Speaker:Dr Thomas Forster (DPMMS)
Venue: Old Combination Room, Trinity College
Time: 05/11/2007 20:30, drinks from 20:15

Russell and Whitehead famously avoided the paradoxes by regimenting sets (and languages) into disjoint levels in a system called Type Theory. Over the years this approach and the Zermelo-Fraenkel approach have diverged greatly; since the ZF approach is much better known there are now some interesting backwaters which invite closer attention than they usually get. This talk will be an introduction to the descendents of type theory and will try to make connections with other themes in the philosophy of mathematics.

Speaker:Prof. Neil Turok (DAMTP)
Venue: Old Combination Room, Trinity College
Time: 22/10/2007 20:30, drinks from 20:15

The last decade has seen huge advances in our understanding of the makeup and history of the universe. Some properties of the universe – its geometry and the nature of the primordial density inhomogeneities – are astonishingly simple. Other properties – like the existence of dark energy – are very hard to reconcile with standard cosmology. And the cosmic singularity from which everything emerged remains a deep mystery. I will discuss a radical new approach, the cyclic model, based on ideas from string theory and M theory, which explains the observations without invoking a period of cosmic inflation. I will describe how future observations could distinguish the inflationary and cyclic models.

Speaker:Prof. Béla Bollobás (DPMMS)
Venue: Old Combination Room, Trinity College
Time: 15/10/2007 20:30, drinks from 20:15

The sum S of k sets of integers A₁,A₂,…,A_k is defined as S=A₁+A₂+…+A_k={a₁+…+a_k:a_i&isin A_i for every i}. For non-empty finite sets A_i, it is easily seen that the size |S| of the sum is at least |A₁|+…+|A_k|-k+1. There are similar classical inequalities for subsets of additive groups – indeed, such an equality was proved by Cauchy and rediscovered by Davenport. In the talk, aimed at first year undergraduates, we shall consider some related inequalities concerning the minima and maxima of set sums. For example, given |A₁+A₂|, |A₁+A₃| and |A₂+A₃|, what can we say about the sum of the three sets? As we shall see, these problems are intimately connected to inequalities involving the volumes of “canonical” projections of a body in R^k.

Speaker:Prof. Jan Saxl (DPMMS)
Venue: Old Combination Room, Trinity College
Time: 05/03/2007 20:30, drinks from 20:15

Speaker:Dr David Tong (DAMTP)
Venue: Winstanley Lecture Theatre, Trinity College
Time: 19/02/2007 20:30, drinks from 20:15

The talk is available.

Big circles are the same as small, topology is ambiguous, and quantum geometry is pointless (because there aren’t any points).

Speaker:Dan Jane (DPMMS)
Venue: Old Combination Room, Trinity College
Time: 05/02/2007 20:30, drinks from 20:15

The Ricci Flow has caused much activity and excitement over the last twenty five years. For surfaces embedded in three dimensions the situation is easily visualised; I will try to give a brief overview of some of the ideas in order that we have a little geometric intuition in the area. Then I will explain a method to investigate the effects the Ricci Flow has on the straight lines of our (not straight at all) space.

Speaker:Prof. Imre Leader (DPMMS)
Venue: Old Combination Room, Trinity College
Time: 22/01/2007 20:30, drinks from 20:15

The talk is available.

Speaker:Prof. Michael Proctor, FRS (DAMTP)
Venue: Old Combination Room, Trinity College
Time: 20/11/2006 20:30, drinks from 20:15

We are accustomed to thinking of the stability of a configuration of a physical system in black and white terms: either small disturbances grow or they decay. But there are many important situations where the system is ultimately stable, but which can act as a powerful amplifier for a long period of time. The situation is particularly important when the system has a long spatial extent, so that these non-instabilities (convective instabilities) can produce large amplitude structures which can be sustained by small amounts of noise. In contrast, when the system is absolutely unstable no noise is needed to sustain the structures. This dichotomy is related to the behaviour of linear dynamical systems with non-normal matrices.

Speaker:Dr Emily Shuckburgh (DAMTP)
Venue: Old Combination Room, Trinity College
Time: 06/11/2006 20:30, drinks from 20:15

The talk is available.

Many aspects of weather and climate can be understood by considering idealised models and using basic physical principles together with standard mathematical techniques used in all branches of applied mathematics. This talk will explore the mathematics behind the weather and climate by exploring two case studies which display rather different physics. The first is that of winter storms that hit the UK, and second is the El Nino phenomena which dominates the year-to-year variability of weather over much of the Pacific region. Understanding the physical mechanisms which drive these weather features and their sensitivity to changes allows us to make short-term forecasts and longer-term climate predictions.

Speaker:Prof. Andrew Thomason (DPMMS)
Venue: Old Combination Room, Trinity College
Time: 23/10/2006 20:30, drinks from 20:15

The four colour problem (that the countries of any map can be coloured using only four colours so that no two countries with a common border have the same colour) has generated interest for a long time. Sixty years ago a couple of TMS members, Cedric Smith and William Tutte, made some striking contributions. These will be described, together with more recent developments, in this self-contained talk.