Forthcoming Seminars

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
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
Title to be announced.
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.
Fri, 24/05
10:00 		Michel Chipot (University of Zurich) OxPDE Special Seminar Add to calendar Gibson Grd floor SR
Asymptotic Behavior of Problems in Cylindrical Domains - Lecture 3 of 4
A mini-lecture series consisting of four 1 hour lectures. We would like to consider asymptotic behaviour of various problems set in cylinders. Let $ \Omega_\ell = (-\ell,\ell)\times (-1,1) $ be the simplest cylinder possible. A good model problem is the following. Consider $ u_\ell $ the weak solution to
$$ \cases{ -\partial_{x_1}^2 u_\ell - \partial_{x_2}^2 u_\ell = f(x_2) \quad \hbox{in } \Omega_\ell, \quad \cr \cr u_\ell = 0 \quad \hbox{ on } \quad \partial \Omega_\ell. \cr} $$
When $ \ell \to \infty $ is it trues that the solution converges toward $ u_\infty $ the solution of the lower dimensional problem below ?
$$ \cases{ - \partial_{x_2}^2 u_\infty = f(x_2) \quad \hbox{in }(-1,1), \quad \cr \cr u_\infty = 0 \quad \hbox{ on } \quad \partial (-1,1). \cr} $$
If so in what sense ? With what speed of convergence with respect to $ \ell $ ? What happens when $ f $ is also allowed to depend on $ x_1 $ ? What happens if $ f $ is periodic in $ x_1 $, is the solution forced to be periodic at the limit ? What happens for general elliptic operators ? For more general cylinders ? For nonlinear problems ? For variational inequalities ? For systems like the Stokes problem or the system of elasticity ? For general problems ? ... We will try to give an update on all these issues and bridge these questions with anisotropic singular perturbations problems. Prerequisites : Elementary knowledge on Sobolev Spaces and weak formulation of elliptic problems.
Fri, 24/05
10:00 		Richard Todd (Dept. of Materials) Industrial and Interdisciplinary Workshops Add to calendar DH 1st floor SR
Flash Sintering (precise title to be confirmed)
Fri, 24/05
16:00 		Harry Zheng (London) Nomura Seminar Add to calendar DH 1st floor SR
Markov Modulated Weak Stochastic Maximum Principle
In this paper we prove a weak necessary and sufficient maximum principle for Markov regime switching stochastic optimal control problems. Instead of insisting on the maximum condition of the Hamiltonian, we show that 0 belongs to the sum of Clarke's generalized gradient of the Hamiltonian and Clarke's normal cone of the control constraint set at the optimal control. Under a joint concavity condition on the Hamiltonian and a convexity condition on the terminal objective function, the necessary condition becomes sufficient. We give four examples to demonstrate the weak stochastic maximum principle.
Mon, 27/05
12:00 		Volker Braun (Oxford) String Theory Seminar Add to calendar L3
To Be Announced
Mon, 27/05
14:15 		Martin Bridgeman (Boston College) Geometry and Analysis Seminar Add to calendar L3
The Pressure metric for convex Anosov representations

 Using thermodynamic formalism we introduce a notion of intersection for convex Anosov representations. We produce an Out-invariant Riemannian metric on the smooth points of the deformation  space of convex, irreducible representations of a word hyperbolic group G into SL(m,R) whose Zariski closure contains a generic element. In particular, we produce a mapping class group invariant Riemannian metric on Hitchin components which restricts to the Weil-Petersson metric on the Fuchsian locus. 
This is joint work with R. Canary, F. Labourie and A. Sambarino.
Tue, 28/05
12:00 		Kai Groh (Nottingham) Quantum Field Theory Seminar Add to calendar L3
to be announced
Tue, 28/05
14:30 		Christina Goldschmidt (University of Oxford) Combinatorial Theory Seminar Add to calendar L3
The scaling limit of the minimum spanning tree of the complete graph
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 Erdös-Rényi 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, 28/05
15:30 		Michael Bate (York) Algebra Seminar Add to calendar L2
To Be Announced
Tue, 28/05
16:30 		Po-Shen Loh (CMU) Combinatorial Theory Seminar Add to calendar SR2
The critical window for the Ramsey-Turan problem
The first application of Szemeredi's regularity method was the following celebrated Ramsey-Turan result proved by Szemeredi in 1972: any K_4-free graph on N vertices with independence number o(N) has at most (1/8 + o(1))N^2 edges. Four years later, Bollobas and Erdos gave a surprising geometric construction, utilizing the isodiametric inequality for the high dimensional sphere, of a K_4-free graph on N vertices with independence number o(N) and (1/8 - o(1)) N^2 edges. Starting with Bollobas and Erdos in 1976, several problems have been asked on estimating the minimum possible independence number in the critical window, when the number of edges is about N^2 / 8. These problems have received considerable attention and remained one of the main open problems in this area.  More generally, it remains an important problem to determine if, for certain applications of the regularity method, alternative proofs exist which avoid using the regularity lemma and give better quantitative estimates.  In this work, we develop new regularity-free methods which give nearly best-possible bounds, solving the various open problems concerning this critical window. Joint work with Jacob Fox and Yufei Zhao.
Tue, 28/05
17:00 		Yives Cornulier (Orsay) Algebra Seminar Add to calendar L2
To Be Announced
Tue, 28/05
17:00 		Menita Carozza (Università degli Studi di Napoli Federico II) Partial Differential Equations Seminar Add to calendar Gibson 1st Floor SR
Regularity Results for an Optimal Design Problem with a Volume Constraint
Wed, 29/05
11:30 		Lukasz Grabowski Algebra Kinderseminar Add to calendar Queen's College
To Be Announced
Thu, 30/05
12:00 		James Robinson (University of Warwick) OxPDE Lunchtime Seminar Add to calendar Gibson 1st Floor SR
A coupled parabolic-elliptic system arising in the theory of magnetic relaxation
    In 1985 Moffatt suggested that stationary flows of the 3D Euler equations with non-trivial topology could be obtained as the time-asymptotic limits of certain solutions of the equations of magnetohydrodynamics. Heuristic arguments also suggest that the same is true of the system
    \[ -\Delta u+\nabla p=(B\cdot\nabla)B\qquad\nabla\cdot u=0\qquad \]
    \[ B_t-\eta\Delta B+(u\cdot\nabla)B=(B\cdot\nabla)u \]
    when $ \eta=0 $. In this talk I will discuss well posedness of this coupled elliptic-parabolic equation in the two-dimensional case when $ B(0)\in L^2 $ and $ \eta>0 $.
    Crucial to the analysis is a strengthened version of the 2D Ladyzhenskaya inequality: $ \|f\|_{L^4}\le c\|f\|_{L^{2,\infty}}^{1/2}\|\nabla f\|_{L^2}^{1/2} $, where $ L^{2,\infty} $ is the weak $ L^2 $ space. I will also discuss the problems that arise in the case $ \eta=0 $.
    This is joint work with David McCormick and Jose Rodrigo.

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

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