Speakers: Prof Imre Leader and Dr Thomas Forster (DPMMS)
Venue: MR4, Centre for Mathematical Sciences
Time: 28/2/2012 18:30
Is the axiom of choice a bit of a joke?
Why is Banach-Tarski not a paradox? Or is it after all as weird as you thought?
Come hear Imre Leader and Thomas Forster debate the right way to use – or not – the axiom of choice.
Non-constructive views and non-well-orderly behaviour tolerated.
(organised by Nik Sultana)
Speaker: Prof Gabriel Paternain (DPMMS)
Venue: Winstanley Lecture Theatre
Time: 20/2/2012 20:30, drinks from 20:15
We have known for a long time how to write down the equations of motion of a satellite that moves under the influence of the gravitational fields of the Earth and the Moon, but surprisingly, we still do not fully understand the long term behaviour of the satellite since we cannot explicitly solve the equations. At the end of the 19th century, Poincare noticed the presence of chaos in the system and kick-started the modern theory of dynamical systems. Recently a new type of geometry called contact geometry (the odd dimensional relative of symplectic geometry) has been proposed as a tool for understanding this old problem in celestial mechanics. In the talk I will try to explain what contact geometry is and why it is relevant for the 3-body problem.
Speaker:Dr Natalia Berloff (DAMPT)
Venue: Winstanley Lecture Theatre
Time: 21/11/2011 20:30, drinks from 20:15
When in 1937 liquid helium was first observed to flow with negligible viscosity through a narrow gap, it was clear that, at low temperatures, helium was different from ordinary fluids. The attemps to understand this phenomenon (called superfluidity by Pyotr Kapitza) led to the development of a two-fluid theory by Lev Landau. In this theory the fluid is modelled as an interacting mixture of superfluid and normal fluid components. In more recent times, an aspect of superfluidity that has been emphasized as most central is that the superfluid velocity is associated with the gradient of the phase of the macroscopic classical complex-valued matter field. Such a description impies that the system possesses a Bose–Einstein condensate (a form of matter that emerges when particles collapse into the same lowest-energy state) — with the matter field being the condensate wavefunction — and, therefore, can be described by a nonlinear equation for classical waves, known as the nonlinear Schrodinger equation. This description has the ingredients necessary to produce many of the aspects of superfluidity, such as frictionless flow below the Landau critical velocity, two-fluid hydrodynamics, quantized vortices, and metastable persistent flow in a doughnut-shaped geometry. These features of superfluidity have been experimentally observed not only in liquid helium, but also in ultracold gases and very recently in condensates of semiconductor microcavity polaritons — entities comprising both matter and light. How the condensate model can be modified and applied to study the dynamics of these various superfluid systems is the subject of my talk.
Speaker:Prof Kevin Buzzard (Imperial College)
Venue: Winstanley Lecture Theatre
Time: 7/11/2011 20:30, drinks from 20:15
Are there any rational solutions to x²+y²=-1? No, because there are no real solutions. How about x²+y²=3? Again the answer is no, but one way of showing this is by constructing a ‘local field’ — the 3-adic numbers — which contains the rationals as a dense subfield, and in which it’s easy to check that there are no solutions. It is far easier to solve equations in these local fields than in global fields such as the rationals, and conversely, sometimes solutions in all local fields can imply solutions in a global field too.
Speaker:Prof. Béla Bollobás
Venue: MR2, Centre for Mathematical Sciences
Time: 31/10/2011 7:15
The solution of a good mathematical problem often leads to new questions that are even deeper and more important than the original problem. In the talk I shall present some questions with close Trinity ties which arose about hundred years ago, have gone through several incarnations, and are still alive today. I shall also present the striking proof of a recent result concerning one of these questions
Speaker:Prof Zoubin Ghahramani (Dept. of Engineering)
Venue: Winstanley Lecture Theatre
Time: 24/10/2011 20:30, drinks from 20:15
Information plays a central role in 21st century science, commerce and society. We have huge data sets of measurements collected from large-scale scientific experiments, exciting commercial opportunities arising from exploiting web-scale information, and vast stores of knowledge available to society on the internet. Probabilistic approaches for modelling uncertainty and learning from data are essential to the effective use of these vast stores of information. Modern probabilistic approaches to building learning machines are grounded in the mathematics of the 18th century Reverend Thomas Bayes. I will describe the foundations of this field and our recent work on stochastic processes and nonparametric statistics, along with examples of a number of applications to big data problems such as information retrieval, recommendation, genomic data analysis, financial prediction, and robotics.
Speaker:Dr. Piers Bursill-Hall (DPMMS)
Venue: Winstanley Lecture Theatre
Time: 10/10/2011 20:30, drinks from 20:15
So you think you know about the world? And just because you’re a mathmo, you understand the world? How unlikely is that? This talk will be about how a bunch of mathmos noticed that they regularly talk to God (like all mathmos do) and this changed the course of history and created the modern world.”
Speaker:Dr Richard Nickl (Statslab
Venue: Winstanley Lecture Theatre
Time: 07/03/2011 20:30, drinks from 20:15
Even after C.F. Gauss had published the Disquistiones Arithmeticae, that contain some of his most fundamental number-theoretical work, in 1801, he was known only to specialists in Europe. This changed drastically after he predicted, late in 1801, the position of the planet Ceres after it had ‘disappeared behind the sun’. Gauss immediately achieved fame throughout Europe. A technique that Gauss used in this prediction, as well as in much of his subsequent observational work, was the method of least squares to correct ‘intrinsic’ measurement errors in an efficient way. This method, in conjunction with the normal or ‘Gaussian’ distribution, has been a cornerstone of modern statistics ever since, reaching into the foundations of likelihood-based inference. I shall discuss the main mathematical and methodological ideas behind Gauss’ invention and trace some key aspects of its history into the 21st century, highlighting a variety of key statistical ideas that derive from it.
Speaker:Prof Martin Hyland (DPMMS
Venue: Old Combination Room, Trinity College
Time: 21/02/2011 20:30, drinks from 20:15
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 from algebras 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.
Speaker:Dr James Cranch (University of Leicester
Venue: Old Combination Room, Trinity College
Time: 07/02/2011 20:30, drinks from 20:15
For decades, mathematicians have motivated much work by referring to several deeply interesting algebraic objects which sadly fail to exist under the normal definitions. I will exhibit several of these, including the field with one element and the localisation of the integers at the infinite prime, and discuss what they might really mean. Not much familiarity is required with any algebraic objects which really do exist.