## Chow Rings, Decomposition of the Diagonal and the Topology of Families

Lecture 4: Integral Coefficients; Application to Birational Invariants

Claire Voisin

CNRS, Institut de Mathematiques de Jussieu, Paris

November 4, 2011

Lecture 4: Integral Coefficients; Application to Birational Invariants

Claire Voisin

CNRS, Institut de Mathematiques de Jussieu, Paris

November 3, 2011

Lecture 3: Decomposition of the Small Diagonal and the Topology of Families

Claire Voisin

CNRS, Institut de Mathematiques de Jussieu, Paris

November 2, 2011

Lecture 2: On the Generalized Bloch and Hodge Conjectures for Complete Intersections

John Mather

Princeton University; Institute for Advanced Study

November 2, 2011

Michael Khanevsky

Institute for Advanced Study

November 2, 2011

Tatyana Shcherbina

Institute for Low Temperature Physics, Kharkov

November 1, 2011

We consider asymptotics of the correlation functions of characteristic polynomials of the hermitian Wigner matrices $H_n=n^{-1/2}W_n$ and the hermitian sample covariance matrices $X_n=n^{-1}A_{m,n}^*A_{m,n}$. We use the integration over the Grassmann variables to obtain a convenient integral representation.

Jeff Kahn

Institute for Advanced Study

October 31, 2011

Sobhan Seyfaddini

University of California at Berkeley

October 28, 2011

After reviewing spectral invariants, I will write down an estimate, which under certain assumptions, relates the spectral invariants of a Hamiltonian to the C^{0}-distance of its flow from the identity. I will also show that, unlike the Hofer norm, the spectral norm is C^{0}-continuous on surfaces. Time permitting, I will present an application to the study of area preserving disk maps.

Fraydoun Rezakhanlou

University of California at Berkeley

October 28, 2011

Xinyi Yuan

Princeton University

October 27, 2011

In this talk, I will present a formulation of the Gross-Zagier formula over Shimura curves using automorphic representations with algebraic coefficients. It is a joint work with Shou-wu Zhang and Wei Zhang.