# Women and Mathematics - Princeton Day

Monday, May 18, 2015 -

9:30am to 7:00pm

The mathematics department will host the Princeton day of this year's Women and Mathematics program on Monday, May 18. Since 1994 the Princeton mathematics department and the Institute for Advanced Study have hosted the Women and Mathematics program. The program brings graduate and undergraduate women together with leading researchers for an 11-day intensive mentoring program.10:00 a.m., Fine 314: "A connection between representation theory and Severi degrees"Yaim Cooper *13Lecturer, Harvard UniversityHundreds of years ago, mathematicians realized that one would expect there to be only finitely many plane curves of degree $d$ and genus $g$ that pass through $3d+g-1$ fixed points. Since then, people have been counting such curves. In the 1990's, Caporaso and Harris gave the first complete solution to this problem, giving a recursive formula for these numbers, called Severi degrees. In this talk, I will discuss work (joint with R. Pandharipande) that gives a new way to compute and think about these numbers, using ideas from representation theory. 11:00 a.m., Fine 314:"Lines in 3-space"János KollárDonnor Professor of Science, Princeton UniversityWe will explore configurations of lines in 3-space that have many intersection points and how this leads to algebraic curves, surfaces and other topics in algebraic geometry.12:00 p.m.: Lunch1:30 p.m., Fine 314"Chern classes of Schubert cells and varieties"June HuhClay Research Fellow & Veblen Fellow, Princeton University and the Institute for Advanced StudyChern-Schwartz-MacPherson class is a factorial Chern class defined for any algebraic variety. I will outline a geometric proof of a 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 arguments do not work for Schubert varieties in more general flag varieties. Should we expect the same positivity for Chern classes of Schubert varieties in $G/P$?2:45 p.m., Fine 314"Locally symmetric spaces and Galois representations"Ana Caraiani '07Veblen Research Instructor, Princeton University and the Institute for Advanced StudyModular curves are quotients of the upper half complex plane but can be reinterpreted as moduli spaces of elliptic curves. They have a canonical algebraic structure which allows us to relate their cohomology to number theoretic objects: Galois representations. I will explain some of the underlying geometry and mention how to study higher-dimensional versions, such as arithmetic hyperbolic 3-manifolds.3:45 p.m., Tea5:00 p.m., Woolworth Music Center, McAlpin Rehearsal HallViolin Concert by Isabelle Nogues '15