（5月25日）香港科技大学陈北方教授和SUNY-Albany大学Changlong Zhong 教授的学术报告
来源：数学科学学院 发布时间：2017-05-18 683
题目：The art of counting: From zero and one to infinity.
摘要：Numbers arise from counting. The addition and product rules are two principles to follow when facing counting finite number of objects. However, when facing counting infinitely many objects, cardinals arise in set theory by applying Cantor's one-to-one correspondence, but cardinals seem to produce no rich mathematics so far. In this talk we demonstrate a few examples of counting discrete and continuous objects from combinatorial viewpoint of finitely additive measures. These examples are selected from the topics of subspace arrangements, chromatic polynomials, group arrangements, Grassmannians, and counting points of algebraic varieties. The conclusion is that various polynomials and power series arise from the counting patterns of infinitely many objects with structures.
PS: This talk is best to senior undergraduates.
报告人：Changlong Zhong (SUNY-Albany)
题目：Hecke algebra and equivariant cohomology of flag varieties.
摘要：The algebraic/combinatorial method in the study of cohomology of flag varieties was started by Demazure and Bernstein-Gelfand-Gelfand in 1970s (for ordinary Chow groups), and were continued by Arabia, Kostant-Kumar, Bressler-Evens in 1980s-1990s (for equivariant singular cohomology, equivariant K-theory and complex cobordism). It was generalized to general oriented cohomology theory by Calmes-Petrov-Zainoulline, and later by myself with Calmes and Zainoulline.
Such method is based on the Bruhat decomposition of flag variety, and the fact that the convolution action of divided difference operators on the fundamental class of identity point generates the whole cohomology ring. The dual of the algebra generated by divided difference operators will be the algebraic model of equivariant oriented cohomology of flag varieties, and many important structures (Bott-Samelson classes, push-pull maps, characteristic map) can be seen from this model. I will give main ideas of this construction.
This construction is closely related with cohomology theory of Steinberg variety, which is the geometric model of Hecke algebra.