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.
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.