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.
Speaker:Prof. Tim Gowers, FRS (DPMMS)
Venue: Old Combination Room, Trinity College
Time: 09/10/2006 20:30, drinks from 20:15
The talk is available.
Suppose you are given a number n and asked to determine whether it is prime. One time-honoured method is to see whether it is a multiple of 2, then of 3, then of 5, and so on, all the way up to the square root of n. This works fine for a number such as 147, but is not very practical if n has a hundred digits, say. A related problem, of great importance in cryptography, is to factorize a large integer that somebody gives you. Again, it can be done by simply searching through all the primes until you stumble on a factor, but again this takes far too long if the number is large. It is not at all obvious how one might go about finding faster approaches to these computational tasks. However, some very clever techniques have been discovered, and some of these are not especially hard to understand. This talk will present a few of them.
Speaker:Prof. Geoffrey Grimmett (Stats Lab)
Venue: Old Combination Room, Trinity College
Time: 06/03/2006 20:30, drinks from 20:15
Drop n points at random into a bounded subset of the plane, and find the area of the smallest triangle thus formed. This elementary problem involves the least arcane geometrical shape, but is related to a variety of questions of current mathematical interest including Poisson convergence, Kolmogorov complexity, and the Heilbronn triangle problem. It is linked also to a beautiful formula discovered by Morgan Crofton of Trinity College (Dublin) and published in the 9th edition of Encyclopedia Britannica in 1868.
Speaker:James Cranch (Sheffield)
Venue: Old Combination Room, Trinity College
Time: 20/02/2006 20:30, drinks from 20:15
Sometimes natural geometric questions in low dimensions can be hard. Despite being much harder to visualize, things can be easier with lots of dimensions. There are ways of replacing some difficult low-dimensional problems with easier high-dimensional ones. These ideas lead naturally to the construction of spectra, the abstract objects that many algebraic topologists really spend their time thinking about. This talk will be a quick tour of these ideas, with several pictures.
Speaker:Dominic Vella (DAMTP)
Venue: Old Combination Room, Trinity College
Time: 06/02/2006 20:30, drinks from 20:15
The physics of an air-water interface seems strange to those of us who are too big to stand still on water and too slow to run across it. In the “real world” there are many phenomena that seem counterintuitive but can be understood using mathematics… and a bit of physics. I will discuss some of these phenomena, how animals use them to their advantage and the mathematics that allows us humans to understand what they are doing.