*Tuesday 26th April*–

*Tuesday 26th April 2022*

Tuesday 26th April 2022: 15.00 – 16.00

University of Bristol

We are delighted to welcome Andreas Strömbergsson, Uppsala University, as the Heilbronn Distinguished Visiting Professor, to deliver a Heilbronn Colloquium in person, at the University of Bristol in 2.04, Fry Building.

**Title:** Rational points on horospheres, random abelian Cayley graphs, and the Frobenius coin problem

**Abstract: **I will discuss a result about asymptotic equidistribution of certain point sets in the homogeneous space SL(d,Z)\SL(d,R), i.e. the space of lattices in the Euclidean space R^d. This result was first proved by Einsiedler, Mozes, Shah and Shapira (2016). As I will explain, the result has applications to limit laws for various metric parameters of random Cayley graphs of a large finite abelian group, and also to the so called Frobenius coin problem. I will discuss a new proof of the equidistribution result, which leads to an explicit rate of convergence. This proof makes use of tools from algebraic geometry (recent work of Erdelyi and Toth giving bounds on matrix Kloosterman sums) and tools from geometry of numbers (an integration formula by Rogers from 1955).

Joint work with Daniel El-Baz and Min Lee.

Spaces are limited in the room, so we ask that you please register via the form if you are intending to come in person. Once capacity is reached, we will close registration and any current remaining spaces will be allocated on a first come basis. The talk will be streamed via Zoom, but please note, it will be a basic stream and so not entirely interactive for those joining online. If you wish to attend via zoom please use the details below:

Meeting ID: 957 5549 2327

Passcode: 826183

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