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Events happening on April 28, 2015

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Apr. 28, 2015 11am (MATH 350)	Number Theory John Boxall (Universit� de Caen Basse-Normandie) X Let $K$ be a CM-field of degree 2g with maximal reals subfield $K0$ . The CM torus associated to $K$ is a torus $W_{K}$ over $Q$ whose $Q$ -rational points identify with the subgroup of $K^{\times}$ whose norm down to $K0$ lies in $Q$ . We discuss asymptotic estimates for the number of integral points on $W_{K}$ that satisfy various properties. Counting points on CM tori
Apr. 28, 2015 12:10pm (MATH …	Kempner Charles Vial (Cambridge and IAS) X While toying with the Riemann-Roch formula for surfaces, I observed that a certain winding number in the modular group SL(2,Z) is related to the signature of a certain tridiagonal matrix M. I will of course give a precise statement, and I hope that the audience will help me understand why such a statement is true! A strange linear algebra statement
Apr. 28, 2015 2pm (Math 350)	Functional Analysis Danny Crytser (Kansas State University) X An abelian core for a C-algebra is a certain MASA which is useful in the study of representation theory. Not all C-algebras admit abelian cores, but those that do often have particularly nice structure. Two examples are the abelian core of a graph algebra, and the abelian core C(X) inside C(X) \rtimes G, where G is a countable discrete group acting topologically freely on X. We study the trace space of a graph C*-algebra as it relates to the abelian core. This is ongoing work with Gabriel Nagy. Tracial states and abelian cores Sponsored by the Meyer Fund
Apr. 28, 2015 3pm (Math 350)	Algebraic Geometry Charles Vial (Cambridge and IAS) X In the first part of the talk, I will introduce Chow groups and their relations to usual cohomology groups. The Chow groups of varieties are still largely mysterious and encompass geometric and arithmetic properties of varieties. I will review some of their important established properties and the web of conjectures that surround them. More specifically, given a smooth projective variety X, I will explain why the diagonal, when seen as an element of the Chow group of X \times X, controls the "motive" of X. In the second part of the talk, I will explain why the small diagonal {(x,x,x), x \in X} \subset X\times X\times X controls the intersection theory on X. I will then review joint work with Mingmin Shen where we give evidence that the Chow ring of hyperKaehler varieties has a similar structure as the Chow ring of abelian varieties. Examples of hyperKaehler varieties are given by K3 surfaces, and Hilbert schemes of length-n subschemes on K3 surfaces and their deformations. On diagonals and small diagonals in intersection theory Sponsored by the Meyer Fund

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