Wed, 20 Apr 2022

10:00 - 11:00
C1

A geometric fundamental class for Smale spaces

Mike Whittaker
(Glasgow)
Abstract

A few years back, Smale spaces were shown to exhibit noncommutative Poincaré duality (with Jerry Kaminker and Ian Putnam). The fundamental class was represented as an extension by the compacts. In current work we describe a Fredholm module representation of the fundamental class. The proof uses delicate approximations of the Smale space arising from a refining sequence of (open) Markov partition covers. I hope to explain all these notions in an elementary manner. This is joint work with Dimitris Gerontogiannis and Joachim Zacharias.

Mon, 13 Nov 2017
17:00
L5

A computer search for ribbon alternating links

Brendan Owens
(Glasgow)
Abstract

I will report on a joint project with Frank Swenton whose goal is to develop an algorithm to determine whether an alternating knot is ribbon.  We can’t do this yet but we have an algorithm that has been remarkably, and indeed mysteriously, successful in finding a great deal of new slice knots.

Tue, 21 Feb 2017
17:00
C1

KMS states on self-similar groupoid actions

Michael Whittaker
(Glasgow)
Abstract

A self-similar groupoid action (G,E) consists of a faithful action of a groupoid G on the path space of a graph which displays a notion of self-similarity. In this talk I will explain this concept and consider KMS states on associated Cuntz-Pimsner C*-algebras. This talk is based on joint work with Marcelo Laca, Iain Raeburn, and Jacqui Ramagge

Tue, 11 Oct 2016

12:00 - 13:15
L4

tt*-geometry and Hermitian structures on the big phase space

Ian Strachan
(Glasgow)
Abstract

The big phase space is an infinite dimensional manifold which is the arena
for topological quantum field theories and quantum cohomology (or
equivalently, dispersive integrable systems). tt*-geometry was introduced by
Cecotti and Vafa and is a way to introduce an Hermitian structure on what
would be naturally complex objects, and the theory has many links with
singularity theory, variation of Hodge structures, Higgs bundles, integrable
systems etc.. In this talk the two ideas will be combined to give a
tt*-geometry on the big phase space.

(joint work with Liana David)

Mon, 29 Feb 2016
15:45
L6

Bordered Floer homology via immersed curves

Liam Watson
(Glasgow)
Abstract

Bordered Floer homology is a variant of Heegaard Floer homology adapted to manifolds with boundary. I will describe a class of three-manifolds with torus boundary for which these invariants may be recast in terms of immersed curves in a punctured torus. This makes it possible to recast the paring theorem in bordered Floer homology in terms of intersection between curves leading, in turn, to some new observations about Heegaard Floer homology. This is joint work with Jonathan Hanselman and Jake Rasmussen. 

Tue, 16 Jun 2015

12:00 - 13:00
L5

A panoramic view of infrared singularities

Chris White
(Glasgow)
Abstract
The study of infrared singularities, due to the emission of “soft” (low momentum) gauge bosons, remains a highly active research area in a variety of quantum field theories. After motivating both phenomenological and formal reasons as to why we should care about IR singularities, this talk will review their structure in QED, QCD and quantum gravity, examining the similarities and differences between these three contexts. The role of Wilson lines will be examined, which provide a useful unifying language. Finally, I will examine recent work on moving beyond the soft approximation, and why this might be useful.
Mon, 23 Feb 2015
15:45
L6

Affine Deligne-Lusztig varieties and the geometry of Euclidean reflection groups

Anne Thomas
(Glasgow)
Abstract

Let $G$ be a reductive group such as $SL_n$ over the field $k((t))$, where $k$ is an algebraic closure of a finite field, and let $W$ be the affine Weyl group of $G$.  The associated affine Deligne-Lusztig varieties $X_x(b)$ were introduced by Rapoport.  These are indexed by elements $x$ in $G$ and $b$ in $W$, and are related to many important concepts in algebraic geometry over fields of positive characteristic.  Basic questions about the varieties $X_x(b)$ which have remained largely open include when they are nonempty, and if nonempty, their dimension.  We use techniques inspired by geometric group theory and representation theory to address these questions in the case that $b$ is a translation.  Our approach is constructive and type-free, sheds new light on the reasons for existing results and conjectures, and reveals new patterns.  Since we work only in the standard apartment of the building for $G$, which is just the tessellation of Euclidean space induced by the action of the reflection group $W$, our results also hold over the p-adics.  This is joint work with Elizabeth Milicevic (Haverford) and Petra Schwer (Karlsruhe).

Tue, 25 Nov 2014
17:00
C1

The structure of quantum permutation groups

Christian Voigt
(Glasgow)
Abstract

Quantum permutation groups, introduced by Wang, are a quantum analogue of permutation groups.
These quantum groups have a surprisingly rich structure, and they appear naturally in a variety of contexts,
including combinatorics, operator algebras, and free probability.
In this talk I will give an introduction to these quantum groups, starting with some background and basic definitions.
I will then present a computation of the K-groups of the C*-algebras associated with quantum permutation groups,
relying on methods from the Baum-Connes conjecture.

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