Forthcoming Seminars

12:00	Tony Padilla (Nottingham)	Quantum Field Theory Seminar	L3
	From classical duals to cleaning Lambda

14:30	Jozef Skokan (LSE)	Combinatorial Theory Seminar	L3
	Strong Ramsey saturation for cycles
	We call a graph $H$ Ramsey-unsaturated if there is an edge in the complement of $H$ such that the Ramsey number $r(H)$ of $H$ does not change upon adding it to $H$ . This notion was introduced by Balister, Lehel and Schelp who also showed that cycles (except for $C_4$ ) are Ramsey-unsaturated, and conjectured that, moreover, one may add any chord without changing the Ramsey number of the cycle $C_n$ , unless $n$ is even and adding the chord creates an odd cycle. We prove this conjecture for large cycles by showing a stronger statement: If a graph $H$ is obtained by adding a linear number of chords to a cycle $C_n$ , then $r(H)=r(C_n)$ , as long as the maximum degree of $H$ is bounded, $H$ is either bipartite (for even $n$ ) or almost bipartite (for odd $n$ ), and $n$ is large. This motivates us to call cycles strongly Ramsey-unsaturated. Our proof uses the regularity method.

15:45	Timo Schurg (Bonn)	Algebraic and Symplectic Geometry Seminar	L3
	From perfect obstruction theories to commutative differential graded algebras
	A perfect obstruction theory for a commutative ring is a morphism from a perfect complex to the cotangent complex of the ring satisfying some further conditions. In this talk I will present work in progress on how to associate in a functorial manner commutative differential graded algebras to such a perfect obstruction theory. The key property of the differential graded algebra is that its zeroth homology is the ring equipped with the perfect obstruction theory. I will also indicate how the method introduced can be globalized to work on schemes without encountering gluing issues.

17:00	Dr. M. de Visscher (City)	Algebra Seminar	L2
	On simple modules for the Brauer algebra

Wed, 23/05 10:15	Samuel Isaacson (Boston University)	OCCAM Wednesday Morning Event	OCCAM Common Room (RI2.28)
	Relationships between several particle-based stochastic reaction-diffusion models
	Particle-based stochastic reaction-diffusion models have recently been used to study a number of problems in cell biology. These methods are of interest when both noise in the chemical reaction process and the explicit motion of molecules are important. Several different mathematical models have been used, some spatially-continuous and others lattice-based. In the former molecules usually move by Brownian Motion, and may react when approaching each other. For the latter molecules undergo continuous time random-walks, and usually react with fixed probabilities per unit time when located at the same lattice site. As motivation, we will begin with a brief discussion of the types of biological problems we are studying and how we have used stochastic reaction-diffusion models to gain insight into these systems. We will then introduce several of the stochastic reaction-diffusion models, including the spatially continuous Smoluchowski diffusion limited reaction model and the lattice-based reaction-diffusion master equation. Our work studying the rigorous relationships between these models will be presented. Time permitting, we may also discuss some of our efforts to develop improved numerical methods for solving several of the models.

Wed, 23/05 11:30	Dawid Kielak	Algebra Kinderseminar
	An introduction to sheaf cohomology – St Hugh's, 80WR18

Thu, 24/05 12:00	Rosalinda Juer	Junior Geometry and Topology Seminar	L3
	To Be Announced

Thu, 24/05 12:30	Mikhail Feldman (University of Wisconsin)	OxPDE Lunchtime Seminar	Gibson 1st Floor SR
	Regularity and stability of solutions to shock reflection problem
	We discuss shock reflection problem for compressible gas dynamics, and von Neumann conjectures on transition between regular and Mach reflections. Then we will talk about some recent results on existence, regularity and geometric properties of regular reflection solutions for potential flow equation. In particular, we discuss optimal regularity of solutions near sonic curve, and stability of the normal reflection soluiton. Open problems will also be discussed. The talk will be based on the joint work with Gui-Qiang Chen, and with Myoungjean Bae.

Thu, 24/05 13:00	N/A	Mathematical Finance Internal Seminar	DH 1st floor SR
	Open Problem Session

Thu, 24/05 14:00	Dr Elias Jarlebring (KTH Stockholm)	Computational Mathematics and Applications	Gibson Grd floor SR
	A linear eigenvalue algorithm for nonlinear eigenvalue problems
	The Arnoldi method for standard eigenvalue problems possesses several attractive properties making it robust, reliable and efficient for many problems. We will present here a new algorithm equivalent to the Arnoldi method, but designed for nonlinear eigenvalue problems corresponding to the problem associated with a matrix depending on a parameter in a nonlinear but analytic way. As a first result we show that the reciprocal eigenvalues of an infinite dimensional operator. We consider the Arnoldi method for this and show that with a particular choice of starting function and a particular choice of scalar product, the structure of the operator can be exploited in a very effective way. The structure of the operator is such that when the Arnoldi method is started with a constant function, the iterates will be polynomials. For a large class of NEPs, we show that we can carry out the infinite dimensional Arnoldi algorithm for the operator in arithmetic based on standard linear algebra operations on vectors and matrices of finite size. This is achieved by representing the polynomials by vector coefficients. The resulting algorithm is by construction such that it is completely equivalent to the standard Arnoldi method and also inherits many of its attractive properties, which are illustrated with examples.

Thu, 24/05 16:00	James Newton (Cambridge)	Number Theory Seminar	L3
	Weights in Serre's conjecture for Hilbert modular forms

Thu, 24/05 16:00	Anne Juel (Manchester)	Industrial and Applied Mathematics Seminar	DH 1st floor SR
	Bubble instabilities in rigid and flexible vessels
	The displacement of a liquid by an air finger is a generic two-phase flow that underpins applications as diverse as microfluidics, thin-film coating, enhanced oil recovery, and biomechanics of the lungs. I will present two intriguing examples of such flows where, firstly, oscillations in the shape of propagating bubbles are induced by a simple change in tube geometry, and secondly, flexible vessel boundaries suppress viscous fingering instability. 1) A simple change in pore geometry can radically alter the behaviour of a fluid displacing air finger, indicating that models based on idealized pore geometries fail to capture key features of complex practical flows. In particular, partial occlusion of a rectangular cross-section can force a transition from a steadily-propagating centred finger to a state that exhibits spatial oscillations via periodic sideways motion of the interface at a fixed location behind the finger tip. We characterize the dynamics of the oscillations and show that they arise from a global homoclinic connection between the stable and unstable manifolds of a steady, symmetry-broken solution. 2) Growth of complex dendritic fingers at the interface of air and a viscous fluid in the narrow gap between two parallel plates is an archetypical problem of pattern formation. We find a surprisingly effective means of suppressing this instability by replacing one of the plates with an elastic membrane. The resulting fluid-structure interaction fundamentally alters the interfacial patterns that develop and considerably delays the onset of fingering. We analyse the dependence of the instability on the parameters of the system and present scaling arguments to explain the experimentally observed behaviour.

Thu, 24/05 17:00	Pierre Simon (Ecole Normale Superiore)	Logic Seminar	L3
	S-independence in NIP theories
	I will explain how to define a notion of stable-independence in NIP theories, which is an attempt to capture the "stable part" of types.

Fri, 25/05
11:00

David Howey (Department of Engineering Science, University of Oxford)

Industrial and Interdisciplinary Workshops

DH 1st floor SR

Parameter estimation for electrochemical cells

Please note the unusual start-time.

In order to run accurate electrochemical models of batteries (and other devices) it is necessary to know a priori the values of many geometric, electrical and electrochemical parameters (10-100 parameters) e.g. diffusion coefficients, electrode thicknesses etc. However a basic difficulty is that the only external measurements that can be made on cells without deconstructing and destroying them are surface temperature plus electrical measurements (voltage, current, impedance) at the terminals. An interesting research challenge therefore is the accurate, robust estimation of physically realistic model parameters based only on external measurements of complete cells. System identification techniques (from control engineering) including ‘electrochemical impedance spectroscopy’ (EIS) may be applied here – i.e. small signal frequency response measurement. However It is not clear exactly why and how impedance correlates to SOC/ SOH and temperature for each battery chemistry due to the complex interaction between impedance, degradation and temperature.

I will give a brief overview of some of the recent work in this area and try to explain some of the challenges in the hope that this will lead to a fruitful discussion about whether this problem can be solved or not and how best to tackle it.

Fri, 25/05 14:00	Professor Simon Davis (Weatherall Institute for Molecular Medicine)	Mathematical Biology and Ecology Seminar
	Single-molecule and system-level studies of signaling in T cells
	Please note that this is a joint seminar with the William Dunn School of Pathology and will be held in the EPA Seminar Room

Fri, 25/05 14:15	Prof Dorje Brody (Brunel Univeristy)	Nomura Seminar	DH 1st floor SR
	General theory of geometric Lévy models for dynamic asset pricing
	The geometric Lévy model (GLM) is a natural generalisation of the geometric Brownian motion (GBM) model. The theory of such models simplifies considerably if one takes a pricing kernel approach. In one dimension, once the underlying Lévy process has been specified, the GLM has four parameters: the initial price, the interest rate, the volatility and the risk aversion. The pricing kernel is the product of a discount factor and a risk aversion martingale. For GBM, the risk aversion parameter is the market price of risk. In this talk I show that for a GLM, this interpretation is not valid: the excess rate of return above the interest rate is a nonlinear function of the volatility and the risk aversion such that it is positive, and is increasing with respect to these variables. In the case of foreign exchange, Siegel’s paradox implies that one can construct foreign exchange models for which the excess rate of return is positive for both the exchange rate and the inverse exchange rate. Examples are worked out for a range of Lévy processes. (The talk is based on a recent paper: Brody, Hughston & Mackie, Proceedings of the Royal Society London, to appear in May 2012).

Mon, 28/05 12:00	Sungjay Lee (University of Cambridge)	String Theory Seminar	L3
	Instanton - a window into physics of M5-branes
	Instantons and W-bosons in 5d N=2 Yang-Mills theory arise from a circle compactification of the 6d (2,0) theory as Kaluza-Klein modes and winding self-dual strings, respectively. We study an index which counts BPS instantons with electric charges in Coulomb and symmetric phases. We first prove the existence of unique threshold bound state of U(1) instantons for any instanton number. By studying SU(N) self-dual strings in the Coulomb phase, we find novel momentum-carrying degrees on the worldsheet. The total number of these degrees equals the anomaly coefficient of SU(N) (2,0) theory. We finally propose that our index can be used to study the symmetric phase of this theory, and provide an interpretation as the superconformal index of the sigma model on instanton moduli space.

Mon, 28/05 14:15	Eugenie Hunsicker (Loughborough)	Geometry and Analysis Seminar	L3
	"Pseudodifferential operators on noncompact manifolds".

Mon, 28/05
14:15

CHRISTOPHE SABOT (Universite Lyon 1)

Stochastic Analysis Seminar

Oxford-Man Institute

Edge reinforced random walks, Vertex reinforced jump process, and the SuSy hyperbolic sigma model.

Edge-reinforced random walk (ERRW), introduced by Coppersmith and Diaconis in 1986, is a random process which takes values in the vertex set of a graph G, and is more likely to cross edges it has visited before. We show that it can be represented in terms of a Vertex-reinforced jump process (VRJP) with independent gamma

conductances: the VRJP was conceived by Werner and first studied by Davis and Volkov (2002,2004), and is a continuous-time process favouring sites with more local time. We show that the VRJP is a mixture of time-changed Markov jump processes and calculate the mixing measure. The mixing measure is interpreted as a marginal of the supersymmetric hyperbolic sigma model introduced by Disertori, Spencer and Zirnbauer.

This enables us to deduce that VRJP and ERRW are strongly recurrent in any dimension for large reinforcement (in fact, on graphs of bounded degree), using a localisation result of Disertori and Spencer (2010).

(Joint work with Pierre Tarrès.)

Mon, 28/05 15:45	HUGO DUMINIL (Unversity of Geneva)	Stochastic Analysis Seminar	Oxford-Man Institute
	Critical point for some planar statistical models
	<> abstract:In this talk, we describe how to compute the critical point for various lattice models of planar statistical physics. We will first introduce the percolation, Ising, Potts and random-cluster models on the square lattice. Then, we will discuss how critical points of these different models are related. In a final part, we will compute the critical point of these models. This last part harnesses two main ingredients that we will describe in details: duality and sharp threshold theorems. No background is necessary.