Wednesday, October 14, 2015 — 2:30 PM EDT

Kiumars Kaveh, University of Pittsburgh

“Lattice points, convex bodies and algebraic geometry”

I will start by discussing some basic facts about the semigroup of finite subsets of Zn. This leads us to beautiful results in toric geometry (Bernstein-Kushnirenko theorem on the number of solutions of a system of polynomial equations). I will discuss generalizations to arbitrary varieties/graded algebras and theory of Newton-Okounkov bodies. Beside applica- tions in study of line bundles on varieties, this extension introduces stunning new tools and ideas in a number of other areas such local commutative algebra (Hilbert-Samuel multiplicity), symplectic geometry (moment map and integrable systems) and representation theory (flag varieties and Schubert calculus). For the most part the talk is accessible to anybody with a basic knowledge of algebra and geometry.

MC 5403 **Please note Room**

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