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.

Speaker:Prof. Béla Bollobás (DPMMS / Memphis)
Venue: Old Combination Room, Trinity College
Time: 23/01/2006 20:30, drinks from 20:15

In the talk we shall present some unusual proofs of several combinatorial results.

Speaker:Dr Peter Smith (Faculty of Philosophy)
Venue: Old Combination Room, Trinity College
Time: 21/11/2005 20:30, drinks from 20:15

The talk is available.

Gödel famously showed that, in any theory in which you do enough arithmetic, there will be unprovable true sentences of arithmetic. Is this just a logical curiosity? Or does his Incompleteness Theorem impact on ‘ordinary’ mathematics?

Speaker:Dr Arthur Norman (Computing Laboratory)
Venue: Old Combination Room, Trinity College
Time: 07/11/2005 20:30, drinks from 20:15

In some respects quite a lot of calculus is easy to automate in the form of computer programs. However when people have done that they always seem to end up with systems that can be caused to give nonsense results. This talk looks at some of the pitfalls and considers the underlying questions (a) are computers a natural cause of confusion? (b) is calculus a natural cause of confusion?

Speaker:Prof. John Hinch, FRS (DAMTP)
Venue: Old Combination Room, Trinity College
Time: 24/10/2005 20:30, drinks from 20:15