Abstract:

Many important posets (partially ordered sets) in combinatorics have algebriac interpretations. We will go over three families of examples: toric varieties, Schubert varieties and matroid Schubert varieties. We will discuss how to translate some of the combinatorical invariants into the geometric ones, and the application of intersection cohomology groups in solving combinatorical problems.

Bio:

Botong Wang is an Associate Professor in the Department of Mathematics at the University of Wisconsin-Madison. He received his PhD from Purdue University in 2012 and BS from Beijing University in 2006. He was postdoctoral fellow at University of Notre Dame and KU Leuven before coming to University of Wisconsin-Madison. He has a broad interest in several different subjects in mathematics, including combinatorics, algebraic geometry and topology. Of notable achievements, Dr. Wang was in a joint paper with June Huh, where they used methods of algebraic geometry to solve conjecture of Dowling and Wilson in combinatorics that had been open since the 1970s.

Video： http://archive.ymsc.tsinghua.edu.cn/pacm_lecture?html=Intersection_cohomology_in_combinatorics.html