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- Algebraic Geometry and Representation Theory Seminar

# Algebraic Geometry and Representation Theory Seminar

SundayFeb 21, 202109:00

Algebraic Geometry and Representation Theory Seminar

Speaker:Paul Nelson Title:The orbit method,microlocal analysis and applications to L-functionsAbstract:opens in new windowin html pdfopens in new windowhttps://weizmann.zoom.us/j/98304397425I will describe how the orbit method can be developed in a quantitative form, along the lines of microlocal analysis, and applied to local problems in representation theory and global problems concerning automorphic forms. The local applications include asymptotic expansions of relative characters. The global applications include moment estimates and subconvex bounds for L-functions. These results are the subject of two papers, the first joint with Akshay Venkatesh:

WednesdayMar 10, 202116:30

Algebraic Geometry and Representation Theory Seminar

Speaker:David VoganTitle:Weyl group representations and Harish-Chandra cellsAbstract:opens in new windowin html pdfopens in new windowhttps://weizmann.zoom.us/j/98304397425One of the fundamental contributions of Kazhdan and Lusztig's 1979 Inventiones paper was the notion of "cells" in Weyl groups. They gave a decomposition of the left regular representation of W as a direct sum of "left cell" representations, which encode deep and powerful information about group representations. In the case of the symmetric group S_n=W, the left cells are irreducible representations. In all other cases they are not. Lusztig in his 1984 book gave a beautiful description of all left cells in terms of the geometry of nilpotent orbits.
Part of Lusztig's description uses Springer's parametrization of W representations by irreducible representations of the equivariant fundamental group A(O) for a nilpotent orbit O. I will discuss the "opposite" part of Lusztig's description, involving conjugacy classes in A(O).

WednesdayMar 17, 202116:30

Algebraic Geometry and Representation Theory Seminar

Speaker:Paul Nelson Title:The orbit method, microlocal analysis and applications to L-functionsAbstract:opens in new windowin html pdfopens in new windowhttps://weizmann.zoom.us/j/98304397425I will describe how the orbit method can be developed in a quantitative form, along the lines of microlocal analysis, and applied to local problems in representation theory and global problems concerning automorphic forms. The local applications include asymptotic expansions of relative characters. The global applications include moment estimates and subconvex bounds for L-functions. These results are the subject of two papers, the first joint with Akshay Venkatesh:
https://arxiv.org/abs/1805.07750
https://arxiv.org/abs/2012.0218