真人百家le威尼斯人

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真人百家le威尼斯人:Hodge Theory in Combinatorial Geometry

来源: 09-04

时间:Mon、Wed、Fri 13:30 - 15:30 2023-9-4~2023-9-13

地点:美金换人民币第四教学楼 四教102(9月4、6、8日) 四教103(9月11、13日)

主讲人:Botong Wang 王博潼 Associate Professor University of Wisconsin - Madison

Speaker

I am interested in the topology of algebraic varieties, and its interaction with combinatorics and algebraic statistics. I am currently interested in the following topics.

?The topological aspects of algebraic optimization problems

?Fourier-Mukai (or Mellin) transformation and the generic vanishing theorems

?Kazhdan-Lusztig theory for matroids

?Schubert varieties of hyperplane arrangements and their generalizations


Course Description

The purpose of these lectures is to give a survey on the recent resolution of two conjectures in matroid theory. The first one is the Heron-Rota-Welsh conjecture by Adiprasito-Huh-Katz, and the second one is the Dowling-Wilson conjecture by Braden-Huh-Matherne-Proudfoot-Wang. The main idea is to attach algebraic geometric invariants to a given matroid, and use ideas from Hodge theory to derive combinatorial properties. If time permits, we will also survey some ongoing developments of intersection cohomology of matroids and some new applications.