*Wednesday 15th May*–

*Friday 17th May 2019*

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.

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