Seminario / Shalev
TOPIC: GOThIC - Ischia Online Group Theory Conference
The Ischia Group Theory 2020 Conference
(http://www.dipmat2.unisa.it/ischiagrouptheory/) was planned for 30
March - 4 April 2020. It has now been postponed to 2021. In the
meantime, we are offering a series of online lectures by leading
TIME: July 2, 2020 17:00 CEST (UTC+2)
COFFEE BREAK: The talk will start at 17:00 CEST.
The conference room will open at 16:45 CEST for a coffee break
- Bring Your Own tea/coffeemug - biscuits appreciated -
and join us for some smalltalk before the event.
SPEAKER: Aner Shalev (Hebrew University of Jerusalem)
TITLE: Subsets products and derangements
- The TIME OF THE TALK is 17:00 CEST.
- The Zoom link is NEW.
- You are welcome to share the Zoom link with other interested
parties, but PLEASE DO NOT POST THE LINK PUBLICLY.
- When joining, please MAKE SURE THAT
YOUR NICKNAME IS YOUR NAME AND SURNAME, or close to it,
so that the organisers can recognise you and let you in
ABSTRACT: In the past two decades there has been considerable interest
in products of subsets in finite groups. Two important examples are
Gowers' theory of Quasi Random Groups and its applications by Nikolov,
Pyber, Babai and others, and the theory of Approximate Subgroups and
the Product Theorem of Breuillard-Green-Tao and Pyber-Szabo on growth
in finite simple groups of Lie type of bounded rank, extending
Helfgott's work. These deep theories yield strong results on products
of three subsets (covering, growth). What can be said about products
of two subsets?
I will discuss a recent joint work with Michael Larsen and Pham Tiep
on this challenging problem, focusing on products of two normal
subsets of finite simple groups. As a main application we show that
any element of a sufficiently large simple transitive permutation
group is a product of two derangements. The proofs apply
Fulman-Guralnick's work on the proportion of derangements, and involve
algebraic geometry, representation theory and other tools.