Speaker:Prof Raymond Lickorish (DPMMS)
Venue: Old Combination Room, Trinity College
Time: 27/10/2008 20:30, drinks from 20:15

The study of knots and links of curves in ordinary 3-dimensional space is an easily visualisable example of topology as ‘flexible geometry’. Knots are divided into various classes, tabulations are produced, yet (as with prime numbers) no real classification seems feasible. Even telling whether two knots are really different can be tricky.

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