## Chern classes of Schubert cells and varieties

June Huh

Princeton University; Veblen Fellow, School of Mathematics

March 30, 2015

Chern-Schwartz-MacPherson class is a functorial Chern class defined for any algebraic variety. I will give a geometric proof of a positivity conjecture of Aluffi and Mihalcea that Chern classes of Schubert cells and varieties in Grassmannians are positive. While the positivity conjecture is a purely combinatorial statement, a combinatorial 'counting' proof is known only in very special cases. In addition, the current geometric argument do not work for Schubert varieties in more general flag varieties.