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-Sketch: Botong Wang is an associate professor at University of Wisconsin at Madison. He got his B.S. in mathematics from Peking University in 2006, and got his PhD from Purdue University in 2012. Botong Wang has made significant contribution in the topology of algebraic varieties, and was awarded Sloan Fellowship in 2019.