Link to termcard: Termcard Michaelmax 2018

All talks will take place in the Winstanley Lecture Theatre unless stated otherwise.

*Wednesday 3 October, 7:30PM*

**TMS Freshers’ Squash**

Held in the Junior Parlour

Come and meet all the other freshers who share a common interest in mathematics! We’ll have plenty of free snacks and drinks so please come along and enjoy yourselves!

*Friday 12 October, 7:00PM*

**A Simple Proof of a Major Result**

Prof. Béla Bollobás (DPMMS)

Held in the CMS, MR2

The solutions of highly rated problems that have remained unsolved for decades tend to be long and complicated. Although this is what we have come to expect, this is not always the case: occasionally a novel approach leads to a remarkably short and beautiful solution. In my talk I shall give a particularly striking example of a simple solution of a notoriously difficult problem emerging out of the blue.

*Monday 22 October, 8:30PM*

**Film Night**

We will be screening ‘Travelling Salesman’, an exciting thriller concerning P=NP.

*Monday 29 October, 8:30PM*

**Stein’s Paradox**

Prof. Richard Samworth (Statslab)

Stein’s paradox is one of the most striking results in Statistics. Although it appears to be a toy problem in mathematical statistics, it turns out to have profound implications for the analysis of modern, high-dimensional data. I will describe both the result and some of its consequences.

*Monday 12 November, 8:30PM*

**Approximation on the Real Line**

Prof. Arieh Iserles (DAMTP)

The purpose of the exercise is simple, to design an orthogonal basis in the space of square-integrable functions on the real line such that the linear map taking the basis to its derivatives is skew symmetric. Such bases possess numerous advantages in the computation of ODEs and PDEs. In this talk, based on a joint work with Marcus Webb, I will completely characterise all such orthogonal systems using Fourier analysis and the theory of orthogonal polynomials. The extension of this work to complex-valued skew-Hermitian `differentiation matrices’ is trivial but it leads to a beautiful outcome, an orthogonal system of rational functions designed (in a different context) almost a century ago by Malmquist and Takenaka and which exhibits some truly miraculous properties.

*Monday 19 November, 8:30PM*

**Rolls, Squares and Hexagons: pattern formation through instabilities**

Prof. Michael Proctor (DAMTP)

It is an experimental fact that when an extended system in a simple amorphous state becomes unstable, the new realised state is typically one exhibiting a pattern. It can be shown even for very complicated physical systems that the dynamical processes near the point in parameter space where stability is lost can be represented by a small number of ordinary differential equations. The form of these equations, and the interactions of any possible patterns that can result from the instability, is strongly influenced, and in many cases determined, by the symmetries of the system being studied. One the symmetry group is known, the different patterns can be identified with different representations of the group. I will discuss a number of examples of varying complexity.

*Monday 26 November, 8:30PM*

**TMS Call My Bluff**

You?

An annual tradition, held by the TMS, in which a team of freshers test their lying capabilities against a team of other students in a reconstruction of the cult British TV show.