Past Seminars

Thu, 23/05
17:00 		Andrew Lewis (Leeds) Logic Seminar Add to calendar L3
Digital morphogenesis via Schelling segregation
The Schelling segregation model has been extensively studied, by researchers in fields as diverse as economics, physics and computer science. While the explicit concern when the model was first introduced back in 1969, was to model the kind for racial segregation observed in large American cities, the model is sufficiently abstract to apply to almost situation in which agents or nodes arrange themselves geographically according to a preference not to be of a minority type within their own neighbourhhood. Kirman and Vinkovik have established, for example, that Schelling's model is a finite difference version of a differential equation describing interparticle forces (and applied in the modelling of cluster formation). Despite the large literature relating to the model, however, it has largely resisted rigorous analysis – it has not been possible to prove the segregation behaviour easily observed when running simulations. For the first time we have now been able to rigorously analyse the model, and have also established some rather surprising threshold behaviour. This talk will require no specialist background knowledge.
Thu, 23/05
16:00 		Jim Oliver (Oxford) Industrial and Applied Mathematics Seminar Add to calendar DH 1st floor SR
On contact line dynamics with mass transfer
We investigate the effect of mass transfer on the evolution of a thin two-dimensional partially wetting drop. While the effects of viscous dissipation, capillarity, slip and uniform mass transfer are taken into account, the effects of inter alia gravity, surface tension gradients, vapour transport and heat transport are neglected in favour of mathematical tractability. Our matched asymptotic analysis reveals that the leading-order outer formulation and contact-line law that is selected in the small-slip limit depends delicately on both the sign and size of the mass transfer flux. We analyse the resulting evolution of the drop and report good agreement with numerical simulations.
Thu, 23/05
16:00 		Jonathan Bober (Bristol) Number Theory Seminar Add to calendar L3
Some structure of character sums
I'll discuss questions about the structure of long sums of Dirichlet characters — that is, sums of length comparable to the modulus. For example: How often do character sums get large? Where do character sums get large? What do character sums "look like" when then get large? This will include some combination of theorems and experimental data.
Thu, 23/05
16:00 		Eric Weinstein (Oxford) Special Lecture Add to calendar Martin Wood Lecture
Geometric Unity

A program for Geometric Unity is presented to argue that the seemingly baroque features of the standard model of particle physics are in fact inexorable and geometrically natural when generalizations of the Yang-Mills and Dirac theories are unified with one of general relativity.

Thu, 23/05
15:00 		Rafael Torres (Oxford) Junior Geometry and Topology Seminar Add to calendar SR1
"Geometry and topology in dimension five"
"Among the first successes of the h-cobordism theorem was the classification of simply connected closed 5-manifolds. Dimension five is sufficiently large to be able to implement the tools of surgery theory, yet low enough to allow an explicit classification of the manifolds. These traits make dimension five interesting in terms of existence results of geometric structures, like Riemannian metrics of positive Ricci/nonnegative sectional/positive sectional curvature, Einstein metrics, contact structures, Sasakian structures, among others. The talk will be a limited survey of the five-dimensional symbiosis between topology and geometry"
Thu, 23/05
14:00 		Professor Gitta Kutyniok (TU Berlin) Computational Mathematics and Applications Add to calendar Gibson Grd floor SR
Compressive Imaging: Stable Sampling Strategies using Shearlets
In imaging science, efficient acquisition of images by few samples with the possibility to precisely recover the complete image is a topic of significant interest. The area of compressed sensing, which in particular advocates random sampling strategies, has had already a tremendous impact on both theory and applications. The necessary requirement for such techniques to be applicable is the sparsity of the original data within some transform domain. Recovery is then achieved by, for instance, $ \ell_1 $ minimization. Various applications however do not allow complete freedom in the choice of the samples. Take Magnet Resonance Imaging (MRI) for example, which only provides access to Fourier samples. For this particular application, empirical results still showed superior performance of compressed sensing techniques.

In this talk, we focus on sparse sampling strategies under the constraint that only Fourier samples can be accessed. Since images – and in particular images from MRI – are governed by anisotropic features and shearlets do provide optimally sparse approximations of those, compactly supported shearlet systems will be our choice for the reconstruction procedure. Our sampling strategy then exploits a careful variable density sampling of the Fourier samples with $ \ell_1 $-analysis based reconstruction using shearlets. Our main result provides success guarantees and shows that this sampling and reconstruction strategy is optimal.

This is joint work with Wang-Q Lim (Technische Universität Berlin).
Thu, 23/05
12:00 		Francesco Solombrino (Technical University of Munich) OxPDE Lunchtime Seminar Add to calendar Gibson 1st Floor SR
Quasistatic evolution problems in perfect plasticity for generalized multiphase materials
Inspired by some recents developments in the theory of small-strain elastoplasticity, we both revisit and generalize the formulation of the quasistatic evolutionary problem in perfect plasticity for heterogeneous materials recently given by Francfort and Giacomini. We show that their definition of the plastic dissipation measure is equivalent to an abstract one, where it is defined as the supremum of the dualities between the deviatoric parts of admissible stress fields and the plastic strains. By means of this abstract definition, a viscoplastic approximation and variational techniques from the theory of rate-independent processes give the existence of an evolution statisfying an energy- dissipation balance and consequently Hill's maximum plastic work principle for an abstract and very large class of yield conditions.
Thu, 23/05
11:00 		Franziska Jahnke (U.of Muenster) Advanced Class Logic Add to calendar SR2
'Model completeness and henselianity'

 A classical question in the model theory of fields is to find out which fields are model complete in the language of rings. It turns out that all well-known examples of model complete fields are quite rigid when it comes to henselianity. We discuss some first results which indicate that in residue characteristic zero, definable henselian valuations prevent model completeness.
Wed, 22/05
16:00 		Thomas Wasserman (University of Oxford) Junior Geometric Group Theory Seminar Add to calendar SR2
Constructing a sigma model for the symmetric product of $ R^D $
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, 22/05
11:30 		Lukasz Grabowski Algebra Kinderseminar Add to calendar Queen's College
Tilings and uniformly finite homology
I will give a gentle introduction to uniformly finite homology. The highlight application will be showing existence of aperiodic tilings of the hyperbolic plane.
Tue, 21/05
17:00 		Anreas Doering (Oxford) Algebra Seminar Add to calendar L2
Spectral presheaves as generalised (Gelfand) spectra
The spectral presheaf of a nonabelian von Neumann algebra or C*-algebra was introduced as a generalised phase space for a quantum system in the so-called topos approach to quantum theory. Here, it will be shown that the spectral presheaf has many features of a spectrum of a noncommutative operator algebra (and that it can be defined for other classes of algebras as well). The main idea is that the spectrum of a nonabelian algebra may not be a set, but a presheaf or sheaf over the base category of abelian subalgebras. In general, the spectral presheaf has no points, i.e., no global sections. I will show that there is a contravariant functor from unital C*-algebras to their spectral presheaves, and that a C*-algebra is determined up to Jordan *-isomorphisms by its spectral presheaf in many cases. Moreover, time evolution of a quantum system can be described in terms of flows on the spectral presheaf, and commutators show up in a natural way. I will indicate how combining the Jordan and Lie algebra structures may lead to a full reconstruction of nonabelian C*- or von Neumann algebra from its spectral presheaf.
Tue, 21/05
14:30 		Paul Seymour (Princeton) Combinatorial Theory Seminar Add to calendar L3
Criticality for multicommodity flows
The “k-commodity flow problem” is: we are given k pairs of vertices of a graph, and we ask whether there are k flows in the graph, where the ith flow is between the ith pair of vertices, and has total value one, and for each edge, the sum of the absolute values of the flows along it is at most one. We may also require the flows to be 1/2-integral, or indeed 1/p-integral for some fixed p. If the problem is feasible (that is, the desired flows exist) then it is still feasible after contracting any edge, so let us say a flow problem is “critical” if it is infeasible, but becomes feasible when we contract any edge. In many special cases, all critical instances have only two vertices, but if we ask for integral flows (that is, p = 1, essentially the edge-disjoint paths problem), then there arbitrarily large critical instances, even with k = 2. But it turns out that p = 1 is the only bad case; if p>1 then all critical instances have bounded size (depending on k, but independent of p), and the same is true if there is no integrality requirement at all. The proof gives rise to a very simple algorithm for the k edge-disjoint paths problem in 4-edge-connected graphs.

For any corrections/updates to these listings, please contact seminars [-at-] maths [dot] ox [dot] ac [dot] uk.

Syndicate content