The Wagner Performances at Bayreuth

Algebraic Combinatorics in Bayreuth

I should like to give a brief introduction of our group, describe its main activities in the field of Algebraic Combinatorics, and illustrate them by a few typical examples.

2 Fabrizio Catanese Universität Bayreuth

We introduce a new equivalence relation for complete algebraic varieties with canonical singularities, generated by birational equivalence, by flat algebraic deformations (of varieties with canonical singularities), and by quasi-´ etale morphisms, i.e., morphisms which are unramified in codimen-sion 1. We denote the above equivalence by A.Q.E.D. : = Algebraic-Quasi-´ Etale-Deformation. A comple...

The Mermin-Wagner Theorem

LetA be a C∗ algebra such as the algebra of quasi-local observables of a quantum spin system on Z, and suppose {αt}t∈R is a strongly continuous one-parameter group of automorphisms of A, which we will refer to as the dynamics of the system. The examples we have in mind are the dynamics of a quantum spin system generated by a not-too-long-range interaction Φ, e.g., one that satsifies, for some λ...

Mass murder: the Wagner case.

On the Livingstone-Wagner Theorem

Let G be a permutation group on the set Ω and let S be a collection of subsets of Ω, all of size ≥ m for some integer m . For s ≤ m let ns(G, S) be the number of G-orbits on the subsets of Ω which have a representative y ⊆ x with |y| = s and y ⊆ x for some x ∈ S . We prove that if s < t with s + t ≤ m then ns(G, S) ≤ nt(G, S) . A special case of this theorem is the Livingstone-Wagner Theorem wh...