To Be Announced

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Special Year 2022-23: Dynamics, Additive Number Theory and Algebraic Geometry - Seminar

To Be Announced

To Be Announced

A conjecture of Erdős states that for every large enough prime q, every reduced residue class modulo q is the product of two primes less than q. I will discuss my on-going work with Kaisa Matomäki establishing among other things a ternary variant of...

Diophantine approximation deals with quantitative and qualitative aspects of approximating numbers by rationals. A major breakthrough by Kleinbock and Margulis in 1998 was to study Diophantine approximations for manifolds using homogeneous dynamics...

We will survey general definitions and facts about ultrafilters, and how the algebraic operations on the integers extend to the space of ultrafilters. We will also discuss some applications in combinatorial number theory and ergodic theory.

If a set of integers is syndetic (finitely many translates cover the integers), must it contain two integers whose ratio is a square? No one knows. In the broader context of the disjointness between additive and multiplicative configurations and...

A discrete subgroup of PSL(2,C) is called a Kleinian group. I will present a criterion on when a discrete faithful representation of a Kleinian group into PSL(2,C) is a conjugation, or equivalently a criterion on when an equivariant embedding of...

The goal of this learning seminar is to explain some of the core model theoretic notions which are behind Tao’s algebraic regularity lemma about definable graphs in finite fields (Tao 2012).

We will assume minimal knowledge of model theory and...