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Department of Mathematics
Columbia House
London School of Economics
Houghton Street
London WC2A 2AE, UK

Email: maths.info@lse.ac.uk
Tel: +44(0)207 955 7732/7925

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# Lunchtime Seminar

Below you'll find the program for the Lunchtime Seminar. The Seminar normally takes place on Fridays from 12.05 pm - 12.35 pm in room 32L.LG.18 (32 Lincoln's Inn Fields). Follow this link for a map of the School.

Questions, suggestions, etc., about the seminar can be forwarded to the seminar administrator (Room COL 3.14), by sending an e-mail to: seminar@maths.lse.ac.uk

#### Upcoming Speakers:

Friday 24 October - Benny Sudakov (ETH Zurich)
Grid Ramsey problem and related questions

The Hales-Jewett theorem is one of the pillars of Ramsey theory, from which many other results follow.

A celebrated result of Shelah says that Hales-Jewett numbers are primitive recursive. A key tool used in his proof, known as the cube lemma, has become famous in its own right. In its simplest form, it says that if we color the edges of the Cartesian product $K_n \times K_n$ in $r$ colors then, for $n$ sufficiently large, there is a rectangle with both pairs of opposite edges receiving the same color.

Hoping to improve Shelah's result, Graham, Rothschild and Spencer asked more than 20 years ago whether the cube lemma holds with $n$ which is polynomial in $r$. We show that this is not possible by providing a superpolynomial lower bound in $r$. We also discuss a number of related questions, among them a solution of a problem of Erdos and Gyarfas on generalized Ramsey numbers.

This is joint work with Conlon, Fox and Lee.

Friday 31 October - speaker, title and abstract TBC

Friday 7 November - Frank Page
Title and abstract TBC

Friday 14 November - speaker, title and abstract TBC

Friday 21 November - speaker, title and abstract TBC

Friday 28 November - speaker, title and abstract TBC