Tue, 27 Jan 2015

17:00 - 18:00
C2

Regular maps and simple groups

Martin Liebeck
(Imperial College London)
Abstract

A regular map is a highly symmetric embedding of a finite graph into a closed surface. I will describe a programme to study such embeddings for a rather large class of graphs: namely, the class of orbital graphs of finite simple groups.

Tue, 10 Feb 2015

17:00 - 18:00
C2

Spin projective representations of Weyl groups, Green polynomials, and nilpotent orbits

Dan Ciubotaru
(Oxford)
Abstract

The classification of irreducible representations of pin double covers of Weyl groups was initiated by Schur (1911) for the symmetric group and was completed for the other groups by A. Morris, Read and others about 40 years ago. Recently, a new relation between these projective representations, graded Springer representations, and the geometry of the nilpotent cone has emerged. I will explain these connections and the relation with a Dirac operator for (extended) graded affine Hecke algebras.  The talk is partly based on joint work with Xuhua He.

Fri, 12 Dec 2014

14:15 - 15:15
C2

On the Ramdas layer

Vasudeva Murthy
(Tata Institute of Fundamental Research (TIFR) Bangalore)
Abstract

On calm clear nights a minimum in air temperature can occur just above the ground at heights of order 0.5m or less. This is contrary to the conventional belief that ground is the point of minimum. This feature is paradoxical as an apparent unstable layer (the height below the point of minimum) sustains itself for several hours. This was first reported from India by Ramdas and his coworkers in 1932 and was disbelieved initially and attributed to flawed thermometers. We trace its history, acceptance and present a mathematical model in the form of a PDE that simulates this phenomenon.

Thu, 04 Dec 2014

16:00 - 17:00
C2

Introduction to Concepts of General Relativity

Felix Tennie
(Oxford University)
Abstract

Since its genesis in 1915, General Relativity has proven to be one of the most successful physical theories ever invented. Providing a description of the large scale structure of the universe it continues to be in agreement with all experimental tests to high accuracy. By merging Classical Mechanics and Electrodynamics to a consistent geometrical theory of space-time it has become one of the two pillars of modern theoretical physics alongside Quantum Mechanics. This talk aims to give an introduction to the ideas and concepts of General Relativity. After briefly reviewing Classical (Newtonian) Mechanics and experiments in contradiction with it the framework and axioms of General Relativity will be introduced. This will be followed by a survey on major implications of the (new) geometrical description of gravity. Finally an outlook on physics beyond General Relativity will be provided. 

Tue, 02 Dec 2014

17:00 - 18:00
C2

Branch groups: groups that look like trees

Alejandra Garrido
(Oxford)
Abstract

Groups which act on rooted trees, and branch groups in particular, have provided examples of groups with exotic properties for the last three decades. This and their links to other areas of mathematics such as dynamical systems has made them the object of intense research.
One of their more useful properties is that of having a "tree-like" subgroup structure, in several senses. 
I shall explain what this means in the talk and give some applications.

Wed, 26 Nov 2014
16:00
C2

Set functions.

Leobardo Fernández Román
(UNAM Mexico)
Abstract
A continuum is a non-empty
compact connected metric space.
Given a continuum X let P(X) be the
power set of X. We define the following
set functions:
 
T:P(X) to P(X) given by, for each A in P(X),
T(A) = X \ { x in X : there is a continuum W
such that x is in Int(W) and W does not
intersect A}.
 
K:P(X) to P(X) given by, for each A in P(X)
K(A) = Intersection{ W : W is a subcontinuum
of X and A is in the interior of W}.
 
Also, it is possible to define the arcwise
connected version of these functions.
Given an arcwise connected continuum X:
 
Ta:P(X) to P(X) given by, for each A in P(X),
Ta(A) = X \ { x in X : there is an arcwise
connected continuum W such that x is in
Int(W) and W does not intersect A}.
 
Ka:P(X) to P(X) given by, for each A in P(X),
Ka(A) = Intersection{ W : W is an arcwise
connected subcontinuum of X and A is in
the interior of W}
 
Some properties, examples and relations
between these functions are going to be
presented.
Tue, 18 Nov 2014

17:00 - 18:00
C2

Commuting probabilities of finite groups

Sean Eberhard
(Oxford)
Abstract

The commuting probability of a finite group is defined to be the probability that two randomly chosen group elements commute. Not all rationals between 0 and 1 occur as commuting probabilities. In fact Keith Joseph conjectured in 1977 that all limit points of the set of commuting probabilities are rational, and moreover that these limit points can only be approached from above. In this talk we'll discuss a structure theorem for commuting probabilities which roughly asserts that commuting probabilities are nearly Egyptian fractions of bounded complexity. Joseph's conjectures are corollaries.

Thu, 13 Nov 2014

16:00 - 17:00
C2

Non-commutative topology and K-theory for applications to topological insulators

Guo Chuan Thiang
(Oxford University)
Abstract

I will recall basic notions of operator K-theory as a non-commutative (C*-algebra) generalisation of topological K-theory. Twisted crossed products will be introduced as generalisations of group C*-algebras, and a model of Karoubi's K-theory, which makes sense for super-algebras, will be sketched. The motivation comes from physics, through the study of quantum mechanical symmetries, charged free quantum fields, and topological insulators. The relevant theorems, which are interesting in their own right but scattered in the literature, will be consolidated.

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