Speaker:Prof Terence Tao (UCLA Dept of Mathematics)
Venue: Winstanley Lecture Theatre
Time: 24/01/2011 20:30, drinks from 20:00

It is a remarkable phenomenon in nature and in mathematics that the statistical behaviour of large complex systems are often governed by _universal laws_ that, miraculously, are almost completely independent of the microscopic mechanics of such systems. Well known examples of such universal laws include the laws of thermodynamics, Benford’s law, and the central limit theorem; the zeroes of the zeta function are also conjectured to be governed by another universal law arising from random matrix theory. We will survey some of these laws, including some recent theoretical developments by several authors (including the speaker) that have rigorously established universality for some random matrix models.

Speaker:Prof Martin Hyland (DPMMS)
Venue: Winstanley Lecture Theatre, Trinity College
Time: 22/11/2010 20:30, drinks from 20:15

This talk has been cancelled owing to unforeseen circumstances. We apologise, and hope to bring it to you next term instead.

Algebras are vector spaces equipped with a multiplication (for example, the cross product in 3-space). Quadratic algebras are a special class of algebra with a duality theory involving the so-called dual numbers. The dual numbers give the algebra of differentiation. One can pass fromalgebras to suitable algebraic theories called operads. There is a notion of a ‘quadratic operad’ with an analogous rich theory involving Lie algebras. Using examples, I shall try to explain some of this and its significance.

Venue: Winstanley Lecture Theatre, Trinity College
Time: 08/11/2010 20:30, drinks from 20:15

D. E. Twigg – Supersymmetry and the Witten Index.

A. D. J. Shannon – Geometry without Geometry.

C. J. Donnelly – The Magnetorotational Instability.

Speaker:Dr David Tong (DAMTP)
Venue: Winstanley Lecture Theatre, Trinity College
Time: 25/10/2010 20:30, drinks from 20:15

Leopold Kronecker once said “God made the integers, the rest is the work of man”. In this talk I will show that this statement is experimentally wrong. I will explain how the integers arise in Nature and explain that they are emergent objects, no more fundamental than the concept of smell. I will also comment on the yet-to-be-discovered laws of physics and provide some (admittedly circumstantial) evidence that they are not based on the integers. We are not living in the world of “The Matrix”. (Probably).

Speaker:Prof Imre Leader (DPMMS
Venue: Winstanley Lecture Theatre, Trinity College
Time: 11/10/2010 20:30, drinks from 19:45

Suppose we are presented with a long string of beads. The beads come in two colours, red and blue, but there is not necessarily any `pattern’ to the way they are threaded on the string. Can we guarantee to find three equally-spaced beads of the same colour? For example, if the 5th, 7th and 9th beads were all blue then this would count. This question leads on to some beautiful mathematics.

Speaker:Dr Jeremy Butterfield (Faculty of Philosophy)
Venue: Winstanley Lecture Theatre, Trinity College
Time: 01/03/2010 20:30, drinks from 20:15

The talk is available.

‘Emergence’ and ‘reduction’ are buzz-words in both physics and philosophy. Both physicists and philosophers disagree about the extent to which we can understand large-scale or complex phenomena in terms of their microscopic parts. Examples include everyday phenomena, like the freezing and boiling of liquids, and fancy ideas like fractals. I will pour some oil on these troubled waters by arguing that many cases exemplify both emergence and reduction.

Speaker:Prof David Spiegelhalter, FRS (Statslab)
Venue: Winstanley Lecture Theatre, Trinity College
Time: 15/02/2010 20:30, drinks from 20:15

A Bayesian perspective allows probability theory to be used as a formalism for epistemic uncertainty: ie a measure of our confidence in a current or past state of the world about which we are ignorant (although someone else might know the truth). This allows probability to be used to quantify our uncertainty about a suspect’s guilt, the image on the Turin shroud, the average effect of a medical treatment, or whether Jane Austen died before Napoleon. I will look at how these ideas have developed and are being used in practice, and how scoring rules can be used to assess how well you can quantify your doubt. A test will be given at the end, and a small prize awarded for the person who best knows what they don’t know.

Speaker:Dr Jacob Rasmussen (DPMMS)
Venue: Winstanley Lecture Theatre, Trinity College
Time: 01/02/2010 20:30, drinks from 20:15

The tangent bundle to the n-dimensional sphere is the set of all pairs (x,v), where x is a point in the sphere, and v is a vector in R^{n+1} tangent to x at p. I’ll discuss the geometry and topology of this space and of a more general class of spaces known as vector bundles on spheres.

Speaker:Paul Smith (DPMMS)
Venue: Winstanley Lecture Theatre, Trinity College
Time: 18/01/2010 20:30, drinks from 20:15

Graphs (or networks) have a rich history of study stretching back over 250 years. I shall talk about one particular infinite graph, some of its surprising properties, how it arises naturally out of coin tossing, and how to beat Derren Brown at his own game.

Speaker:Dr Gabriel Paternain (DPMMS)
Venue: Winstanley Lecture Theatre, Trinity College
Time: 23/11/2009 20:30, drinks from 20:15

I will try to explain connections between some of the equations you study in IB Fluids and the field of contact topology. I will make a deliberate attempt to convince you to read the wonderful book by Arnold and Khesin ‘Topological methods in Hydrodynamics’.