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Characteristic Polynomials of the Hermitian Wigner and Sample Covariance Matrices

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.

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

Claire Voisin
CNRS, Institut de Mathematiques de Jussieu, Paris
November 1, 2011

Summary: These lectures are devoted to the interplay between cohomology and Chow groups of a complex algebraic variety, and also to the consequences, on the topology of a family of smooth projective varieties, of statements concerning Chow groups of the general fiber. A crucial notion is that of coniveau of the cohomology and its conjectural relation with the shape of Chow groups of small dimension. A common theme will be that of decomposition of the diagonal, which will appear in various contexts.