $$S$$ is often assumed to be finite, especially in geometric group theory, which corresponds to $$\Gamma$$ being locally finite and $$G$$ being finitely generated.

The set $$S$$ is sometimes assumed to be symmetric ($$S = S^{-1}$$) and not containing the group identity element. In this case, the uncolored Cayley graph can be represented as a simple undirected graph.

Examples

 * Suppose that $$G=\Z$$ is the infinite cyclic group and the set $$S$$ consists of the standard generator 1 and its inverse (−1 in the additive notation); then the Cayley graph is an infinite path.
 * Similarly, if $$G=\Z_n$$ is the finite cyclic group of order $$n$$ and the set $$S$$ consists of two elements, the standard generator of $$G$$ and its inverse, then the Cayley graph is the cycle $$C_n$$. More generally, the Cayley graphs of finite cyclic groups are exactly the circulant graphs.
 * The Cayley graph of the direct product of groups (with the cartesian product of generating sets as a generating set) is the cartesian product of the corresponding Cayley graphs. Thus the Cayley graph of the abelian group $$\Z^2$$ with the set of generators consisting of four elements $$(\pm 1,0),(0,\pm 1)$$ is the infinite grid on the plane $$\R^2$$, while for the direct product $$\Z_n \times \Z_m$$ with similar generators the Cayley graph is the $$n\times m$$ finite grid on a torus.

1 & x & z\\ 0 & 1 & y\\ 0 & 0 & 1\\ \end{pmatrix},\ x,y,z \in \Z\right\} $$ is depicted to the right. The generators used in the picture are the three matrices $$X, Y, Z$$ given by the three permutations of 1, 0, 0 for the entries $$x, y, z$$. They satisfy the relations $$Z = XYX^{-1}Y^{-1}, XZ = ZX, YZ = ZY$$, which can also be understood from the picture. This is a non-commutative infinite group, and despite being a three-dimensional space, the Cayley graph has four-dimensional volume growth.
 * A Cayley graph of the dihedral group $$D_4$$ on two generators $$a$$ and $$b$$ is depicted to the left. Red arrows represent composition with $$a$$. Since $$b$$ is self-inverse, the blue lines, which represent composition with $$b$$, are undirected. Therefore the graph is mixed: it has eight vertices, eight arrows, and four edges. The Cayley table of the group $$D_4$$ can be derived from the group presentation $$ \langle a, b \mid a^4 = b^2 = e, a b = b a^3 \rangle. $$ A different Cayley graph of $$D_4$$ is shown on the right. $$b$$ is still the horizontal reflection and is represented by blue lines, and $$c$$ is a diagonal reflection and is represented by pink lines. As both reflections are self-inverse the Cayley graph on the right is completely undirected. This graph corresponds to the presentation $$ \langle b, c \mid b^2 = c^2 = e, bcbc = cbcb \rangle. $$
 * The Cayley graph of the free group on two generators $$a$$ and $$b$$ corresponding to the set $$S = \{a, b, a^{-1}, b^{-1}\}$$ is depicted at the top of the article, with $$e$$ being the identity. Travelling along an edge to the right represents right multiplication by $$a,$$ while travelling along an edge upward corresponds to the multiplication by $$b.$$ Since the free group has no relations, the Cayley graph has no cycles: it is the 4-regular infinite tree. It is a key ingredient in the proof of the Banach–Tarski paradox.
 * More generally, the Bethe lattice or Cayley tree is the Cayley graph of the free group on $$n$$ generators. A presentation of a group $$G$$ by $$n$$ generators corresponds to a surjective homomorphism from the free group on $$n$$ generators to the group $$G,$$ defining a map from the Cayley tree to the Cayley graph of $$G$$. Interpreting graphs topologically as one-dimensional simplicial complexes, the simply connected infinite tree is the universal cover of the Cayley graph; and the kernel of the mapping is the fundamental group of the Cayley graph.
 * A Cayley graph of the discrete Heisenberg group $$\left\{ \begin{pmatrix}

Characterization
The group $$G$$ acts on itself by left multiplication (see Cayley's theorem). This may be viewed as the action of $$G$$ on its Cayley graph. Explicitly, an element $$h\in G$$ maps a vertex $$g\in V(\Gamma)$$ to the vertex $$hg\in V(\Gamma).$$ The set of edges of the Cayley graph and their color is preserved by this action: the edge $$(g,gs)$$ is mapped to the edge $$(hg,hgs)$$, both having color $$c_s$$. In fact, all automorphisms of the colored directed graph $$\Gamma$$ are of this form, so that $$G$$ is isomorphic to the symmetry group of $$\Gamma$$.

The left multiplication action of a group on itself is simply transitive, in particular, Cayley graphs are vertex-transitive. The following is a kind of converse to this:

$$

To recover the group $$G$$ and the generating set $$S$$ from the unlabeled directed graph $$\Gamma$$, select a vertex $$v_1\in V(\Gamma)$$ and label it by the identity element of the group. Then label each vertex $$v$$ of $$\Gamma$$ by the unique element of $$G$$ that maps $$v_1$$ to $$v.$$ The set $$S$$ of generators of $$G$$ that yields $$\Gamma$$ as the Cayley graph $$\Gamma(G,S)$$ is the set of labels of out-neighbors of $$v_1$$. Since $$\Gamma$$ is uncolored, it might have more directed graph automorphisms than the left multiplication maps, for example group automorphisms of $$G$$ which permute $$S$$.

Elementary properties

 * The Cayley graph $$\Gamma(G,S)$$ depends in an essential way on the choice of the set $$S$$ of generators. For example, if the generating set $$S$$ has $$k$$ elements then each vertex of the Cayley graph has $$k$$ incoming and $$k$$ outgoing directed edges. In the case of a symmetric generating set $$S$$ with $$r$$ elements, the Cayley graph is a regular directed graph of degree $$r.$$
 * Cycles (or closed walks) in the Cayley graph indicate relations among the elements of $$S.$$ In the more elaborate construction of the Cayley complex of a group, closed paths corresponding to relations are "filled in" by polygons. This means that the problem of constructing the Cayley graph of a given presentation $$\mathcal{P}$$ is equivalent to solving the Word Problem for $$\mathcal{P}$$.
 * If $$f: G'\to G$$ is a surjective group homomorphism and the images of the elements of the generating set $$S'$$ for $$G'$$ are distinct, then it induces a covering of graphs $$ \bar{f}: \Gamma(G',S')\to \Gamma(G,S),$$ where $$S = f(S').$$ In particular, if a group $$G$$ has $$k$$ generators, all of order different from 2, and the set $$S$$ consists of these generators together with their inverses, then the Cayley graph $$\Gamma(G,S)$$ is covered by the infinite regular tree of degree $$2k$$ corresponding to the free group on the same set of generators.
 * For any finite Cayley graph, considered as undirected, the vertex connectivity is at least equal to 2/3 of the degree of the graph. If the generating set is minimal (removal of any element and, if present, its inverse from the generating set leaves a set which is not generating), the vertex connectivity is equal to the degree.  The edge connectivity is in all cases equal to the degree.
 * If $$\rho_{\text{reg}}(g)(x) = gx$$ is the left-regular representation with $$|G|\times |G|$$ matrix form denoted $$[\rho_{\text{reg}}(g)]$$, the adjacency matrix of $$\Gamma(G,S)$$ is $A = \sum_{s\in S} [\rho_{\text{reg}}(s)]$.
 * Every group character $$\chi$$ of the group $$G$$ induces an eigenvector of the adjacency matrix of $$\Gamma(G,S)$$. The associated eigenvalue is $$\lambda_\chi=\sum_{s\in S}\chi(s),$$ which, when $$G$$ is Abelian, takes the form $$\sum_{s\in S} e^{2\pi ijs/|G|}$$ for integers $$j = 0,1,\dots,|G|-1.$$ In particular, the associated eigenvalue of the trivial character (the one sending every element to 1) is the degree of $$\Gamma(G,S)$$, that is, the order of $$S$$. If $$G$$ is an Abelian group, there are exactly $$|G|$$ characters, determining all eigenvalues. The corresponding orthonormal basis of eigenvectors is given by $$v_j = \tfrac{1}{\sqrt{|G|}}\begin{pmatrix} 1 & e^{2\pi ij/|G|} & e^{2\cdot 2\pi ij/|G|} & e^{3\cdot 2\pi ij/|G|} & \cdots & e^{(|G|-1)2\pi ij/|G|}\end{pmatrix}.$$ It is interesting to note that this eigenbasis is independent of the generating set $$S$$.  More generally for symmetric generating sets, take $$\rho_1,\dots,\rho_k$$ a complete set of irreducible representations of $$G,$$ and let $\rho_i(S) = \sum_{s\in S} \rho_i(s)$  with eigenvalue set $$\Lambda_i(S)$$. Then the set of eigenvalues of $$\Gamma(G,S)$$ is exactly $\bigcup_i \Lambda_i(S),$  where eigenvalue $$\lambda$$ appears with multiplicity $$\dim(\rho_i)$$ for each occurrence of $$\lambda$$ as an eigenvalue of $$\rho_i(S).$$

Schreier coset graph
If one instead takes the vertices to be right cosets of a fixed subgroup $$H,$$ one obtains a related construction, the Schreier coset graph, which is at the basis of coset enumeration or the Todd–Coxeter process.

Connection to group theory
Knowledge about the structure of the group can be obtained by studying the adjacency matrix of the graph and in particular applying the theorems of spectral graph theory. Conversely, for symmetric generating sets, the spectral and representation theory of $$\Gamma(G,S)$$ are directly tied together: take $$\rho_1,\dots,\rho_k$$ a complete set of irreducible representations of $$G,$$ and let $\rho_i(S) = \sum_{s \in S} \rho_i(s)$ with eigenvalues $$\Lambda_i(S)$$. Then the set of eigenvalues of $$\Gamma(G,S)$$ is exactly $\bigcup_i \Lambda_i(S),$ where eigenvalue $$\lambda$$ appears with multiplicity $$\dim(\rho_i)$$ for each occurrence of $$\lambda$$ as an eigenvalue of $$\rho_i(S).$$

The genus of a group is the minimum genus for any Cayley graph of that group.

Geometric group theory
For infinite groups, the coarse geometry of the Cayley graph is fundamental to geometric group theory. For a finitely generated group, this is independent of choice of finite set of generators, hence an intrinsic property of the group. This is only interesting for infinite groups: every finite group is coarsely equivalent to a point (or the trivial group), since one can choose as finite set of generators the entire group.

Formally, for a given choice of generators, one has the word metric (the natural distance on the Cayley graph), which determines a metric space. The coarse equivalence class of this space is an invariant of the group.

Expansion properties
When $$S = S^{-1}$$, the Cayley graph $$\Gamma(G,S)$$ is $$|S|$$-regular, so spectral techniques may be used to analyze the expansion properties of the graph. In particular for abelian groups, the eigenvalues of the Cayley graph are more easily computable and given by $\lambda_\chi = \sum_{s\in S} \chi(s)$ with top eigenvalue equal to $$|S|$$, so we may use Cheeger's inequality to bound the edge expansion ratio using the spectral gap.

Representation theory can be used to construct such expanding Cayley graphs, in the form of Kazhdan property (T). The following statement holds:

For example the group $$G = \mathrm{SL}_3(\Z)$$ has property (T) and is generated by elementary matrices and this gives relatively explicit examples of expander graphs.

Integral classification
An integral graph is one whose eigenvalues are all integers. While the complete classification of integral graphs remains an open problem, the Cayley graphs of certain groups are always integral. Using previous characterizations of the spectrum of Cayley graphs, note that $$\Gamma(G,S)$$ is integral iff the eigenvalues of $$\rho(S)$$ are integral for every representation $$\rho$$ of $$G$$.

Cayley integral simple group
A group $$G$$ is Cayley integral simple (CIS) if the connected Cayley graph $$\Gamma(G,S)$$ is integral exactly when the symmetric generating set $$S$$ is the complement of a subgroup of $$G$$. A result of Ahmady, Bell, and Mohar shows that all CIS groups are isomorphic to $$\mathbb{Z}/p\mathbb{Z}, \mathbb{Z}/p^2\mathbb{Z}$$, or $$\mathbb{Z}_2 \times \mathbb{Z}_2$$ for primes $$p$$. It is important that $$S$$ actually generates the entire group $$G$$ in order for the Cayley graph to be connected. (If $$S$$ does not generate $$G$$, the Cayley graph may still be integral, but the complement of $$S$$ is not necessarily a subgroup.)

In the example of $$G=\mathbb{Z}/5\mathbb{Z}$$, the symmetric generating sets (up to graph isomorphism) are The only subgroups of $$\mathbb{Z}/5\mathbb{Z}$$ are the whole group and the trivial group, and the only symmetric generating set $$S$$ that produces an integral graph is the complement of the trivial group. Therefore $$\mathbb{Z}/5\mathbb{Z}$$ must be a CIS group.
 * $$S = \{1,4\}$$: $$\Gamma(G,S)$$ is a $$5$$-cycle with eigenvalues $$2, \tfrac{\sqrt{5}-1}{2},\tfrac{\sqrt{5}-1}{2},\tfrac{-\sqrt{5}-1}{2},\tfrac{-\sqrt{5}-1}{2}$$
 * $$S = \{1,2,3,4\}$$: $$\Gamma(G,S)$$ is $$K_5$$ with eigenvalues $$4, -1,-1,-1,-1$$

The proof of the complete CIS classification uses the fact that every subgroup and homomorphic image of a CIS group is also a CIS group.

Cayley integral group
A slightly different notion is that of a Cayley integral group $$G$$, in which every symmetric subset $$S$$ produces an integral graph $$\Gamma(G,S)$$. Note that $$S$$ no longer has to generate the entire group.

The complete list of Cayley integral groups is given by $$\mathbb{Z}_2^n\times \mathbb{Z}_3^m,\mathbb{Z}_2^n\times \mathbb{Z}_4^n, Q_8\times \mathbb{Z}_2^n,S_3$$, and the dicyclic group of order $$12$$, where $$m,n\in \mathbb{Z}_{\ge 0}$$ and $$Q_8$$ is the quaternion group. The proof relies on two important properties of Cayley integral groups:
 * Subgroups and homomorphic images of Cayley integral groups are also Cayley integral groups.
 * A group is Cayley integral iff every connected Cayley graph of the group is also integral.

Normal and Eulerian generating sets
Given a general group $$G$$, a subset $$S \subseteq G$$ is normal if $$S$$ is closed under conjugation by elements of $$G$$ (generalizing the notion of a normal subgroup), and $$S$$ is Eulerian if for every $$s \in S$$, the set of elements generating the cyclic group $$\langle s \rangle$$ is also contained in $$S$$. A 2019 result by Guo, Lytkina, Mazurov, and Revin proves that the Cayley graph $$\Gamma(G,S)$$ is integral for any Eulerian normal subset $$S \subseteq G$$, using purely representation theoretic techniques.

The proof of this result is relatively short: given $$S$$ an Eulerian normal subset, select $$x_1,\dots, x_t\in G$$ pairwise nonconjugate so that $$S$$ is the union of the conjugacy classes $$\operatorname{Cl}(x_i)$$. Then using the characterization of the spectrum of a Cayley graph, one can show the eigenvalues of $$\Gamma(G,S)$$ are given by $\left\{\lambda_\chi = \sum_{i=1}^t \frac{\chi(x_i) \left|\operatorname{Cl}(x_i)\right|}{\chi(1)}\right\}$ taken over irreducible characters $$\chi$$ of $$G$$. Each eigenvalue $$\lambda_\chi$$ in this set must be an element of $$\mathbb{Q}(\zeta)$$ for $$\zeta$$ a primitive $$m^{th}$$ root of unity (where $$m$$ must be divisible by the orders of each $$x_i$$). Because the eigenvalues are algebraic integers, to show they are integral it suffices to show that they are rational, and it suffices to show $$\lambda_\chi$$ is fixed under any automorphism $$\sigma$$ of $$\mathbb{Q}(\zeta)$$. There must be some $$k$$ relatively prime to $$m$$ such that $$\sigma(\chi(x_i)) = \chi(x_i^k)$$ for all $$i$$, and because $$S$$ is both Eulerian and normal, $$\sigma(\chi(x_i)) = \chi(x_j)$$ for some $$j$$. Sending $$x\mapsto x^k$$ bijects conjugacy classes, so $$\operatorname{Cl}(x_i)$$ and $$\operatorname{Cl}(x_j)$$ have the same size and $$\sigma$$ merely permutes terms in the sum for $$\lambda_\chi$$. Therefore $$\lambda_\chi$$ is fixed for all automorphisms of $$\mathbb{Q}(\zeta)$$, so $$\lambda_\chi$$ is rational and thus integral.

Consequently, if $$G=A_n$$ is the alternating group and $$S$$ is a set of permutations given by $$\{ (12i)^{\pm 1} \}$$, then the Cayley graph $$\Gamma(A_n,S)$$ is integral. (This solved a previously open problem from the Kourovka Notebook.) In addition when $$G = S_n$$ is the symmetric group and $$S$$ is either the set of all transpositions or the set of transpositions involving a particular element, the Cayley graph $$\Gamma(G,S)$$ is also integral.

History
Cayley graphs were first considered for finite groups by Arthur Cayley in 1878. Max Dehn in his unpublished lectures on group theory from 1909–10 reintroduced Cayley graphs under the name Gruppenbild (group diagram), which led to the geometric group theory of today. His most important application was the solution of the word problem for the fundamental group of surfaces with genus ≥ 2, which is equivalent to the topological problem of deciding which closed curves on the surface contract to a point.

title: Cayley graph


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Hairspray (musical)

Hairspray is an American musical with music by Marc Shaiman and lyrics by Marc Shaiman and Scott Wittman, with a book by Mark O'Donnell and Thomas Meehan, based on John Waters's 1988 film of the same name. The songs include 1960s-style dance music and "downtown" rhythm and blues. Set in 1962 Baltimore, Maryland, the production follows teenage Tracy Turnblad's dream to dance on The Corny Collins Show, a local TV dance program based on the real-life Buddy Deane Show. When Tracy wins a role on the show, she becomes a celebrity overnight, leading to social change as Tracy campaigns for the show's integration.

The musical opened in Seattle in 2002 and moved to Broadway later that year. In 2003, Hairspray won eight Tony Awards, including one for Best Musical, out of 13 nominations. It ran for 2,642 performances, and closed on January 4, 2009. Hairspray has also had national tours, a West End production, and numerous foreign productions and was adapted as a 2007 musical film. The London production was nominated for a record-setting eleven Laurence Olivier Awards, winning four, including Best New Musical.

Background
According to interviews included as an extra feature on the 2007 film's DVD release, theater producer Margo Lion first conceived of Hairspray as a stage musical in 1998 after seeing the original film on television. "I was home looking at a lot of movies, and one of those movies was Hairspray." She contacted John Waters, who gave her his blessing, then acquired the rights from New Line Cinema. Lion contacted Marc Shaiman, who expressed interest in the project only if his partner, Scott Wittman, could participate, and Lion agreed. The two enlisted the help of actress and singer Annie Golden to produce a demo recording containing three songs, one of which, "Good Morning Baltimore", became the show's opening number. Based on their initial work, Lion was confident that she had hired the right team.

Lion contacted Rob Marshall about directing the musical. At the time he was involved in negotiations to direct the screen adaptation of Chicago, but he agreed to become involved in the early development stages of Hairspray with the stipulation he would drop out if assigned the film. Marshall remembered Marissa Jaret Winokur from her brief appearance in the film American Beauty and arranged a meeting with Shaiman and Wittman. The two immediately felt she was right to play Tracy Turnblad but hesitated to commit without seeing any other auditions. They hired Winokur to work with them on the project with the understanding she might be replaced later. A year later, Winokur was diagnosed with cervical cancer. Certain she would lose the role if the creative team learned about her condition, she underwent a hysterectomy, telling only her immediate family. The treatment and surgery succeeded, and Winokur returned to the project. Meanwhile, Marshall began work on Chicago, and Lion hired Jack O'Brien and Jerry Mitchell to direct and to choreograph, respectively. Winokur was one of the first to audition for the role of Tracy and spent two years preparing with voice and dance lessons. Divine portrayed Tracy's mother, Edna Turnblad, in the original film, and Shaiman liked the idea of maintaining the tradition of casting a man as Edna. Harvey Fierstein auditioned for the role with a "half-hour vocal audition". He thought they were "pacifying" him, but was told, "They don't want anyone but you".

According to Shaiman, one song, "I Know Where I've Been", became controversial during the genesis of the score:

"This was ... inspired by a scene late in the [1988] movie that takes place on the black side of town. It never dawned on us that a torrent of protest would follow us from almost everyone involved with the show. 'It's too sad. ... It's too preachy. ... It doesn't belong. ... Tracy should sing the eleven o'clock number.' We simply didn't want our show to be yet another showbiz version of a civil rights story where the black characters are just background. And what could be more Tracy Turnblad-like than to give the 'eleven o'clock number' to the black family at the heart of the struggle? Luckily ... the audiences embraced this moment, which enriches the happy ending to follow, and it is our proudest achievement of the entire experience of writing Hairspray."

Original Broadway production
After a successful tryout at Seattle's 5th Avenue Theatre, Hairspray opened on Broadway at the Neil Simon Theatre on August 15, 2002. Jack O'Brien directed the production, which Jerry Mitchell choreographed, with set design by David Rockwell, costume design by William Ivey Long, lighting design by Kenneth Posner, sound design by Steve C. Kennedy, and the show's many distinctive wigs by Paul Huntley. The performances were conducted by Lon Hoyt, with approximately 15 musicians. The original Broadway cast included Marissa Jaret Winokur and Harvey Fierstein as Tracy and Edna, respectively, Matthew Morrison as Link, Laura Bell Bundy as Amber, Kerry Butler as Penny, Linda Hart as Velma, Mary Bond Davis as Motormouth Maybelle, Corey Reynolds as Seaweed, Jackie Hoffman as Matron, Dick Latessa as Wilbur, and Clarke Thorell as Corny Collins. Kamilah Marshall, Shayna Steele, and Judine Richard played the Dynamites.

Hairspray received Tony Award nominations in 13 categories, winning eight, including for best musical, book, score and direction. Winokur, Fierstein and Latessa received awards for their performances. The production ran for more than six years, closing on January 4, 2009, after 2,642 performances. Thorell returned to the cast for the final ten months. Fierstein and Winokur returned to the cast for the final performances.

Original London production
The West End production opened at the Shaftesbury Theatre on October 11, 2007, for previews before its official opening on October 30. Michael Ball played Edna, with Mel Smith as Wilbur Turnblad, Leanne Jones as Tracy, Tracie Bennett as Velma, Paul Manuel as Corny Collins, Rachael Wooding as Amber, Elinor Collett as Penny, and Ben James-Ellis as Link. The original creative team of the Broadway production, with the director Jack O'Brien and choreographer Jerry Mitchell, reunited for the London production. The show garnered a record-setting 11 Olivier Award nominations and won Best New Musical, as well as Best Actress and Actor in a musical (Jones and Ball). The production closed on March 28, 2010, after nearly two and a half years and over 1,000 performances.

2021 London revival
The production was due to return to the West End at the London Coliseum for a limited 18-week season from 23 April to 29 August 2020, but the COVID-19 pandemic caused all public theatres to close indefinitely in mid-March. The production was initially delayed to 1 September to 8 November, and then delayed again to 21 June to 29 September 2021.

Michael Ball reprised his Olivier Award-winning role as Edna, reuniting him with director Jack O'Brien and choreographer Jerry Mitchell. Full casting includes Lizzie Bea as Tracy, Marisha Wallace as Motormouth Maybelle, Les Dennis as Wilbur Turnblad, Rita Simons as Velma Von Tussle, Jonny Amies as Link Larkin, and Mari McGinlay as Penny Pingleton. Paul Merton was originally set to make his West End debut as Wilbur but after several delays he was unable to join the company and was replaced by Dennis.

2010 Australian production
An Australian production of Hairspray opened in Melbourne at the Princess Theatre on October 2, 2010, to critical acclaim. It was directed by David Atkins and choreographed by So You Think You Can Dance Australia judge Jason Coleman. The show moved to Sydney on June 23, 2011. The cast included Jaz Flowers as Tracy, Trevor Ashley as Edna, Jack Chambers as Link, and Tevin Campbell reprising his role from the Broadway production as Seaweed. Atkins redesigned the production using new technology. The set used enormous LED screens that moved around the stage in various combinations as the characters interacted with animated landscapes generated across the screens. The musical opened at Sydney's Lyric Theatre at The Star Casino on 11 June 2011 and closed on 25 September 2011, two weeks earlier than anticipated.

2022 Australian Broadway revival
A revival of the original Broadway production opened at Melbourne's Regent Theatre in August 2022, 20 years after the original production opened on Broadway. The original direction and choreography (by Jack O'Brien and Jerry Mitchell, respectively), was recreated by director Matt Lenz and choreographer Dominic Shaw. The cast included Carmel Rodrigues as Tracy, Shane Jacobson as Edna, Rhonda Burchmore as Velma, Todd McKenney as Wilbur, Rob Mills as Corny Collins, and Asabi Goodman as Motormouth Maybelle. The production moved on to Adelaide's Festival Centre in December 2022 where the role of Corny Collins was taken over by Irish born Australian, Bobby Fox. The Adelaide production closed on 29 January 2023. The production then continued to Sydney's Lyric Theatre where it opened on 9 February 2024 and closed on 2 April 2024.

Tours
The first U.S. national tour started in September 2003 in Baltimore and ended in June 2006. It starred Carly Jibson as Tracy, Bruce Vilanch as Edna, Terron Brooks as Seaweed, Sandra DeNise as Penny, Susan Cella as Velma, and Ramona Cole (soon replaced by Charlotte Crossley) as Motormouth Maybelle. When the tour came to Los Angeles, Winokur reprised her role as Tracy, together with the original Broadway Link, Matthew Morrison. The same creative team of O'Brien and Mitchell was at the helm. Lon Hoyt served as music supervisor. Jim Vukovich served as music director for the entire 33 months on the road.

In July 2006, a non-Equity U.S. and Asian tour opened in Atlantic City's Harrah's Casino. The shorter "casino version" was used for a six-week run, but when the tour moved on, it continued with the full version minus the character of Lorraine. The production starred Brooklynn Pulver as Tracy, Jerry O'Boyle as Edna, Dan Ferretti as Wilbur, Constantine Rousouli as Link, Christian Dante White as Seaweed, Alyssa Malgeri as Penny, Jarret Mallon as Corny, Happy McPartlin as Velma, Pearl Thomas as Amber, and Yvette Clark as Motormouth Maybelle. The tour played sit-down engagements in Tokyo, Shanghai and Beijing. It gave its final performance on April 25, 2010, at the Fox Performing Arts Center in Riverside, California.

After the West End production closed, Hairspray began touring the UK and Ireland, starting at the Wales Millennium Centre in Cardiff on April 7, 2010, following previews from March 30. The tour starred Michael Ball as Edna, alternating with Michael Starke and Brian Conley; Les Dennis, Nigel Planer and Micky Dolenz alternating as Wilbur, and Laurie Scarth as Tracy.

Hairspray toured the UK and Ireland in 2013. The show opened on February 13 in The Lowry Theatre in Manchester with Mark Benton as Edna, Lucy Benjamin as Velma, Sandra Marvin as Motormouth Maybelle, Marcus Collins as Seaweed, and Freya Sutton as Tracy. MM Musicals presented the show at FairfieldHalls, Croydon, in the Ashcroft Theatre, from 19 to 22 November 2014, with Corin Miller as Tracy, Andy Lingfield as Edna, and Natalie Cave as Penny.

Mark Goucher produced a Hairspray tour in the UK from September 2015, starting at the Curve, Leicester. The production returned at the end of summer 2017 to once again tour the UK, starring Norman Pace as Wilbur, Brenda Edwards as Motormouth, Layton Williams, and Rebecca Mendoza as Tracy. The Curve production and subsequent tours were directed by Paul Kerryson with choreography by Drew McOnie.

The production toured the UK and Ireland again in 2021 directed by Paul Kerryson and starring Brenda Edwards as Motormouth Maybelle and Norman Pace as Wilbur. It opened in Plymouth on 24 June 2021 before touring around the UK into 2022.

Other productions
A Las Vegas production ran at the Luxor Hotel in 2006 starring Katrina Rose Dideriksen as Tracy, Austin Miller as Link, and Fierstein and Latessa reprising their roles as Edna and Wilbur. This 90-minute version was played in one act. Cut songs included "The Big Dollhouse", "(The Legend of) Miss Baltimore Crabs", "Velma's Revenge", "Good Morning Baltimore (Reprise)", and "Cooties".
 * Las Vegas

Royal Caribbean International presented the show on their first Oasis Class ship MS Oasis of the Seas, which made its maiden voyage in December 2009. The show was performed in the ship's 1350 seat Opal Theater three times on each seven-night cruise but was later replaced by Cats.
 * Royal Caribbean International

In 2018 the MS Symphony of the Seas made its maiden voyage, and due to multiple requests, Hairspray was added as a show. It is still being performed in one act, restoring "(The Legend of) Miss Baltimore Crabs" but like the Las Vegas version omitting "The Big Dollhouse", "Velma's Revenge", "Good Morning Baltimore (Reprise)", and "Cooties". The second verse of "It Takes Two" is also omitted. This show includes multiple uses of technology, combined with a company of singers and dancers. It is usually performed three or four times a week, along with a Royal Caribbean Production called “Flight: Dare to Dream”.

U.S. regional premiere
Weathervane Playhouse, in Newark, Ohio, performed the U.S. regional premiere from July 29 to August 7, 2010, immediately followed by The Riverton Arts Council in Riverton, Utah, at the Sandra N. Lloyd Performing Arts Center from July 30 to August 21, 2010.

Production at the Hollywood Bowl ran from August 5–7, 2011, directed and choreographed by Jerry Mitchell. Original Broadway cast members Fierstein and Winokur reprised their roles as Edna and Tracy. The cast also featured Corbin Bleu (Seaweed), Drew Carey (Wilbur), Diana DeGarmo (Penny), Mo Gaffney (Prudy and others), Nick Jonas (Link Larkin), Darlene Love (Motormouth Maybelle), Susan Anton (Velma), and John Stamos (Corny).
 * Hollywood Bowl

International productions
The first international production opened in Toronto at the Princess of Wales Theatre in April 2004 and ran for 245 performances. Vanessa Olivarez, a former American Idol contestant, starred as Tracy, and Jay Brazeau starred as Edna. The cast also included Tom Rooney as Wilbur, Fran Jaye as Motormouth Maybelle, Matthew Morgan as Seaweed, Shennel Campbell as Little Inez, Jennifer Stewart as Penny, Michael Torontow as Link, Susan Henley as Velma, Tara Macri as Amber, Kevin Meaney and Charlotte Moore as the Authority Figures, and Paul McQuillan as Corny. Rounding out the opening night cast were Caissie Levy, Steven Cutts, Felicia Dinwiddie, Karen Burthwright, Jesse Weafer, Clyde Alves, Breanne Arrigo, Lisa Bell, Adam Bolton, Amanda DeFreitas, Starr Dominigue, Nicolas Dromard, Desmond Osborne, Melanie Phillipson, Stephanie Pitsiladis, Christine Rossi, Avery Saltzman, Sheldon Smith, Alison Smyth, Lindsay Thomas, Darren Voros, Derek Wiens, and Ryan Wilson.

A South African production opened in Johannesburg in October 2007 with the original direction and choreography recreated by Matt Lenz and Greg Graham. New set and costume designs were by Michael Bottari and Ronald Case. A production in Buenos Aires, Argentina, opened on July 16, 2008, starring Enrique Pinti as Edna. The role of Tracy was cast through a reality-competition show called Yo Quiero Ser la Protagonista de Hairspray (I Want to Be Hairspray's Protagonist).

On November 14, 2008, a production of Hairspray in Manila, the Philippines, starred Madel Ching as Tracy and Michael de Mesa as Edna. The production closed on December 7, 2008. On July 10, 2009, a Brazilian production opened in Rio de Janeiro, starring Simone Gutierrez as Tracy and Edson Celulari as Edna. A 2010 Brazilian tour stopped in São Paulo, Brasilia, Curitiba and Porto Alegre.

A Dutch production ran during the 2009/2010 season. Edna was played by Arjan Ederveen and Link was Jim Bakkum (runner-up in the first season of the Dutch American Idol). On December 6, 2009 a German production opened in Cologne. Edna was played alternately by Uwe Ochsenknecht and comedian Tetje Mierendorf. Tracy was played by Maite Kelly, a former member of The Kelly Family, and Penny was Jana Stelley. The first production of Hairspray in the German language took place at the Theater St. Gallen, Switzerland. A re-creation of the Broadway/West End production of the show opened in Dubai in July 2010 with Leanne Jones, from the West End production, reprising her role as Tracy and Antony Stuart-Hicks as Edna.

A Japanese production was scheduled to run at the Toshima Arts and Culture Theatre, Tokyo in June 2020 and at Umeda Arts Theater, Osaka in July 2020. It was canceled due to the COVID-19 outbreak. It featured Naomi Watanabe as Tracy, Yuichiro Yamaguchi as Edna, Zen Ishikawa as Wilbur, Crystal Kay as Motormouth Maybelle, Jun Sena as Velma, Kohei Ueguchi as Corny, Kurumi Shimizu as Penny, Hiroki Miura as Link, Soichi Hirama as Seaweed, and Meimi Tamura (former ANGERME member) as Amber.

Other productions opened in Canada, Finland, Japan, South Korea, Italy, St. Gallen, Switzerland, and Brazil. The musical also played in Shanghai, China, at the Shanghai Grand Theatre in July 2008, Stockholm, Sweden in September 2008, and in Tivoli Gardens, Copenhagen, Denmark in March 2016. Other productions are planned for France, Israel, Iceland, Norway and Mexico. Hairspray has been translated into German, Finnish, Spanish, Dutch, Japanese, Korean, Italian, Portuguese, French, and Hebrew.

A production was performed at the Hong Kong Cultural Center by a performing arts company called Face Production. They won an HK Heckler Award for Best Musical, Best Actress and Best Set Design.

Another Japanese production was scheduled to run at the Toshima Arts and Culture Theatre, Tokyo from September 17 to October 2, 2022 and at Umeda Arts Theater, Osaka in August 2022. It featured Naomi Watanabe as Tracy, Yuichiro Yamaguchi as Edna, Zen Ishikawa as Wilbur, Eliana as Motormouth Maybelle, Jun Sena as Velma, Kohei Ueguchi as Corny, Kurumi Shimizu as Penny, Hiroki Miura as Link, Soichi Hirama as Seaweed, and Meimi Tamura as Amber.

School adaptation
In August 2008, the British television channel Sky 1 began broadcasting Hairspray: The School Musical, which followed the development of a North London comprehensive school's production of Hairspray from audition to performance, with input from various actors and creatives, including members of the Broadway production team and the West End cast.

The Junior version released by MTI excludes the musical numbers "I Can Hear the Bells", "(The Legend of) Miss Baltimore Crabs", "Velma's Revenge", "Big, Blonde, and Beautiful", "(You're) Timeless To Me", "(You're) Timeless To Me (Reprise)" and the character Harriman F. Spritzer.

NBC live television
Hairspray was a live musical produced by NBC and broadcast on December 7, 2016. Maddie Baillio played Tracy. Jennifer Hudson and Harvey Fierstein starred as Motormouth Maybelle and Edna, respectively. Martin Short portrayed Wilbur and Derek Hough played Corny. Kristin Chenoweth starred as Velma, and Ariana Grande played Penny. The roles of Amber, Link, and Seaweed were played by Dove Cameron, Garrett Clayton, and Ephraim Sykes, respectively. Sean Hayes portrayed Mr. Pinky, and Rosie O'Donnell played the gym teacher.

Act I
It is June 1962 in Baltimore. Tracy Turnblad, an overweight high school student, wakes up ("Good Morning Baltimore") and goes to school, where she receives a warning for "inappropriate hair height". After school, Tracy rushes home with her best friend, Penny, to catch the local teenage dance show, The Corny Collins Show ("The Nicest Kids in Town"). Edna, Tracy's shy and overweight mother, is ironing and complains about the noise of the music coming from the television, while Penny's mother, Prudy, complains about it being "race music". After an announcement that auditions for a place on the show will be held because Brenda (one of the Corny Collins Council Members) has taken a leave of absence from the show for "nine months", Tracy begs her mother for permission to audition. Fearing that Tracy will be laughed at due to her weight, Edna refuses. Penny and Amber (the main dancer on The Corny Collins Show) have similar arguments with their mothers ("Mama, I'm a Big Girl Now").

After gaining permission and support from her father, Wilbur, Tracy auditions for the show and bumps into a teenage heartthrob, Link Larkin, which leads into a dream sequence ("I Can Hear the Bells"). Velma Von Tussle, the racist producer of The Corny Collins Show, rejects Tracy at the audition because of her size ("(The Legend of) Miss Baltimore Crabs"), and rejects a black girl, Little Inez.

Back at school, Tracy is sent to detention for her "monumental hair-don't". There she meets black dancer Seaweed J. Stubbs (the son of the hostess of "Negro Day" on The Corny Collins Show, Motormouth Maybelle), who teaches her several dance moves. She uses the new dance steps at the Sophomore Hop the next day to introduce herself to Corny Collins ("The Madison"). After Corny sees Tracy dance, he gives her a place on the show ("The Nicest Kids in Town" (Reprise)). During the broadcast, Link, at Corny's suggestion, sings "It Takes Two" to Tracy, much to Amber's dismay. After the show, Mr. Spritzer, the show's worrisome sponsor, appeals to Velma over Tracy's appointment to the Council. Threatening to fire Corny from the show, Velma is eventually left distraught and determines to ruin Tracy ("Velma's Revenge").

At the Turnblad house, Edna is receiving calls from fans who saw Tracy on the show. A call comes in from Mr. Pinky, the owner of a plus-size dress shop, for an endorsement. Tracy pleads with her mother to come with her and to act as her agent although Edna has not left their apartment in years. Finally making it outside, Edna is given a huge makeover ("Welcome to the 60's") and Tracy becomes the shop's spokes-girl. At school, signs of Tracy's fame are evident in the schoolyard, with graffiti on the walls and Shelly, another Council Member, sporting Tracy's signature hairdo. During a game of dodgeball, a jealous Amber knocks Tracy out, and Link rushes to her side. Penny and Seaweed, who have developed a liking for each other, rush to fetch the school nurse, only to find her out sick. Seaweed, suggesting that some fun would make Tracy feel better, invites all of them to his mother's record shop for a platter party ("Run and Tell That").

At the shop, Tracy rallies everyone to march against the station on the following day's Mother-Daughter Day, as blacks are not allowed on the show except on the monthly Negro Day. Before they start, Motormouth Maybelle convinces the initially reluctant Edna and Wilbur to march as well. Link declined to participate for the sake of his contract with the show. During the protest, led by Motormouth, Velma calls the police and fights break out. When the police arrive on the scene, almost everyone is arrested ("Big, Blonde and Beautiful").

Act II
After the march, most of the women are locked up in a women's penitentiary ("The Big Dollhouse"). Because of Velma's dirty tactics, the governor pardons and releases her and Amber. Wilbur bails out the rest, except Tracy, who is forced to remain in jail through another one of Velma's manipulations. Tracy is alone and wishes that Link could be with her ("Good Morning Baltimore" (Reprise)). Back at the Har-De-Har Hut (Wilbur's joke shop), Wilbur and Edna are left destitute because of the money it took to bail everyone out. Edna sympathizes with Tracy's dream—she had dreamed of making her "own line of queen-sized dress patterns". Edna and Wilbur reminisce about their past and how they can never be parted from each other ("(You're) Timeless to Me"). During the night, Link sneaks into the jail, where he finds Tracy in solitary confinement. As Link and Tracy reunite, Penny's mother, Prudy, punishes Penny for "going to jail without her permission" and ties her up in her bedroom, where Seaweed comes to her rescue. Both couples declare their love ("Without Love"). After escaping their respective prisons, the couples seek refuge at Motormouth Maybelle's Record Shop. Tracy thinks it unfair that after all their hard work, The Corny Collins Show is still segregated. They devise a plan to integrate the show, and Motormouth remembers their long fight for equality ("I Know Where I've Been").

On the day of the Miss Teenage Hairspray competition, Corny Collins starts the show with a song ("(It's) Hairspray"). Amber shows off her talents in a bid to get more votes from the viewers ("Cooties"). As the results are about to be announced, Tracy stuns Amber as she makes her entrance in a magenta dress without any petticoat underneath, taking over the stage, and is joined by Link, Penny, Seaweed, Edna, Wilbur, Little Inez, Corny, and Motormouth. Tracy is declared the winner of the competition. Amber and Velma protest the results, claiming that it is all wrong. Little Inez then tries to take the crown by force when Amber refuses to hand it over, but Tracy stops her, claiming that her heart is set on something more important: Link's and her future. She then proclaims The Corny Collins Show is "now and forevermore" racially integrated, to much applause. When all is announced, Spritzer runs onstage thrilled with the public's response to the telecast, announces that the governor has pardoned Tracy and given her a full college scholarship, and offers Link a recording contract and Velma the position of vice president of Ultra Glow – beauty products for women of color, much to her chagrin. Prudy arrives at the station and, seeing how happy Penny is with Seaweed, accepts her daughter for who she is. At the height of the moment, the company invites Amber and Velma to join the celebration. With the station in joyous celebration, Tracy and Link cement their love with a kiss ("You Can't Stop the Beat").

Characters
Principal roles and casts of major productions of stage productions of Hairspray:

Musical numbers

 * Act I
 * "Good Morning Baltimore" – Tracy and Ensemble
 * "The Nicest Kids in Town" – Corny and Council Members
 * "Mama, I'm a Big Girl Now" – Edna, Tracy, Prudy, Penny, Velma, Amber, and Female Ensemble
 * "I Can Hear the Bells" – Tracy and Ensemble
 * "(The Legend of) Miss Baltimore Crabs" – Velma and Council Members
 * "The Nicest Kids in Town (Reprise)"† – Corny, Tracy, and Council Members
 * "It Takes Two" – Link, Tracy, and Male Ensemble
 * "Velma's Revenge"† – Velma
 * "Welcome to the 60's" – Tracy, Edna, The Dynamites, Mr. Pinky, and Ensemble
 * "Run and Tell That!" – Seaweed, Little Inez, and Motormouth Kids
 * "Big, Blonde and Beautiful" – Motormouth, Little Inez, Tracy, Edna, Wilbur, and Ensemble

†Not on the cast recording.
 * Act II
 * "The Big Dollhouse" – Matron, Edna, Velma, Tracy, Amber, Penny, Motormouth, Little Inez, and Female Ensemble
 * "Good Morning Baltimore (Reprise)" – Tracy
 * "(You're) Timeless to Me" – Edna and Wilbur
 * "(You're) Timeless to Me (Reprise)"† – Edna and Wilbur
 * "Without Love" – Tracy, Link, Penny, Seaweed, and Ensemble
 * "I Know Where I've Been" – Motormouth and Ensemble
 * "(It's) Hairspray" – Corny and Council Members
 * "Cooties" – Amber and Council Members
 * "You Can't Stop the Beat" – Tracy, Link, Penny, Seaweed, Edna, Wilbur, Motormouth, Velma, Amber, and Company

Score revisions and additional songs
Hairspray went through several revisions during its pre-Broadway run in Seattle, in the process eliminating and replacing several musical numbers. In Seattle, an infomercial about safety on the road titled "Blood on the Pavement" followed "The Nicest Kids in Town", and is included on the cast album following "You Can't Stop the Beat". Early versions of the show featured "Velma's Cha-Cha" and "The Status Quo" (Seattle) (with its short reprise "Rage") during Tracy's audition and dismissal, but the team instead opted for "(The Legend of) Miss Baltimore Crabs". After Tracy's rejection from the Council, there was a scene in the Har-De-Har Hut in which Wilbur tried to cheer Tracy up, singing that "It Doesn't Get Better than This". Later replaced by the similar "Positivity", the scene was cut early in the Seattle tryout as it was deemed emotionally redundant.

After Tracy eventually made it on the show, there was a song, "The New Girl in Town", sung first by the Councilettes and later by the Black girls. Although cut during the Seattle tryout, it was included in the 2007 film and appears in the show's instrumental score. "The Mother-Daughter Cha-Cha-Cha" was another cut number that originally followed "Big, Blonde, and Beautiful". Later, the writers absorbed the protest rally and Mother-Daughter Day into the number, thus deleting the song and folding the sequence into a single scene. A song called "Step on Up" was also cut in favor of "I Know Where I've Been". Early on in the genesis of the show, the plot involved a "Miss Auto Show" competition, as in the 1988 film, instead of "Miss Teenage Hairspray". For this competition, later revised due to the cost of cars onstage, there was a song called "Take a Spin" sung by Corny in the place of "(It's) Hairspray". After Amber's rendition of "Cooties", Tracy had a song before the finale, "It Ain't Over 'Til the Fat Lady Sings", that was cut after readings of the show; it was included as a track on the Special Edition of the 2007 motion picture's soundtrack.

Instrumentation and chorus
Hairspray's orchestration calls for 15 musicians: two keyboards, the first of which is played by the conductor, electric bass, two guitars, drums, percussion, two trumpets, trombone, two woodwind players, two violins, and cello. The guitarists both double on acoustic and electric guitars, with the first playing lead and the second rhythm, and the trumpet doubles on flugelhorn; the original production also featured a piccolo trumpet double during tryouts. The first woodwind player doubles on tenor and alto saxophones and flute. The second woodwind player doubles on tenor, alto, soprano and baritone saxophones and flute, while the backup chorus calls for three males and three females.

In the original Broadway production, a few of the actors mimed on musical instruments in order to fulfil a minimum musician requirement at the Neil Simon Theatre.

Touring productions often use smaller/reduced orchestrations to save on costs – the UK 2017/18 tour which used a 12-piece orchestration – two keyboards (Of which the first is played by the conductor), two guitars, electric bass, drums, percussion, two woodwind players (in which the second one is playing alto, tenor, soprano and baritone saxophones and flute), trombone and two trumpets and a 12-piece background chorus: six males and six females.

Themes
Hairspray explores racial prejudice and freedom of expression. It highlights individuality, and the importance of everyone working together for something to become revolutionary. The musical is empowering, as although it touches on racial issues prevalent in 1960s America, it focuses more on the associated attitudes, and the power we have to change discrimination. The musical encourages individuality, acceptance and freedom. It applies to any social context and time, as it highlights ongoing issues such as fat-shaming, racism and discrimination. It also explores femininity. Notably, Edna Turnblad is performed in drag. Allowing a drag role adds queerness to the musical, which has no gay characters. Edna is considered to be the non-racialized who is part of the story. The musical also challenges societal norms of femininity. Edna's body size emphasizes the show's diva roles. The musical highlights female characters who are strong and associated with diva characteristics.

Hairspray emphasizes issues of acceptance and discrimination within society. Set in the 1960s, it highlights racial discrimination against African-Americans during the Civil Rights Movement, with a focus on popular culture. The Civil Rights Movement gained African-Americans the right to vote, gave them a voice, and introduced freedom for all, but African-Americans still experienced vast inequality during this time. This reality, of the whites holding all institutional and political power, is portrayed in Hairspray in The Corny Collins Show. African-Americans are allowed to dance on the show only once a month, and there is a stereotypical racial representation of dance style. The social representation in Hairspray parallels the reality of the 1960s. By the end of the show, African-Americans are allowed to dance on the show. The show acknowledges the challenges and limitations enforced on African Americans during this time, and reminds audiences of the Civil Rights Movement's achievements. Its message can also be used to empower change for other forms of discrimination relevant in today’s society.

Critics
According to Variety, Hairspray received 13 favorable and four mixed reviews. In his Variety review, Charles Isherwood wrote: "this sweet, infinitely spirited, bubblegum-flavored confection won't be lacking for buyers any time soon. Arriving in an aerosol fog of advance hype, it more than lives up to its promise." Ben Brantley wrote: "So what if it's more than a little pushy in its social preaching? Stocked with canny, deliriously tuneful songs by Marc Shaiman and Scott Wittman and directed by Jack O'Brien with a common touch that stops short of vulgarity, 'Hairspray' is as sweet as a show can be without promoting tooth decay. ...[it] succeeds in recreating the pleasures of the old-fashioned musical comedy without seeming old-fashioned. ...Shaiman... is taking the infectious hooks and rhythms from period pop and R&B and translating them into the big, bouncy sound that Broadway demands.... And while the savvy arrangements... nod happily to Motown, Elvis, Lesley Gore ballads and standards like 'Higher and Higher', the score's appeal isn't nostalgic. It's music that builds its own self-contained, improbably symmetrical world". New York's Daily News wrote, "As Tracy, Marissa Jaret Winokur has the heft, the pipes and an enormously appealing stage presence. Her dancing may not be as special as the plot suggests, but she wins your heart... With this role, Fierstein places himself in the great line of Broadway divas."

Box office and business
Hairspray opened with a $12 million advance; after the 2003 Tony Awards, it was expected to do five times the business it normally did on a Monday. The entire $10.5 million investment was recouped by May 2003 (about nine months after it opened on Broadway). In 2002–03 it averaged 99% capacity; in 2007 it averaged 86%.

Adaptations
A film version was released in July 2007. The film was directed and choreographed by Adam Shankman and starred John Travolta as Edna, Christopher Walken as Wilbur, Queen Latifah as Maybelle, Michelle Pfeiffer as Velma, James Marsden as Corny, and Nikki Blonsky as Tracy. Hugh Jackman and Joey McIntyre were also considered to play Corny. NBC's Hairspray Live!, directed by Kenny Leon and Alex Rudzinski, aired in December 2016 to mostly positive reviews.

Original Broadway production
Sources: PlaybillVault; Internet Broadway Database; Playbill; Playbill

Original London production
Sources: Playbill; Playbill; Olivier Awards The Telegraph

title: Hairspray (musical)


text:
Ralph Emerson (disambiguation)

Ralph Waldo Emerson (1803–1882) was an American philosopher and essayist.

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Otto Warburg may refer to:

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Sydney Symphony Orchestra

The Sydney Symphony Orchestra (SSO) is an Australian symphony orchestra based in Sydney. With roots going back to 1908, the orchestra was made a permanent professional orchestra on the formation of the Australian Broadcasting Commission in 1932. The orchestra has performed at the Sydney Opera House as its home concert hall, since the venue's opening in 1973. Simone Young is the orchestra's chief conductor and the first female conductor in the post.

Venues and programming
The Sydney Symphony performs around 150 concerts a year to a combined annual audience of more than 350,000. The regular subscription concert series are mostly performed at the Sydney Opera House, but other venues around Sydney are used as well, including the City Recital Hall at Angel Place and the Sydney Town Hall. The Town Hall was the home of the orchestra until the opening of the Opera House in 1973. Since then, most concerts have been taking place in the Opera House's Concert Hall (capacity: 2,679 seats). A major annual event for the orchestra is Symphony in the Domain, a free evening outdoor picnic concert held in the summer month of January in the large city park known as The Domain. Lately it has been presented in Parramatta. This event draws audiences of over 80,000 and is a long-established part of the Sydney summer cultural calendar.

History
The first concert by a group calling themselves the Sydney Symphony Orchestra was held on 30 September 1905. Sponsored by the Musicians Union, this group was formed from musicians who had come together to form an orchestra to accompany the pianist Ignacy Jan Paderewski's Sydney concerts when he toured Australia in 1904. A more sustained effort to establish an orchestra began in 1908 when an alliance between musicians, their union and leading business and legal figures organised regular subscription concerts. Between 1908 and 1917, a total of 47 concerts was held by a group calling themselves the Sydney Symphony Orchestra. These concerts included many Sydney premieres of key works of the classical repertoire including Schumann's Symphony No. 1 in B-flat, Brahms' Symphony No. 1 in C minor, and in 1910, Berlioz's Symphonie Fantastique as well as a number of quite recent, even modernist works including, in 1910, Richard Strauss's tone-poem Don Juan; in 1911, Debussy's Prélude à l'après-midi d'un faune; in 1912, Elgar's Enigma Variations; in 1913, Rimsky-Korsakov's Scheherazade; in 1914, Borodin's In the Steppes of Central Asia; and in 1917, Borodin's Symphony in B minor and Glazunov's Symphony in C minor. This initiative folded when most of the orchestra's members were recruited by the New South Wales State Conservatorium of Music's orchestra, then conducted by its founding director, Henri Verbrugghen.

Verbrugghen resigned from the Conservatorium in 1922 amidst controversy regarding funding for his orchestra. The Conservatorium student orchestra, supplemented by teachers continued to give concerts throughout the 1920s. Although there were regular calls for the government to provide funding for a permanent full-time professional orchestra, no such orchestra had been established in Sydney when the ABC began operation in 1932. Despite expectations, according to Fraser, the ABC's initial intervention was quite modest. It simply adopted the 20 piece orchestra already engaged in the Sydney studio by the ABC's predecessor, the privately run Australian Broadcasting Company. Within the year, this orchestra was expanded to a 24-player concert orchestra used primarily for the purposes of broadcasting. However it sometimes combined for concerts with the NSW State Conservatorium under different names including the ABC Symphony Orchestra and the NSW State Symphony Orchestra. It was not until 1936 that the ABC sponsored a new series of orchestra concerts in Sydney under the name of the "Sydney Symphony Orchestra". At this time the orchestra was increased to 45 players, and sometimes augmented to 70 players for public performances. It also again inaugurated annual concert seasons in that year. In 1937, the ABC purchased the name "Sydney Symphony Orchestra" from George Plummer who had been instrumental in establishing the initial Sydney Symphony Orchestra in 1908.

Because of the political instability in Europe in the 1930s, many leading artists spent large amounts of time in Australia. Performances were given under the direction of Antal Doráti and Sir Thomas Beecham. Soloists appearing with the orchestra included Arthur Rubinstein, Bronisław Huberman, Artur Schnabel and Jascha Spivakovsky.

At the end of World War II, the ABC reached agreement with the Sydney City Council and the New South Wales state government to jointly fund the orchestra. The new 80-member Sydney Symphony Orchestra gave its first concert in January 1946.

Eugene Goossens joined the orchestra as its first chief conductor in 1947. Goossens introduced outdoor concerts and conducted Australian premieres of contemporary music. In 1948, he uttered the prophetic words, "Sydney must have an opera house!". Goossens was knighted in 1955, the year before his term was due to end. His tenure was abruptly cut short in March 1956 under personal circumstances deemed 'scandalous' at the time, and he was forced to return to England in disgrace.

Sir Eugene Goossens was succeeded by Nikolai Malko, Dean Dixon, Moshe Atzmon and Willem van Otterloo. Under van Otterloo, the orchestra made an eight-week European tour in 1974 which culminated in two concerts in Amsterdam and The Hague. Also under van Otterloo, the orchestra established the Concert Hall of the Sydney Opera House as its home base for most of its concerts.

In 1982, Sir Charles Mackerras, a former oboist with the orchestra, became the first Australian to be appointed its chief conductor. His term ended in 1985, although illness prevented him from conducting some later concerts. Zdeněk Mácal was initially appointed on a three-year contract from 1986 until 1988, which was reduced to one year, at his request; he nevertheless left abruptly in the first season. The young Australian conductor Stuart Challender, who had taken over some of Mackerras's commitments in 1985, became the orchestra's chief conductor in 1987. In Australia's bicentennial year (1988), Challender led the orchestra in a successful tour of the United States. He remained as chief conductor until his death in December 1991.

In 1994, the orchestra received increased support from the federal government, enabling it to raise the number of players to 110, increase touring and recording ventures, and improve orchestral salaries. That year, it also appointed Edo de Waart as the orchestra's chief conductor and artistic director. de Waart held the post until 2003.

Since de Waart's tenure, the Sydney Opera House has been the orchestra's full-time home, with all rehearsals taking place in the Opera House Concert Hall. Highlights of his tenure in Sydney included Wagner's Ring Cycle in concert, a focus on the works of his personal favourite Mahler and tours of Europe (1995), Japan (1996) and the United States (1998).

Gianluigi Gelmetti was chief conductor from 2004 to 2008, succeeded by Vladimir Ashkenazy (2009–2013). In May 2012, David Robertson was named as the SSO's next chief conductor, with an initial contract from 2014 to 2018. In July 2017, the SSO announced the extension of Robertson's contract by one year, through to the end of 2019. Robertson concluded his SSO chief conductorship in 2019.

Simone Young first guest-conducted the SSO in 1996. In December 2019, the SSO announced the appointment of Young as its next chief conductor, effective in 2022, with an initial contract of 3 years. Young is the first female conductor to be named chief conductor of the Sydney Symphony Orchestra. In February 2024, the SSO announced the extension of Young's contract as its chief conductor through the end of 2026.

Financial structure
The SSO, like all the other major symphony orchestras in Australia, was funded by the federal government as a division of the Australian Broadcasting Corporation from the 1950s until the mid-2000s. A federal government review in 1994 severed the day-to-day management of the orchestra from the ABC and full independence was achieved on 1 January 2007. The orchestra now operates as a public company with a board of directors. Funding is provided by federal and state governments, corporate and private sponsorships and commercial activities as well as ticketing income.

The SSO and the Sydney Opera House
The Sydney Opera House, while among the most famous buildings of the 20th century, is problematic for the orchestra. The SSO was instrumental in calling for a new Opera House to be built and it was always intended to be their home venue. However, control of the Opera House has always rested with a separate body, the Sydney Opera House Trust, and the two institutions have had conflicts.

The longest running point of contention is the refusal by the Opera House Trust to allow the orchestra to drill small holes into the concert hall stage to allow proper seating of the endpins (spikes on the bottom) of their cellos and double basses, which is believed to give a better resonance to these instruments. The orchestra seats their endpins in planks of wood placed on the stage, as the Opera House Trust maintains that the entire building is heritage-listed under Australian law and that such work would therefore be illegal. Edo de Waart was particularly critical of this during his tenure as Chief Conductor in the 1990s, arguing in the press that the building had been specifically constructed for the orchestra and that it was a scandal that the orchestra was being forced to accept a reduced sound quality. However, the Opera House Trust has refused to bend and as of 2012 the orchestra was still using the planks of wood.

In November 2016, temporary sound reflectors were installed in the concert hall of the Opera House, to assist in amelioration of the acoustics. Renovations were completed in 2022.

Chief conductors

 * Eugene Goossens (1947–1956)
 * Nikolai Malko (1957–1961)
 * Dean Dixon (1964–1967)
 * Moshe Atzmon (1967–1971)
 * Willem van Otterloo (1971–1978)
 * Louis Frémaux (1979–1982)
 * Sir Charles Mackerras (1982–1985)
 * Zdeněk Mácal (1986)
 * Stuart Challender (1987–1991)
 * Edo de Waart (1993–2003)
 * Gianluigi Gelmetti (2004–2008)
 * Vladimir Ashkenazy (2009–2013)
 * David Robertson (2014–2019)
 * Simone Young (2022–present)

APRA Classical Music Awards
The APRA Classical Music Awards are presented annually by Australasian Performing Right Association (APRA) and Australian Music Centre (AMC).

 * rowspan="4"| 2003 || Guyuhmgan (Georges Lentz) – Sydney Symphony || Orchestral Work of the Year || Nominated
 * Ngangkar (Georges Lentz) – Sydney Symphony || Orchestral Work of the Year || Nominated
 * Three Miró Pieces (Richard Meale) – Sydney Symphony || Orchestral Work of the Year || Won
 * Adult Themes (2002) – Sydney Symphony Education Program – Sydney Symphony || Most Distinguished Contribution to the Presentation of Australian Composition by an Organisation || Won
 * rowspan="3"| 2005 || Concerto for Cello and Orchestra (Carl Vine) – Steven Isserlis, Sydney Symphony || Best Performance of an Australian Composition || Won
 * Inflight Entertainment (Graeme Koehne) – Diana Doherty, Sydney Symphony, Takuo Yuasa (conductor) || Orchestral Work of the Year || Nominated
 * 2004 Education Program – Sydney Symphony || Outstanding Contribution to Australian Music in Education || Nominated
 * rowspan="2"| 2006 || Mysterium Cosmographicum (Michael Smetanin) – Lisa Moore, Sydney Symphony || Best Performance of an Australian Composition || Nominated
 * Journey to the Horseshoe Bend (Andrew Shultz, Gordon Williams) – Ntaria Ladies Choir, Sydney Philharmonia Motet Choir, Sydney Symphony || Vocal or Choral Work of the Year || Nominated
 * rowspan="4"| 2007 || When the Clock Strikes Me (Nigel Westlake) – Rebecca Lagos (soloist), Sydney Symphony || Best Performance of an Australian Composition || Won
 * Flying Banner (After Wang To) (Liza Lim) – Sydney Symphony, Gianluigi Gelmetti (conductor) || Orchestral Work of the Year || Won
 * Liza Lim – Sydney Symphony Composer Residency || Outstanding Contribution by an Individual || Nominated
 * Sydney Symphony Education Program – Sinfonietta Composition project || Outstanding Contribution to Australian Music in Education || Nominated
 * 2008 || Sydney Symphony Education Program – 2007 Sinfonietta Project || Outstanding Contribution to Australian Music in Education || Nominated
 * 2009 || Monh (Georges Lentz) – Tabea Zimmermann, Sydney Symphony, Steven Sloane (conductor) || Best Composition by an Australian Composer || Won
 * rowspan="2"| 2006 || Mysterium Cosmographicum (Michael Smetanin) – Lisa Moore, Sydney Symphony || Best Performance of an Australian Composition || Nominated
 * Journey to the Horseshoe Bend (Andrew Shultz, Gordon Williams) – Ntaria Ladies Choir, Sydney Philharmonia Motet Choir, Sydney Symphony || Vocal or Choral Work of the Year || Nominated
 * rowspan="4"| 2007 || When the Clock Strikes Me (Nigel Westlake) – Rebecca Lagos (soloist), Sydney Symphony || Best Performance of an Australian Composition || Won
 * Flying Banner (After Wang To) (Liza Lim) – Sydney Symphony, Gianluigi Gelmetti (conductor) || Orchestral Work of the Year || Won
 * Liza Lim – Sydney Symphony Composer Residency || Outstanding Contribution by an Individual || Nominated
 * Sydney Symphony Education Program – Sinfonietta Composition project || Outstanding Contribution to Australian Music in Education || Nominated
 * 2008 || Sydney Symphony Education Program – 2007 Sinfonietta Project || Outstanding Contribution to Australian Music in Education || Nominated
 * 2009 || Monh (Georges Lentz) – Tabea Zimmermann, Sydney Symphony, Steven Sloane (conductor) || Best Composition by an Australian Composer || Won
 * Liza Lim – Sydney Symphony Composer Residency || Outstanding Contribution by an Individual || Nominated
 * Sydney Symphony Education Program – Sinfonietta Composition project || Outstanding Contribution to Australian Music in Education || Nominated
 * 2008 || Sydney Symphony Education Program – 2007 Sinfonietta Project || Outstanding Contribution to Australian Music in Education || Nominated
 * 2009 || Monh (Georges Lentz) – Tabea Zimmermann, Sydney Symphony, Steven Sloane (conductor) || Best Composition by an Australian Composer || Won
 * 2008 || Sydney Symphony Education Program – 2007 Sinfonietta Project || Outstanding Contribution to Australian Music in Education || Nominated
 * 2009 || Monh (Georges Lentz) – Tabea Zimmermann, Sydney Symphony, Steven Sloane (conductor) || Best Composition by an Australian Composer || Won
 * 2009 || Monh (Georges Lentz) – Tabea Zimmermann, Sydney Symphony, Steven Sloane (conductor) || Best Composition by an Australian Composer || Won

ARIA Music Awards
The ARIA Music Awards is an annual awards ceremony that recognises excellence, innovation, and achievement across all genres of Australian music. They commenced in 1987.

! Ref.
 * 1989
 * Australia Day / Child of Australia (with Australian Youth Orchestra, Joan Carden & John Howard)
 * Best Classical Album
 * Nominated
 * 1990
 * Peter and the Wolf/Carnival of the Animals (with Noni Hazlehurst)
 * Best Children's Album
 * Nominated
 * 1991
 * Sculthorpe: Orchestral Works (with Stuart Challender)
 * rowspan="4" | Best Classical Album
 * Won
 * rowspan="4" |
 * 1992
 * Vine: 3 Symphonies (with Stuart Challender)
 * Won
 * 1994
 * Ross Edwards Orchestral Works (with Dene Olding, Stuart Challender & David Porcelijn)
 * Won
 * 2008
 * Brett Dean (with Brett Dean)
 * Nominated
 * 2011
 * Don John of Austria (with Alexander Briger)
 * Best Original Soundtrack, Cast or Show Album
 * Nominated
 * 2012
 * Elgar: The Dream of Gerontius (with Vladimir Ashkenazy)
 * rowspan="2" | Best Classical Album
 * Nominated
 * rowspan="2" |
 * rowspan="2" | 2014
 * Compassion (with Nigel Westlake & Lior)
 * Won
 * Gurrumul: His Life And Music (with Geoffrey Gurrumul Yunupingu)
 * rowspan="3" | Best Original Soundtrack, Cast or Show Album
 * Won
 * rowspan="3" |
 * 2016
 * Live at the Sydney Opera House (with Josh Pyke)
 * Won
 * rowspan="2" | 2017
 * Ali's Wedding (soundtrack) (with Nigel Westlake & Joseph Tawadros, Slava Grigoryan & Lior)
 * Won
 * Live at the Sydney Opera House (with Kate Miller-Heidke )
 * rowspan="3" | Best Classical Album
 * Nominated
 * rowspan="2" |
 * 2019
 * Nigel Westlake: Spirit of the Wild / Steve Reich: The Desert Music (with Diana Doherty, Nigel Westlake, David Robertson & Synergy Vocals)
 * Nominated
 * 2022
 * Ross Edwards: Frog and Star Cycle / Symphonies 2 & 3 (with Amy Dickson, Colin Currie, Lothar Koenigs, Yvonne Kenny, David Zinman & Markus Stenz & Melbourne Symphony Orchestra)
 * Nominated
 * Won
 * rowspan="2" | 2017
 * Ali's Wedding (soundtrack) (with Nigel Westlake & Joseph Tawadros, Slava Grigoryan & Lior)
 * Won
 * Live at the Sydney Opera House (with Kate Miller-Heidke )
 * rowspan="3" | Best Classical Album
 * Nominated
 * rowspan="2" |
 * 2019
 * Nigel Westlake: Spirit of the Wild / Steve Reich: The Desert Music (with Diana Doherty, Nigel Westlake, David Robertson & Synergy Vocals)
 * Nominated
 * 2022
 * Ross Edwards: Frog and Star Cycle / Symphonies 2 & 3 (with Amy Dickson, Colin Currie, Lothar Koenigs, Yvonne Kenny, David Zinman & Markus Stenz & Melbourne Symphony Orchestra)
 * Nominated
 * 2022
 * Ross Edwards: Frog and Star Cycle / Symphonies 2 & 3 (with Amy Dickson, Colin Currie, Lothar Koenigs, Yvonne Kenny, David Zinman & Markus Stenz & Melbourne Symphony Orchestra)
 * Nominated
 * Nominated

Mo Awards
The Australian Entertainment Mo Awards (commonly known informally as the Mo Awards), were annual Australian entertainment industry awards. They recognise achievements in live entertainment in Australia from 1975 to 2016. Sydney Symphony Orchestra won one awards in that time. (wins only)
 * 1989
 * Sydney Symphony Orchestra
 * Classical Performance of the Year
 * Won
 * Won

National Live Music Awards
The National Live Music Awards (NLMAs) commenced in 2016 to recognise contributions to the live music industry in Australia.

! Ref.
 * rowspan="1" | 2023
 * Sydney Symphony Orchestra
 * Best Classical Act
 * Nominated
 * rowspan="1" |
 * rowspan="1" |

title: Sydney Symphony Orchestra


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Possessions of Sweden

This is a list of possessions of Sweden held outside of Sweden proper during the early modern period.

Fiefs
Fiefs that were held for a short period of time.
 * Scania (Agreement of Helsingborg, 1332–1360)
 * Hven (Agreement of Helsingborg, 1332–1360)
 * Blekinge (Agreement of Helsingborg, 1332–1360)
 * Halland (Treaty of Varberg, 1343–1360)
 * Elbing (Treaty of Altmark, 1629–1635)
 * Braunsberg (Treaty of Altmark, 1629–1635)
 * Pillau (Treaty of Altmark, 1629–1635)
 * Fischhausen (Treaty of Altmark, 1629–1635)
 * Lochstädt (Treaty of Altmark, 1629–1635)
 * Memel (Treaty of Altmark, 1629–1635)
 * Bremen (Recess of Stede, 1654–1666)
 * Bornholm (Treaty of Roskilde, 1658–1660)
 * Trøndelag (Treaty of Roskilde, 1658–1660)

Colonies

 * Fort Apollonia, present Beyin: 1655–1657.
 * Fort Christiansborg/Fort Frederiksborg, which became the capital, present Osu: 1652–1658
 * Fort Batenstein, present Butri: 1650–1656.
 * Fort Witsen, present Takoradi: 1653–1658.
 * Carolusborg: April 1650 – January/February 1658, 10 December 1660- 22 April 1663
 * New Sweden on the banks of the Delaware River in North America: 1638–1655
 * Guadeloupe (1813–1814; returned to France)
 * Saint-Barthélemy (1784–1878; sold to France)

Mint cities
Cities, held outside the realm, where Swedish mints were established.
 * Stade (Saxony)
 * Osnabrück (Saxony)
 * Erfurt (Thuringia)
 * Mainz (Electorate of the Palatinate)
 * Würzburg (Bavaria)
 * Fürth (Bavaria)
 * Nuremberg (Bavaria)
 * Augsburg (Bavaria)
 * Elbląg (Poland, 1626–1635 and 1655–1660)
 * Toruń (Poland, 1655–1658)

Territories held under martial law

 * Brodnica, Poland (conquest in the Polish War, held until 1629)
 * Tczew, Poland (conquest in the Polish War, held until 1629)
 * Orneta, Poland (conquest in the Polish War, held until 1629)
 * Melzak, Poland (conquest in the Polish War, held until 1629)
 * Frombork, Poland (conquest in the Polish War, held until 1629)
 * Malbork, Poland (conquest in the Polish War, held until 1629)
 * Sztum, Poland (conquest in the Polish War, held until 1629)
 * Gdańska Głowa, Poland (conquest in the Polish War, held until 1629)
 * Landsberg (Gorzów Wielkopolski) (agreement with Brandenburg, 1641–1643)
 * Frankfurt (Oder) (agreement with Brandenburg, 1641–1643)
 * Leipzig (agreement with Saxony, 1646–1648)
 * Memmingen (agreement with Bavaria, 1647–1648)
 * Überlingen (agreement with Bavaria, 1647–1648)

title: Possessions of Sweden


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Bailiff (Channel Islands)

The Bailiff is the chief justice in each of the Channel Island bailiwicks of Guernsey and Jersey, also serving as president of the legislature and having ceremonial and executive functions. Each bailiwick has possessed its own bailiff since the islands were divided into two jurisdictions in the 13th century. The bailiffs and deputy bailiffs are appointed by the Crown on the advice of the Secretary of State for Justice (not by the governments or legislatures of the islands) and may hold office until retirement age (65 in Guernsey, 70 in Jersey).

Name
After 1212, the King of England appointed a custodian to manage the Crown's affairs in the Channel Islands. At this time, there was no distinction between Warden/Governor and Bailiff, as evolved in later centuries. Officeholder Philip de Aubigné styled his role in 1218 as ballivus insularum, ballivus being the Latin term for a person who looked after the interests of a Lord. With this meaning, ballivus could be translated to the English word 'Warden', by which the office is normally called today and became officially known after 1259.

The Warden was normally absent from the island, only regularly visiting for the triennial assize. Therefore, the Warden's quotidian duties would have been carried out by a team of deputies, who were islanders and who became referred to as the ballivi. As such, one or more ballivi. By the end of the 13th century, the modern position of Bailiff appears in record, emerging from this position of ballivus.

Roles of the bailiffs
Originally, the bailiff was both legislator and judge, but the position has become increasingly concentrated on the judicial functions. The bailiff presides in the main trial court in his island – the Royal Court of Jersey and the Royal Court of Guernsey, where they sit with Jurats, elected lay judges responsible for making finds of fact. The bailiff of each island is also a member of the court of appeal in his island, and that of the other. The bailiffs are the presidents (presiding officers) of the legislatures—the States of Jersey Assembly and the States of Deliberation in Guernsey.

Constitutional changes introduced in Jersey (2005) and Guernsey (2004) created posts of chief minister and in Jersey (but not in Guernsey) created a ministerial system of government. This has altered the executive functions of the bailiffs but they continue to have a residual executive role (for example, they see any correspondence between the chief minister of their island and the UK government and may be involved in any political decisions affecting the constitutional relationship between the islands and the United Kingdom). Each bailiff continues to be the 'first citizen' of the island, carrying out civil and ceremonial roles.

The last lay (that is, not legally-qualified) Bailiff in either jurisdiction was Sir Edgar McCulloch, Bailiff of Guernsey, who served in the role from 1884–1895. By constitutional convention he or she (though to date there have been no women holders of the office) and the deputy bailiff are now invariably selected from among those who have previously held the senior office within the Law Officers of the Crown–the Procureur in Guernsey and the Attorney General in Jersey. Bailiffs and deputy bailiffs in modern times have also invariably been qualified as advocates in their respective islands.

A deputy bailiff in each bailiwick may preside in the Royal Court and States chamber when the bailiff is not available. Senior jurats may be appointed as lieutenant-bailiffs to perform some ceremonial duties in lieu of the bailiff on occasion as well as presiding over judicial proceedings generally of an administrative nature.

In 1617 a Privy Council decision clarified the division of civil and military responsibilities between the bailiffs and the lieutenant governors in Guernsey and Jersey. For the first time, the Crown laid down the bailiff's precedence over the governor in judicial affairs and in the States chamber.

Bailiff of Guernsey
The Bailiff of Guernsey was less clearly delineated as to separation of legislative or administrative and judicial functions than that of the Bailiff of Jersey. He was head of the administration in Guernsey and used to preside over a number of States committees.

In 2000, the European Court of Human Rights held in McGonnell v. United Kingdom that there was a breach of Article 6 in Guernsey where the Bailiff or Deputy Bailiff sat as president of the States of Guernsey when proposed legislation was being debated and then subsequently sat as a judge of the Royal Court of Guernsey in a case where that legislation was relevant. The court, noting that there was no suggestion that the Bailiff 'was subjectively biased', stated that the 'mere fact' that this happened was capable of casting doubt on the Bailiff's impartiality.

The Bailiff remains civil head of the island, as well as head of the judiciary, the Presiding Officer of the States of Deliberation'.

The Bailiff is ex officio, a Judge of the Court of Appeal and its President. The Bailiff represents Guernsey as civic head of the community in and outside the Island, on occasions of a non-political nature and will greet and welcome members of the Royal Family and dignitaries visiting the Island on behalf of the people of Guernsey. May be appointed as a member of the Court of Appeal of Jersey.

Bailiff of Jersey
The Bailiff of Jersey (Bailli de Jersey, Jèrriais: Bailli d'Jèrri) is the chief justice of the island and the presiding officer of the States Assembly.

The position of bailiff was created shortly after the Treaty of Paris 1259 in which the King of England, Henry III, gave up claim to all of the Duchy of Normandy but the Channel Islands. Rather than absorb the islands into the Kingdom of England, a warden (now lieutenant governor) and bailiff were appointed to run the island on his behalf.

Historical development
The origin of the States of Jersey lies in the summoning of representatives of the parishes (the connétable and rectors) to advise the Royal Court on legislation. The States of Jersey thus evolved a separate identity. Although it was already sitting in the 16th century, the first separate minutes of the meetings were not kept until the 17th century.

The Royal Court, under the presidency of the Bailiff, originally not only administered the law of the island but also wrote it. As a Crown appointment, the Bailiff was a powerful figure and the post was the subject of patronage. From the time of George Carteret in the 1660s onwards the position of Bailiff became a political fiefdom of the de Carteret family and the position was de facto hereditary – although many of the de Carteret bailiffs, such as the Earl Granville, preferred to pursue political careers in England. During this period, the absentee bailiffs appointed lieutenant-bailiffs to exercise office.

In 1750 Charles Lemprière was appointed lieutenant-bailiff and set about establishing a powerbase by engineering the election and appointments of members of the Lemprière family to office. A succession of weak lieutenant-governors enabled Lemprière to establish an autocratic régime, making the States subservient to the Royal Court and ensuring, by the handpicked appointment of advocates, that opponents would be unable to get legal representation. A threatened shortage of corn sparked popular protest and led to a mob sacking the Royal Court. The Bailiff and jurats took refuge in Elizabeth Castle and petitioned the king. In 1770 Colonel Bentinck, a Dutchman, was appointed lieutenant-governor with instructions to oversee reform.

In 1771 it was laid down in Jersey that no laws might be adopted without being passed by the States of Jersey. From this time on the bailiff was to be the chief power in Jersey as president of the States, rather than as president of the Royal Court. The party of Charlots (conservative supporters of Lemprière who claimed that the States could not pass legislation without the agreement of the Royal Court) were opposed at elections by Magots, and by 1790 the progressive Magots had majorities in both the Royal Court and the States.

In 1826, the long succession of absentee bailiffs came to an end with the appointment of Thomas Le Breton. Under Jean Hammond (bailiff 1858–1880) the role became established as a politically impartial, if paternalistic, presidency. The introduction of deputies into the States in 1857 added to the democratic weight of the legislative assembly, but the bailiff still guided the government of the bailiwick.

The States continued to use the Royal Court as their debating chamber until the construction of a dedicated States chamber on an adjacent site in 1887.

The process of democratisation through the 19th and 20th centuries shifted the focus of political influence to the elected members of the States.

In 1921, the property and financial powers of the Assembly of Governor, Bailiff and Jurats was taken over by the States of Jersey, leaving that assembly with only power to act as licensing bench. With the power to levy impôts henceforth in the hands of the States, and with the introduction of the Income Tax law of 1928, the legislators now controlled the budget independently of the bailiff.

Alexander Coutanche, appointed in 1935, was the last bailiff appointed before the passage of a law on the bailiff in 1936. He was the last bailiff appointed for life and the last under the sole prerogative of the Crown without the obligation to consult the States of Jersey.

Although the need for centralised administration during the German Occupation 1940-1945 made the bailiff a commanding figure in the circumstances of trying to maintain the life of the bailiwick, the constitutional reforms of 1948 which removed the jurats from the States, replacing them with senators, separated more clearly legislature and judiciary. Political leadership now rested more clearly with the senators as purely political senior elected representatives.

In 1958 the post of deputy bailiff was introduced to spread the workload of bailiff – the deputy bailiff generally proceeding to replace the bailiff on the latter's retirement or death. Commissions of the Royal Court (acting judges) now ensures that the bailiff never sits on a case which relied on a law that he had taken part in the legislative process for.

The States of Jersey Law 2005 removed the bailiff's casting vote in the event of a tied vote in the States chamber. The 2005 law also introduced a ministerial system of government under a Chief Minister, which further removed the Bailiff from involvement in executive decision-making.

Current roles
The modern-day roles of the bailiff are as follows:
 * Head of the judiciary of Jersey
 * President of the Royal Court (chief justice)
 * President of the Court of Appeal, though in practice the bailiff rarely sits in this court
 * Member of the Court of Appeal of Guernsey
 * President of the States Assembly (presiding officer)
 * Deputy governor in the absence of the lieutenant governor
 * President of the College of Electors under the Royal Court (Jersey) Law 1948 for the election of jurats (existing jurats, senators, deputies, connétables and all practising advocates and solicitors); the bailiff is a member, but may only vote in the event of a tie after a second ballot
 * An attendee of the Emergencies Council
 * President of the Assembly of Bailiff, Governor and Jurats, inter alia responsible for regulating the sale of alcohol.
 * Responsibility for giving permission for certain types of public entertainment, including theatre, cinema and cabaret performances. Since 1987, an advisory panel appointed by the States Assembly has delegated authority in the name of the bailiff who is not involved in any respect with the decision-making process.
 * The bailiff has the power to make various judiciary-related appointments:
 * Lieutenant bailiffs (usually jurats) and commissioners, any of whom may preside over the Royal Court and exercise other judicial functions of the bailiff as required.
 * the magistrate, assistant magistrate and relief magistrates.
 * approves the appointment by the Attorney General of Crown Advocates.
 * appoints the Viscount.
 * The bailiff is the civic head of the island, carrying out various ceremonial duties (such as on Liberation Day and Remembrance Sunday) and receiving distinguished visitors to Jersey.
 * The bailiff has a role as ‘guardian of the constitution’. Outgoing official correspondence to the Ministry of Justice (the UK government department responsible for relations with the island) goes from the bailiff via the lieutenant governor, with input from the attorney general. Incoming correspondence takes the reverse route. The substance of the correspondence is settled by the political decision of the chief minister who is responsible for the island's external relations.

The deputy bailiff has a specific function of being the President of the Board of Examiners for the Jersey law examinations.

Proposed reforms
The question whether the office of bailiff should combine roles of chief justice, presiding officer of the legislature and civic functions has long been a matter of debate. The 1947 Report of the Committee of the Privy Council on the Proposed Reforms in the Channel Islands recommended 'that there should be no alteration in the present functions of the Bailiff'. However, both the Clothier committee and the Carswell review  called for reforms. The States of Jersey have not accepted this aspect of the Carswell report. Many prominent islanders do not believe that any change is necessary or desirable.

title: Bailiff (Channel Islands)