Wed, 05 Jun 2013

15:30 - 16:30
SR1

Boundaries of Random Walks

Elisabeth Fink
(University of Oxford)
Abstract

I will talk about random walks on groups and define the Poisson boundary of such. Studying it gives criteria for amenability or growth. I will outline how this can be used and describe recent related results and still open questions.

Wed, 22 May 2013

16:00 - 17:00
SR2

Constructing a sigma model for the symmetric product of $R^D$

Thomas Wasserman
(University of Oxford)
Abstract

In this talk I will describe an attempt to construct a conformal field theory with target space a symmetric product of $R^D$ (referred to by physicists as orbifold sigma model). The construction uses branched covers of $S^2$ to lift the well studied formulation of a sigma model on $S^2$, in terms of vertex operator algebras, to higher genus surfaces. I will motivate and explain this construction.

Wed, 08 May 2013

16:00 - 17:00
SR2

Amenable hyperbolic groups

David Hume
(University of Oxford)
Abstract

The integers (while wonderful in many others respects) do not make for fascinating Geometric Group Theory. They are, however, essentially the only infinite finitely generated group which is both hyperbolic and amenable. In the class of locally compact topological groups, the intersection of these two notions is richer, and the major aim of this talk will be to give the structure of a classification of such groups due to Caprace-de Cornulier-Monod-Tessera, beginning with Milnor's proof that any connected Lie group admitting a left-invariant negatively curved Riemannian metric is necessarily soluble.

Wed, 01 May 2013

16:00 - 17:00
SR2

Some Decision Problems in Groups

Robert Kropholler
(University of Oxford)
Abstract


To continue the day's questions of how complex groups can be I will be looking about some decision problems. I will prove that certain properties of finitely presented groups are undecidable. These properties are called Markov properties and include many nice properties one may want a group to have. I will also hopefully go into an algorithm of Whitehead on deciding if a set of n words generates F_n.

Mon, 29 Apr 2013

15:15 - 16:15
Oxford-Man Institute

Uniqueness of Signature

HORATIO BOEDIHARDJO
(University of Oxford)
Abstract

We relate the expected signature to the Fourier transform of n-point functions, first studied by O. Schramm, and subsequently
by J. Cardy and Simmon, D. Belyaev and J. Viklund. We also prove that the signatures determine the paths in the complement of a Chordal SLE null set. In the end, we will also discuss an idea on how to extend the uniqueness of signatures result by Hambly and Lyons (2006) to paths with finite 1<p<2variations.

Fri, 14 Jun 2013

11:30 - 13:00
OCCAM Common Room (RI2.28)

OCCAM Group Meeting

Various
(University of Oxford)
Abstract
  • Fabian Spill - Stochastic and continuum modelling of angiogenesis
  • Matt Saxton - Modelling the contact-line dynamics of an evaporating drop
  • Almut Eisentraeger - Water purification by (high gradient) magnetic separation
Fri, 10 May 2013

11:30 - 13:00
OCCAM Common Room (RI2.28)

OCCAM Group Meeting

Various
(University of Oxford)
Abstract
  • Sean Lim - Full waveform inversion: a first look
  • Alex Raisch - Bistable liquid crystal displays: modelling, simulation and applications
  • Vladimir Zubkov - Mathematical model of kidney morphogenesis
Tue, 28 May 2013

14:30 - 15:30
L3

The scaling limit of the minimum spanning tree of the complete graph

Christina Goldschmidt
(University of Oxford)
Abstract

Consider the complete graph on n vertices with independent and identically distributed edge-weights having some absolutely continuous distribution. The minimum spanning tree (MST) is simply the spanning subtree of smallest weight. It is straightforward to construct the MST using one of several natural algorithms. Kruskal's algorithm builds the tree edge by edge starting from the globally lowest-weight edge and then adding other edges one by one in increasing order of weight, as long as they do not create any cycles. At each step of this process, the algorithm has generated a forest, which becomes connected on the final step. In this talk, I will explain how it is possible to exploit a connection between the forest generated by Kruskal's algorithm and the Erd\"os-R\'enyi random graph in order to prove that $M_n$, the MST of the complete graph, possesses a scaling limit as $n$ tends to infinity. In particular, if we think of $M_n$ as a metric space (using the graph distance), rescale edge-lengths by $n^{-1/3}$, and endow the vertices with the uniform measure, then $M_n$ converges in distribution in the sense of the Gromov-Hausdorff-Prokhorov distance to a certain random measured real tree.

This is joint work with Louigi Addario-Berry (McGill), Nicolas Broutin (INRIA Paris-Rocquencourt) and Grégory Miermont (ENS Lyon).

Tue, 07 May 2013

14:30 - 15:30
L3

Positivity problems for low-order linear recurrence sequences

Joel Ouaknine
(University of Oxford)
Abstract

We consider two decision problems for linear recurrence sequences(LRS) over the integers, namely the Positivity Problem (are all terms of a given LRS positive?) and the Ultimate Positivity Problem (are all but finitely many terms of a given LRS positive?). We show decidability of both problems for LRS of order 5 or less, and for simple LRS (i.e. whose characteristic polynomial has no repeated roots) of order 9 or less. Moreover, we show by way of hardness that extending the decidability of either problem to LRS of order 6 would entail major breakthroughs in analytic number theory, more precisely in the field of Diophantine approximation of transcendental numbers.
This talk is based on a recent paper, available at
http://www.cs.ox.ac.uk/people/joel.ouaknine/publications/positivity13ab…
joint with James Worrell and Matt Daws.

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