Speaker:Dr Ivan Smith (DPMMS)
Venue: Old Combination Room, Trinity College
Time: 13/10/2008 20:30, drinks from 20:15
We’ll discuss some of the surprising mathematics involved in playing billiards (albeit on some unusually shaped tables without pockets). There are connections to number theory, rainbows and electron transport in metals.
Speaker:Dr Robert Gramacy (Stats Lab)
Venue: Old Combination Room, Trinity College
Time: 03/03/2008 20:30, drinks from 20:15
The talk is available.
Computer experiments often require dense sweeps over input parameters to obtain a qualitative understanding of their response. However, such sweeps are unnecessary in regions where the response is easily predicted; well-chosen designs could allow a mapping of the response with far fewer simulation runs. I explore a modern approach that couples two standard regression models: Gaussian processes and treed partitioning. A Bayesian perspective yields an explicit measure of (nonstationary) predictive uncertainty that can be used to guide sampling. The methods will be illustrated through several examples, including a motivating example which involves the computational fluid dynamics of a NASA re-entry vehicle.
Speaker:Dr Tom Fisher (DPMMS)
Venue: Old Combination Room, Trinity College
Time: 18/02/2008 20:30, drinks from 20:15
An important source of problems in number theory is the study of Diophantine equations, i.e. systems of (usually polynomial) equations that must be solved in integers or rational numbers. One hope is that these “global” problems can be attacked by putting together “local” information, that is by looking at the problem one prime at a time (and over the reals). This works particularly well for quadratic forms, but generalisations are surprisingly hard to come by.
Speaker:Prof. Gary Gibbons (DAMTP)
Venue: Old Combination Room, Trinity College
Time: 04/02/2008 20:30, drinks from 20:15
The talk is available.
If we take light rays as straight lines, and if light is bent by a gravitational field, then the angular sum of a triangle cannot equal 180 degrees. In this talk I will use the Gauss-Bonnet theorem to discuss the angular sum of triangles in the vicinity of black holes, and elsewhere in the universe.
Speaker:Prof. Ben Green (DPMMS)
Venue: Old Combination Room, Trinity College
Time: 21/01/2008 20:30, drinks from 20:15
Every Trinity mathmo ought to know something about the story of the great Indian genius Srinivasa Ramanujan and how he came to Trinity to work with Hardy and Littlewood in the early 20th century. In this talk I hope, in addition, to emphasise some respects in which his work is still highly relevant today.
Speaker:Dr Maciej Dunajski (DAMTP)
Venue: Old Combination Room, Trinity College
Time: 19/11/2007 20:30, drinks from 20:15
The talk is available.
Twistor Theory was originally proposed as a way to unify quantum mechanics with general relativity. Its status as a physical theory remains unclear but it found unexpected applications in pure mathematics – from Hyperk
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,…,Ak is defined as S=A1+A2+…+Ak={a1+…+ak:ai&isin Ai for every i}. For non-empty finite sets Ai, it is easily seen that the size |S| of the sum is at least |A1|+…+|Ak|-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 Rk.
Speaker:Prof. Jan Saxl (DPMMS)
Venue: Old Combination Room, Trinity College
Time: 05/03/2007 20:30, drinks from 20:15