Forthcoming Seminars

Thu, 22/01/2009
14:30 		Stephane Launois (Canterbury) Representation Theory Seminar Add to calendar L3
On the algebra of quantum matrices, and beyond
Thu, 22/01/2009
16:00 		Victor Flynn (Oxford) Number Theory Seminar Add to calendar DH 1st floor SR
Sha and degree 4 del Pezzo surfaces
Thu, 22/01/2009
16:30 		Eugene Benilov (Limerick) Differential Equations and Applications Seminar Add to calendar DH 1st floor SR
On the drag-out problem in liquid film theory
We consider an infinite plate being withdrawn from an infinite pool of viscous liquid. Assuming that the effects of inertia and surface tension are weak, Derjaguin (1943) conjectured that the 'load', i.e. the thickness of the liquid film clinging to the plate, is determined by a certain formula involving the liquid's density and viscosity, the plate's velocity and inclination angle, and the acceleration due to gravity. In the present work, Deryagin's formula is derived from the Stokes equations in the limit of small slope of the plate (without this assumption, the formula is invalid). It is shown that the problem has infinitely many steady solutions, all of which are stable - but only one of these corresponds to Derjaguin’s formula. This particular steady solution can only be singled out by matching it to a self-similar solution describing the non-steady part of the film between the pool and the film’s 'tip'. Even though the near-pool region where the steady state has been established expands with time, the upper, non-steady part of the film (with its thickness decreasing towards the tip) expands faster and, thus, occupies a larger portion of the plate. As a result, the mean thickness of the film is 1.5 times smaller than the load. The results obtained are extended to order-one inclinantion angles and the case where surface tension is present.
Thu, 22/01/2009
17:00 		Sonia L'Innocente (Camerino) Logic Seminar Add to calendar L3
Possible exponentiations over the universal enveloping algebra of sl(2,C)
Abstract available at: http://people.maths.ox.ac.uk/~kirby/LInnocente.pdf
Fri, 23/01/2009
14:00 		Dr Vahid Shahrezaei (Imperial College London) Mathematical Biology Seminar Add to calendar L3
Modeling intrinsic and extrinsic fluctuations in gene expression
Fri, 23/01/2009
14:15 		Tomas Bjork (Stockholm School of Economics) Mathematical Finance Seminar Add to calendar DH 1st floor SR
Time inconsistent stochastic control
We present a theory for  stochastic control problems which, in various ways, are time inconsistent in the sense that they do not admit a Bellman optimality principle. We attach these problems by viewing them within a game theoretic framework, and we look for subgame perfect Nash equilibrium points. For a general controlled Markov process and a fairly general objective functional we derive an extension of the standard Hamilton-Jacobi-Bellman  equation, in  the form of a system of non-linear equations, for the determination for the equilibrium strategy as well as the equilibrium value function. All  known examples of time inconsistency in the literature are easily seen to be special cases of the present theory. We also prove that for every time inconsistent problem, there exists an associated time consistent problem such that the optimal control and the optimal value function for the consistent problem coincides with the equilibrium control and value function respectively for the time inconsistent problem. We also study some concrete examples.
Fri, 23/01/2009
16:00 		Anand Pillay (Leeds) Logic Seminar Add to calendar SR2
Semiabelian varieties over separably closed fields
Given K a separably closed field of finite ( > 1) degree of imperfection, and semiabelian variety A over K, we study the maximal divisible subgroup A^{sharp} of A(K). We show that the {\sharp} functor does not preserve exact sequences and also give an example where A^{\sharp} does not have relative Morley rank. (Joint work with F. Benoist and E. Bouscaren)
Mon, 26/01/2009
12:00 		Andrei Starinets (Oxford) String Theory Seminar Add to calendar L3
Black branes beyond thermal equilibrium
Gauge-string duality relates transport properties of certain strongly interacting quantum field theories at finite temperature/density to spectra of normal modes of black branes in dual supergravity backgrounds. The duality serves as a source of quantitative information about the physics of strongly coupled relativistic plasmas as well as a source of qualitative insights into the properties of nuclear matter created in heavy ion collision experiments. It may also help to understand non-equilibrium behavior of black holes/branes. We reflect on recent progress in this field.
Mon, 26/01/2009
13:30 		Pierluigi Cesana (SISSA, Trieste, Italy) OxPDE Lunchtime Seminar Add to calendar Gibson 1st Floor SR
Analysis of variational models for nematic liquid crystal elastomers
The relaxation of a free-energy functional which describes the order-strain interaction in nematic liquid crystal elastomers is obtained explicitly. We work in the regime of small strains (linearized kinematics). Adopting the uniaxial order tensor theory or Frank model to describe the liquid crystal order, we prove that the minima of the relaxed functional exhibit an effective biaxial microstructure, as in de Gennes tensor model. In particular, this implies that the response of the material is soft even if the order of the system is assumed to be fixed. The relaxed energy density satisfies a solenoidal quasiconvexification formula.
Mon, 26/01/2009
14:15 		Dr Z Qian (Oxford) Stochastic Analysis Seminar Add to calendar Oxford-Man Institute
Stochastic Navier-Stokes equations
Mon, 26/01/2009
15:45 		Karen Vogtmann (Cornell) Topology Seminar Add to calendar L3
Automorphisms of right-angled Artin groups
Mon, 26/01/2009
15:45 		Dr Jon Warren (University of Warwick) Stochastic Analysis Seminar Add to calendar Oxford-Man Institute
The TASEP with deterministic leading particle
Mon, 26/01/2009
17:00 		Florian Theil (University of Warwick) Partial Differential Equations Seminar Add to calendar Gibson 1st Floor SR
Energy Transport by Acoustic Modes of Harmonic Lattices
Tue, 27/01/2009
12:00 		Jacques Smulevici (Cambridge) Relativity Seminar Add to calendar L3
Structure of singularities of spacetimes with toroidal or hyperbolic symmetry
I will present recent results concerning the study of the global Cauchy problem in general relativity under symmetry assumptions. More specifically, I will be focusing on the structure of singularities and the uniqueness in the large for solutions of the Einstein equations, the so-called strong cosmic censorship, under the assumption that the initial data is given on some compact manifold with prescribed symmetry. In particular, I will present some results which concerned the asymptotic behaviour of the area of the orbits of symmetry, a quantity which plays in important role for the study of these solutions. From the point of view of PDE, this corresponds to a global existence theorem for a system of non-linear 1+1 wave equations.  
Tue, 27/01/2009
14:30 		Graham Brightwell (LSE) Combinatorial Theory Seminar Add to calendar L3
Random partial orders and random linear extensions
Random partial orders and random linear extensions Several interesting models of random partial orders can be described via a process that builds the partial order one step at a time, at each point adding a new maximal element. This process therefore generates a linear extension of the partial order in tandem with the partial order itself. A natural condition to demand of such processes is that, if we condition on the occurrence of some finite partial order after a given number of steps, then each linear extension of that partial order is equally likely. This condition is called "order-invariance". The class of order-invariant processes includes processes generating a random infinite partial order, as well as those that amount to taking a random linear extension of a fixed infinite poset. Our goal is to study order-invariant processes in general. In this talk, I shall explain some of the problems that need to be resolved, and discuss some of the combinatorial problems that arise. (joint work with Malwina Luczak)
Tue, 27/01/2009
15:45 		Dominic Joyce (Oxford) Algebraic and Symplectic Geometry Seminar Add to calendar L3
Hamiltonian stationary submanifolds of compact symplectic manifolds
Let $ (M,\omega) $ be a symplectic manifold, and $ g $ a Riemannian metric on $ M $ compatible with $ \omega $. If $ L $ is a compact Lagrangian submanifold of $ (M,\omega) $, we can compute the volume Vol$ (L) $ of $ L $ using $ g $. A Lagrangian $ L $ is called Hamiltonian stationary if it is a stationary point of the volume functional amongst Lagrangians Hamiltonian isotopic to $ L $. Suppose $ L' $ is a compact Lagrangian in $ {\mathbb C}^n $ which is Hamiltonian stationary and rigid, that is, all infinitesimal Hamiltonian deformations of $ L $ as a Hamiltonian stationary Lagrangian come from rigid motions of $ {\mathbb C}^n $. An example of such $ L' $ is the $ n $-torus $  \bigl\{(z_1,\ldots,z_n)\in{\mathbb C}^n:\vert z_1\vert=a_1, \ldots,\vert z_n\vert=a_n\bigr\} $, for small $ a_1,\ldots,a_n>0 $. I will explain a construction of Hamiltonian stationary Lagrangians in any compact symplectic manifold $ (M,\omega) $, which works by `gluing in' $ tL' $ near a point $ p $ in $ M $ for small $ t>0 $.
Tue, 27/01/2009
17:00 		Geordie Williamson (Oxford) Algebra Seminar Add to calendar L2
Singular Soergel Bimodules
To any Coxeter group (W,S) together with an appropriate representation on V one may associate various categories of "singular Soergel bimodules", which are certain bimodules over invariant subrings of regular functions on V. I will discuss their definition, basic properties and explain how they categorify the associated Hecke algebras and their parabolic modules. I will also outline a motivation coming from geometry and (if time permits) an application in knot theory.

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

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