Forthcoming Seminars

Mon, 11/10/2010 12:00	Lotte Hollands (Caltech)	String Theory Seminar	L3
	N=2 instantons, curves and conformal blocks

Mon, 11/10/2010 14:15	Nigel Hitchin (Oxford)	Geometry and Analysis Seminar	L3
	Poisson structures on projective space

Mon, 11/10/2010 14:15	Jie Xiong (University of Tennessee)	Stochastic Analysis Seminar	Eagle House
	Joint continuity for the solutions to a class of nonlinear SPDEs
	For a superprocess in a random environment in one dimensional space, a nonlinear stochastic partial differential equation is derived for its density by Dawson-Vaillancourt-Wang (2000). The joint continuity was left as an open problem. In this talk, we will give an affirmative answer to this problem.

Mon, 11/10/2010 15:45	Ulrike Tillmann (Oxford)	Topology Seminar	L3
	From braid to mapping class groups - from configuration to moduli spaces

Mon, 11/10/2010 15:45	Ben Hambly	Stochastic Analysis Seminar	Eagle House
	Spectral asymptotics for continuum random trees
	We review the problem of determining the high frequency asymptotics of the spectrum of the Laplacian and its relationship to the geometry of a domain. We then establish these asymptotics for some continuum random trees as well as the scaling limit of the critical random graph.

Mon, 11/10/2010 16:00	Damiano Testa (Mathematical Insitute, Oxford)	Junior Number Theory Seminar	L2
	Conics on the Fermat quintic threefold
	(Note that the talk will be in L2 and not the usual SR1) Many interesting features of algebraic varieties are encoded in the spaces of rational curves that they contain. For instance, a smooth cubic surface in complex projective three-dimensional space contains exactly 27 lines; exploiting the configuration of these lines it is possible to find a (rational) parameterization of the points of the cubic by the points in the complex projective plane. After a general overview, we focus on the Fermat quintic threefold X, namely the hypersurface in four-dimensional projective space with equation x^5+y^5+z^5+u^5+v^5=0. The space of lines on X is well-known. I will explain how to use a mix of algebraic geometry, number theory and computer-assisted calculations to study the space of conics on X. This talk is based on joint work with R. Heath-Brown.

Mon, 11/10/2010 17:00	Georg Dolzmann (Universitaet Regensburg)	Partial Differential Equations Seminar	Gibson 1st Floor SR
	Modeling and simulation of vectorfields on membranes
	The fundamental models for lipid bilayers are curvature based and neglect the internal structure of the lipid layers. In this talk, we explore models with an additional order parameter which describes the orientation of the lipid molecules in the membrane and compare their predictions based on numerical simulations. This is joint work with Soeren Bartels (Bonn) and Ricardo Nochetto (College Park).

Tue, 12/10/2010 10:00	(Oxford)	Twistor Workshop	Gibson 1st Floor SR
	Twistor-space polygons and polytopes representing scattering amplitudes II

Tue, 12/10/2010 14:00	Daniel Huybrechts (Bonn)	Algebraic and Symplectic Geometry Seminar	SR1
	(HoRSe seminar) Spherical objects on K3 surfaces I
	Both parts will deal with spherical objects in the bounded derived category of coherent sheaves on K3 surfaces. In the first talk I will focus on cycle theoretic aspects. For this we think of the Grothendieck group of the derived category as the Chow group of the K3 surface (which over the complex numbers is infinite-dimensional due to a result of Mumford). The Bloch-Beilinson conjecture predicts that over number fields the Chow group is small and I will show that this is equivalent to the derived category being generated by spherical objects (which I do not know how to prove). In the second talk I will turn to stability conditions and show that a stability condition is determined by its behavior with respect to the discrete collections of spherical objects.

Tue, 12/10/2010 14:15	Tomas Bjork (Columbia University/Stockholm School of Economics)	Nomura Seminar Oxford-Man Institute Working Seminar	Eagle House
	Time inconsistent stochastic control" (joint with Agatha Murgoci and Xunyu Zhou)
	"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. We give some concrete examples, and in particular we study the case of mean variance optimal portfolios with wealth dependent risk aversion"

Tue, 12/10/2010 14:15	Ioannis Karatzas	Nomura Seminar	Eagle House
	Stable Models for Large Equity Markets
	We introduce and study ergodic multidimensional diffusion processes interacting through their ranks; these interactions lead to invariant measures which are in broad agreement with stability properties of large equity markets over long time-periods. The models we develop assign growth rates and variances that depend on both the name (identity) and the rank (according to capitalization) of each individual asset. Such models are able realistically to capture critical features of the observed stability of capital distribution over the past century, all the while being simple enough to allow for rather detailed analytical study. The methodologies used in this study touch upon the question of triple points for systems of interacting diffusions; in particular, some choices of parameters may permit triple (or higher-order) collisions to occur. We show, however, that such multiple collisions have no effect on any of the stability properties of the resulting system. This is accomplished through a detailed analysis of intersection local times. The theory we develop has connections with the analysis of Queueing Networks in heavy traffic, as well as with models of competing particle systems in Statistical Mechanics, such as the Sherrington-Kirkpatrick model for spin-glasses.

Tue, 12/10/2010 14:15	Dr O. Umurhan (Queen Mary University of London)	Geophysical and Nonlinear Fluid Dynamics Seminar	Dobson Room, AOPP
	Magnetized compact vortices in stably stratified atmospheres

Tue, 12/10/2010 14:30	Mary Cryan (Edinburgh)	Combinatorial Theory Seminar	L3
	A couple of easy cases for counting Euler tours
	The problem of checking existence for an Euler tour of a graph is trivial (are all vertex degrees even?). The problem of counting (or even approximate counting) Euler tours seems to be very difficult. I will describe two simple classes of graphs where the problem can be solved exactly in polynomial time. And also talk about the many many classes of graphs where no positive results are known.

Tue, 12/10/2010 15:45	Daniel Huybrechts (Bonn)	Algebraic and Symplectic Geometry Seminar	L3
	(HoRSe seminar) Spherical objects on K3 surfaces II
	Both parts will deal with spherical objects in the bounded derived category of coherent sheaves on K3 surfaces. In the first talk I will focus on cycle theoretic aspects. For this we think of the Grothendieck group of the derived category as the Chow group of the K3 surface (which over the complex numbers is infinite-dimensional due to a result of Mumford). The Bloch-Beilinson conjecture predicts that over number fields the Chow group is small and I will show that this is equivalent to the derived category being generated by spherical objects (which I do not know how to prove). In the second talk I will turn to stability conditions and show that a stability condition is determined by its behavior with respect to the discrete collections of spherical objects.

Tue, 12/10/2010 16:00	David Hume (Oxford University)	Junior Geometric Group Theory Seminar	DH 3rd floor SR
	Random Walks: Getting from A to A.
	This talk introduces the topic of random walks on a finitely generated group and asks what properties of such a group can be detected through knowledge of such walks.

Tue, 12/10/2010 17:00	Kevin McGerty (Oxford)	Algebra Seminar	L2
	Duality for representations and quantum isogenies
	Recently Frenkel and Hernandez introduced a kind of "Langlands duality" for characters of semisimple Lie algebras. We will discuss a representation-theoretic interpretation of their duality using quantum analogues of exceptional isogenies. Time permitting we will also discuss a branching rule and relations to Littelmann paths.

Wed, 13/10/2010
11:30

David Craven (University of Oxford)

Algebra Kinderseminar

ChCh, Tom Gate, Room 2

Why nice guys lose: impossibility theorems in social choice theory

In this talk we will survey some aspects of social choice theory: in particular, various impossibility theorems about voting systems and strategies. We begin with the famous Arrow's impossibility theorem -- proving the non-existence of a 'fair' voting system -- before moving on to later developments, such as the Gibbard–Satterthwaite theorem, which states that all 'reasonable' voting systems are subject to tactical voting.

Given time, we will study extensions of impossibility theorems to micro-economic situations, and common strategies in game theory given the non-existence of optimal solutions.

Thu, 14/10/2010 12:00	Michael Groechenig (Oxford University Mathematical Institute)	Junior Geometry and Topology Seminar	SR1
	Homotopy theory for C*-algebras
	The theory of C-algebras provides a good realisation of noncommutative topology. There is a dictionary relating commutative C-algebras with locally compact spaces, which can be used to import topological concepts into the C-world. This philosophy fails in the case of homotopy, where a more sophisticated definition has to be given, leading to the notion of asymptotic morphisms. As a by-product one obtains a generalisation of Borsuk's shape theory and a universal boundary map for cohomology theories of C-algebras.

Thu, 14/10/2010 13:00		Mathematical Finance Internal Seminar	DH 1st floor SR
	1st year presentations

Thu, 14/10/2010 14:00	Prof. Klaus Böhmer (Philipps University Marburg)	Computational Mathematics and Applications	Gibson Grd floor SR
	A Nonlinear Discretization Theory with Applications to Meshfree Methods
	We extend for the first time the linear discretization theory of Schaback, developed for meshfree methods, to nonlinear operator equations, relying heavily on methods of Böhmer, Vol I. There is no restriction to elliptic problems or to symmetric numerical methods like Galerkin techniques. Trial spaces can be arbitrary, but have to approximate the solution well, and testing can be weak or strong. We present Galerkin techniques as an example. On the downside, stability is not easy to prove for special applications, and numerical methods have to be formulated as optimization problems. Results of this discretization theory cover error bounds and convergence rates. These results remain valid for the general case of fully nonlinear elliptic differential equations of second order. Some numerical examples are added for illustration.