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Torsten Ekedahl: The Sato-Tate conjecture

Torsten Ekedahl, SU

Time: Wed 2010-11-03 16.00

Location: Room 14, house 5, Kräftriket, Department of Mathematics, Stockholm University

The Sato-Tate conjecture is an equidistribution conjecture for certain
number-theoretically defined sequences. An example of a (generalised)
Sato-Tate conjecture is obtained by defining
\sum_{n=1}^\infty \tau(n) = q\prod_{i=1}^\infty(1-q^n)^{24}.
The conjecture then says that $\{\tau(n)/(2n^{5.5})\}$ is
equi-distributed with respect to a specific well-known distribution.
This is as well as the original Sato-Tate distribution has now been
proved by the combined efforts by a fairly large group of people.

I will mainly discuss how one by experimentation and
pseudo-probabilistic reasoning can arrive at the Sato-Tate conjecture
and then indicate the basic idea for the proof.

Kollokvier 2010

Titel Datum
Torsten Ekedahl: The Sato-Tate conjecture 2010‑11‑03
Jesper Grodal: Finite loop spaces 2010‑11‑10
Amol Sasane: An analogue of Serre’s Conjecture and Control Theory 2010‑10‑13
Reiner Werner: Quantum correlations - how to prove a negative from finitely many observations 2010‑09‑29
Warwick Tucker: Validated Numerics - a short introduction to rigorous computations 2010‑09‑22
Idun Reiten: Cluster categories and cluster algebras 2010‑09‑01
Stefano Demichelis: Use and misuse of mathematics in economic theory 2010‑05‑26
Gregory G. Smith: Old and new perspectives on Hilbert functions 2010‑04‑14
Tony Geramita: Sums of Squares: Evolution of an Idea. 2010‑03‑31
Jens Hoppe: Non-commutative curvature and classical geometry 2010‑03‑24
Margaret Beck: Understanding metastability using invariant manifolds 2010‑03‑03
Jan-Erik Björk: Glimpses from work by Carleman 2010‑02‑10