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.

Axiom - art in the Andrew Wiles Building

As you enter the main entrance lobby of the Andrew Wiles Building you are greeeted by Axiom. Created by artist Mat Chivers, the sculpture is the winner of the Mathematical Institute's Sculpture Competition. The competition invited artists to propose, and eventually create, a substantial and artistically significant sculpture to be placed in the main entrance lobby. We would encourage you all to visit and meanwhile allow Mat to explain the work and its construction.

Tue, 25 Nov 2014

14:00 - 14:30
L5

Efficient optimization algorithms for nonlinear least-squares and inverse problems

Coralia Cartis
(University of Oxford)
Abstract
I will present an on-going project with Simon Tett, Mike Mineter and Kuniko Yamazaki (School of GeoSciences, Edinburgh University) that investigates automatically tuning relevant parameters of a standard climate model to match observations. The resulting inverse/least-squares problems are nonconvex, expensive to evaluate and noisy which makes them highly suitable for derivative-free optimisation algorithms. We successfully employ such methods and attempt to interpret the results in a meaningful way for climate science.
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.
Wed, 03 Dec 2014

16:00 - 17:00
C1

Dehn's problems and Houghton's groups

Charles Cox
(Southampton)
Abstract

Deciding whether or not two elements of a group are conjugate might seem like a trivial problem. However, there exist finitely presented groups where this problem is undecidable: there is no algorithm to output yes or no for any two elements chosen. In this talk Houghton groups (a family of groups all having solvable conjugacy problem) will be introduced as will the idea of twisted conjugacy: a generalisation of the conjugacy problem where an automorphism is also given. This will be our main tool in answering whether finite extensions and finite index subgroups of any Houghton group have solvable conjugacy problem.

Wed, 26 Nov 2014

16:00 - 17:00
C1

There is only one gap in the isoperimetric spectrum

Robert Kropholler
(Oxford)
Abstract

We saw earlier that a subquadratic isoperimetric inequality implies a linear one. I will give examples of groups, due to Brady and Bridson, which prove that this is the only gap in the isoperimetric spectrum. 

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