Subconvex equidistribution of cusp forms

Recent developments in Analytic Number Theory May 01, 2017 - May 05, 2017

May 01, 2017 (02:00 PM PDT - 03:00 PM PDT)

Speaker(s): Paul Nelson (ETH Zürich)

Tags/Keywords

Arithmetic Quantum Chaos
Automorphic forms
arithmetic quantum unique ergodicity
subconvexity bound
L-function

Primary Mathematics Subject Classification

11H31 - Lattice packing and covering (number-theoretic aspects) [See also 05B40, 52C15, 52C17]
11G18 - Arithmetic aspects of modular and Shimura varieties [See also 14G35]
57-03 - History of manifolds and cell complexes [Consider also classification numbers from Section 01-XX]
11G20 - Curves over finite and local fields [See also 14H25]
11H06 - Lattices and convex bodies (number-theoretic aspects) [See also 11P21, 52C05, 52C07]

Secondary Mathematics Subject Classification No Secondary AMS MSC

Video

Nelson

Abstract

Arithmetic quantum chaos concerns the limiting behavior of a sequence of automorphic forms with parameters tending off to infinity. It is now known in many cases that the mass distributions of such forms equidistribute. Unfortunately, the known rates of equidistribution are typically weak (ineffective or logarithmic). I will discuss the problem of obtaining strong rates (power savings) and the related subconvexity problem, emphasizing recent progress concerning the level aspect on hyperbolic surfaces.

Supplements

	Nelson.Notes 641 KB application/pdf	Download

Video/Audio Files

Nelson

H.264 Video	3-Nelson.mp4 522 MB video/mp4 rtsp://videos.msri.org/data/000/028/291/original/3-Nelson.mp4	Download

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