应数学与统计学院的邀请，美国加州理工学院Richard Michael Wilson教授、英国东安格利亚大学Johannes Siemons教授将于近日访问我校，并为师生作学术报告。
报告时间：5月30日16：30
报告地点：理科楼407会议室
报告题目: POLYNOMIAL AND MATRIX METHODS IN EXTREMAL SET THEORY
报 告 人： Prof. Richard M Wilson
报告摘要: We focus on the problem of finding bounds on the maximum cardinality of families F of subsets of an n-set subject to restrictions on the cardinalities of the pairwise intersections of members of F. Various algebraic methods are discusses and illustrated and are used to obtained new results.
报告题目：Designs and Representation Theory
报 告 人: Prof. Johannes Siemons
报告摘要: It is well-known that often combinatorial structures can be represented as f0; 1g-solutions of a suitable system of algebraic equations. For instance, the t (n; k; ) designs on the set V = f1:ng correspond one-to-one to the solutions X of the matrix equation in which M is the incidence matrix between the t- and the k-element subsets of V; and J is a column of 1s. Formally the condition Xi 2 f0; 1g can be replaced by X2i = Xi for all i; and so at least in principle, algebra is su±cient to express the combinatorial requirements. A second feature is that the symmetric group Sym(V ) permutes the k-element sub-sets of V and hence the solutions of (E): It is therefore natural to consider this equation also from the view point of the representation theory of the symmetric group. The solutions of the homogeneous equation MX = 0 form the module of null-designs on V which has been studied extensively. We discuss new and old results concerning the intriguing structure of null-designs as Specht modules. In particular, certain standard polytope bases for null-designs arise naturally from the standard polytabloids of Specht theory. We prove a spectral theorem for the module of all k-element subsets of a set and give some applications to Smith canonical forms and Delsarte's inner distribution of subset-families.
附件：报告人简介
CV_Richard_Wilson.pdf
CV _Johannes_Siemons.pdf
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