Abstract: 

In the first part of the talk, I will give a survey of the proof of the Dowling-Wilson conjecture using the Schubert variety of a hyperplane arrangement. The Schubert variety of a hyperplane arrangement is an equivariant compactification of the vector group with finitely many orbits. In the second part of the talk, we will discuss a recent work of Colin Crowley characterizing Schubert variety of hyperplane arrangements among all equivariant compactification of vector groups, and some on-going work on polymatroid Schubert varieties joint with Colin Crowley and Connor Simpson.

Short 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=Dowling-Wilson_conjecture_and_equivariant_compactification_of_the_vector_group.html