Title: Interactions between Group Theory, Cyber Security, Artificial Intelligence and Quantum Computation

Abstract:

Brief bio:

16th December 2019

University of Bristol

We are very pleased to welcome James Maynard to the University of Bristol for a Heilbronn colloquium.

James is primarily interested in classical number theory, in particular the distribution of prime numbers. His research focuses on using tools from analytic number theory, particularly sieve methods, to study primes.

Title:  Approximating reals by fractions

Abstract: How well can you approximate real numbers by fractions with denominators coming from a given set? Although this old question has applications in many areas, in general this question seems impossibly hard – we don’t even know whether e+pi is rational or not!
If you allow for a tiny number of bad exceptions, then a beautiful dichotomy occurs – either almost everything can be approximated or almost nothing! I’ll talk about this problem and recent joint work with Dimitris Koukoulopoulos which classifies when these options occur, answering an old question of Duffin and Schaeffer. This relies on a fun blend of different ideas, including ergodic theory, analytic number theory and graph theory.

The colloquium will take place in Lecture theatre 2.41, Fry Building at 16:00- 17:00 on Monday 16th December followed by a wine reception in the Fry Common room. To help us plan catering, please complete the short registration form if you are planning to attend the colloquium.

15 – 17 May 2019 University of Bristol

We are pleased to announce we will be hosting two Distinguished Lecture Series in 2019, the second of which will be given by Jordan Ellenberg.

The talks will be over three days:

15th May, Colloquium in SM1, Maths Building, 16.00 followed by wine reception in Maths Common Room

16th May SM2, Maths Building 16.00

17th May, SM2, Maths Building 16:00

Please register for the colloquium here

Registration not required for the talks of the 16th and 17th May.

Colloquium Title and Abstract:

Title: Caps, sets, lines, ranks, polynomials, and (the absence of) arithmetic progressions Abstract:  Here is an innocent-looking problem. Suppose you wish to construct a subset of the numbers from 1 to 1,000,000 — or, more generally, from 1 to some large number N — with the property that no three of the numbers ever form an arithmetic progression. How big can your subset be? It’s not clear that this problem is hard and it’s not clear that it’s important.  In fact it is both! I’ll talk about the long history of this problem and its variants, including the “cap set” problem, which is related to the card game Set: how many cards can be on the table if there is no legal play? This problem sounds different but is in many ways the same. I’ll talk about a sudden burst of progress on the cap set problem that took place in 2016, and explain what it all has to do with polynomials over finite fields, spinning needles (they’re also over finite fields), notions of rank for NxNxN “matrices”, and the data science of embedding points in space.

Support for travel for UK based PhD students may be available, please contact heilbronn-coordinator@bristol.ac.uk with any requests by 15th April.

We are pleased to announce that we are able to consider applications for funding to support care costs*

This event is organised in collaboration with the Heilbronn Institute of Mathematical Research.

*Applies to expenses incurred exceptionally as a result of attending the lecture series. Please contact heilbronn-coordinator@bristol.ac.uk for further information.

1 – 3 April 2019 University of Bristol

We are pleased to announce we will be hosting two Distinguished Lecture Series in 2019, the first of which will be given by Geordie Williamson.

The talks will be held over three days:

Monday 1st April 16:00 (Colloquium) 1.15 Queens building followed by a wine reception in Pugsley foyer

Tuesday 2nd April, 16:00, SM2, Maths Building

Wednesday 3rd  April, 16:00, SM2, Maths Building

Please register for the colloquium here.

Registration not required for the talks of the 2nd and 3rd April.

Colloquium Title and Abstract:

Title: Semi-simplicity in representation theory
Abstract: Representation theory is the study of linear symmetry. Since the first papers on the representation theory of finite groups by Frobenius at the end of the 19th century, the theory has grown to form a fundamental tool of modern pure mathematics, with applications ranging from the standard model in particle physics to the Langlands program in number theory. Some of the most important theorems in representation theory assert some form of semi-simplicity. Examples include Maschke’s theorem on representations of finite groups over the complex numbers (proved in 1897), Weyl’s theorem on representations of compact Lie groups (proved in 1930), and the Kazhdan-Lusztig conjecture (proved by Beilinson-Bernstein and Brylinski-Kashiwara in 1980). The lectures will provide an introduction to these ideas, with an emphasis on our attempts to uncover further layers of hidden semi-simplicity.

Support for travel for UK based PhD students may be available, please contact heilbronn-coordinator@bristol.ac.uk with any requests by 18th March.

We are pleased to announce that we are able to consider applications for funding to support care costs*

This event is organised in collaboration with the Heilbronn Institute of Mathematical Research.

*Applies to expenses incurred exceptionally as a result of attending the lecture series. Please contact heilbronn-coordinator@bristol.ac.uk for further information.