In preparation for Alex Kumjian's lecture next week, I will discuss how we can associate a C*-algebra to a directed graph. There are two approaches -- one using generators and relations, and one using groupoids -- that yield isomorphic C*-algebras.
The (groupoid) C*-algebra of a directed graph Sponsored by the Meyer Fund
Oct. 21, 2014 2pm (MATH 350)
Lie Theory
Matthew Tai (University of Pennsylvania)
X
For certain representations V of certain groups G, we can define a notion of G-harmonic polynomials on V in the sense of Kostant and Chevalley. I will describe a construction of Kirillov's aimed at computing these polynomials when G is a compact Lie group and also talk about connections to matrix algebras over noncommutative bases.
Intro to Family Algebras Sponsored by the Meyer Fund
Oct. 21, 2014 3pm (Math 350)
Algebraic Geometry
Samouil Molcho (University of Colorado)
X
Higher Dimensional Analogues of Stable Maps.
In this talk I will discuss stable maps X-->V where the source X may not be a curve but rather a higher dimensional variety. Specifically, suppose V is a toric variety and H a subtorus of its torus. I will discuss Alexeev's moduli space A(V) of H-equivariant maps X-->V, where the source is a broken toric variety with torus H, and its analogue K(V) where X and V are equipped with logarithmic structures. I will then give an explicit combinatorial description of K(V) as a toric stack. When the dimension of H is 1, this description reduces to the description of the stack of genus 0 logarithmic stable maps of Gross-Siebert.
In the first half of the talk I will give a brief introduction to the ideas and results we need from logarithmic and toric geometry, and discuss how logarithmic geometry appears when studying compactifications of moduli spaces.
The (groupoid) C*-algebra of a directed graph