Tue, 08 Nov 2016

15:45 - 16:45
L4

Towards a compactification of the moduli space of K3 surfaces of degree 2

Alan Thompson
(Warwick)
Abstract

Ever since moduli spaces of polarised K3 surfaces were constructed in the 1980's, people have wondered about the question of compactification: can one make the moduli space of K3 surfaces compact by adding in some boundary components in a "nice" way? Ideally, one hopes to find a compactification that is both explicit and geometric (in the sense that the boundary components provide moduli for degenerate K3's). I will present on joint work in progress with V. Alexeev, which aims to solve the compactification problem for the moduli space of K3 surfaces of degree 2.

Wed, 08 Jun 2016
16:00
C2

Intensional Partial Metric Spaces

Steve Matthews
(Warwick)
Abstract

Partial metric spaces generalise metric spaces by allowing self-distance
to be a non-negative number. Originally motivated by the goal to
reconcile metric space topology with the logic of computable functions
and Dana Scott's innovative theory of topological domains they are now
too rigid a form of mathematics to be of use in modelling contemporary
applications software (aka 'Apps') which is increasingly concurrent,
pragmatic, interactive, rapidly changing, and inconsistent in nature.
This talks aims to further develop partial metric spaces in order to
catch up with the modern computer science of 'Apps'. Our illustrative
working example is that of the 'Lucid' programming language,and it's
temporal generalisation using Wadge's 'hiaton'.

Mon, 15 Jun 2015
15:45
L6

Coarse rigidity for Teichm\"uller space

Brian Bowditch
(Warwick)
Abstract
We describe some results regarding the quasi-isometric rigidity of
Teichm\"uller space in either the Teichm\"uller metric or the Weil-Petersson
metric; as well as some other spaces canonically associated to a surface.
A key feature which these spaces have in common is that they admit
a ternary operation, which in an appropriate sense, satisfies the
axioms of a median algebra, up to bounded distance.  This allows
us to set many of the arguments in a general context.
We note that quasi-isometric rigidity of the Teichm\"uller metric has recently
been obtained independently by Eskin, Masur and Rafi by different methods.
Thu, 16 Jun 2016

16:00 - 17:00
L3

Sensing human behaviour with online data

Suzy Moat
(Warwick)
Abstract

Our everyday usage of the Internet generates huge amounts of data on how humans collect and exchange information worldwide. In this talk, I will outline recent work in which we investigate whether data from sources such as Google, Wikipedia and Flickr can be used to gain new insight into real world human behaviour. I will provide case studies from a range of domains, including disease detection, crowd size estimation, and evaluating whether the beauty of the environment we live in might affect our health.

Fri, 15 May 2015
14:30
L5

The measurable Tarski circle squaring problem

Lukasz Grabowski
(Warwick)
Abstract

Two subsets A and B of R^n are equidecomposable if it is possible to partition A into pieces and rearrange them via isometries to form a partition of B. Motivated by what is nowadays known as Banach-Tarski paradox, Tarski asked if the unit square and the disc of unit area in R^2 are equidecomposable. 65 years later Laczkovich showed that they are, at least when the pieces are allowed to be non-measurable sets. I will talk about a joint work with A. Mathe and O. Pikhurko which implies in particular the existence of a measurable equidecomposition of circle and square in R^2.

Mon, 02 Feb 2015
15:45
C6

Closed geodesics and string homology

John Jones
(Warwick)
Abstract

The  study of closed geodesics on a Riemannian manifold is a classical and important part of differential geometry. In 1969 Gromoll and Meyer used Morse - Bott theory to give a topological condition on the loop space of compact manifold M which ensures that any Riemannian metric on M has an infinite number of closed geodesics.  This makes a very close connection between closed geodesics and the topology of loop spaces.  

Nowadays it is known that there is a rich algebraic structure associated to the topology of loop spaces — this is the theory of string homology initiated by Chas and Sullivan in 1999.  In recent work, in collaboration with John McCleary, we have used the ideas of string homology to give new results on the existence of an infinite number of closed  geodesics. I will explain some of the key ideas in our approach to what has come to be known as the closed geodesics problem.

Mon, 02 Feb 2015
14:15
L5

Geometric structures, Gromov norm and Kodaira dimensions

Weiyi Zhang
(Warwick)
Abstract

Kodaira dimension provides a very successful classification scheme for complex manifolds. The notion was extended to symplectic 4-manifolds. In this talk, we will define the Kodaira dimension for 3-manifolds through Thurston’s eight geometries. This is compatible with other Kodaira dimensions in the sense of “additivity”. This idea could be extended to dimension 4. Finally, we will see how it is sitting in a potential classification of 4-manifolds by exploring its relations with various Kodaira dimensions and other invariants like Gromov norm.

Tue, 11 Nov 2014
17:00
C2

On computing homology gradients over finite fields

Lukasz Grabowski
(Warwick)
Abstract

 Recently several conjectures about l2-invariants of
CW-complexes have been disproved. At the heart of the counterexamples
is a method of computing the spectral measure of an element of the
complex group ring. We show that the same method can be used to
compute the finite field analog of the l2-Betti numbers, the homology
gradient. As an application we point out that (i) the homology
gradient over any field of characteristic different than 2 can be an
irrational number, and (ii) there exists a CW-complex whose homology
gradients over different fields have infinitely many different values.
 

Fri, 09 May 2014
16:00
L6

Some subgroups of topological Kac–Moody groups

Inna Capdeboscq
(Warwick)
Abstract

This talk is based on a joint work with B. Rémy (Lyon) in which we study some subgroups of topological Kac–Moody groups and the implications of this study on the subgroup structure of the ambient Kac–Moody group.

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