Forthcoming Seminars

Tue, 14/06/2011 12:00	Paul Mansfield (Durham)	Quantum Field Theory Seminar	L3
	Faraday's lines of force as strings: from Gauss' law to the arrow of time

Tue, 14/06/2011 12:30	Marshall Slemrod (University of Wisconsin)	OxPDE Special Seminar	Gibson 1st Floor SR
	Entropy and isometric embedding
	The problem of isometric embedding of a Riemannian Manifold into Euclidean space is a classical issue in differential geometry and nonlinear PDE. In this talk, I will outline recent work my co-workers and I have done, using ideas from continuum mechanics as a guide, formulating the problem, and giving (we hope) some new insight into the role of " entropy".

Tue, 14/06/2011 14:30	Jaroslav Nesetril (Prague)	Combinatorial Theory Seminar	L3
	Ramsey Classes of Graphs and Beyond
	It is known that generic and universal structures and Ramsey classes are related. We explain this connection and complement it by some new examples. Particularly we disscuss universal and Ramsey classes defined by existence and non-existence of homomorphisms.

Tue, 14/06/2011 17:00	Benno Kuckuck (Oxford)	Algebra Seminar	L2
	"Subgroups of direct products and finiteness properties of groups"
	Direct products of finitely generated free groups have a surprisingly rich subgroup structure. We will talk about how the finiteness properties of a subgroup of a direct product relate to the way it is embedded in the ambient product. Central to this connection is a conjecture on finiteness properties of fibre products, which we will present along with different approaches towards solving it.

Wed, 15/06/2011 11:00	Horng-Tzer Yau (Harvard, USA)	OxPDE Special Seminar	Gibson 1st Floor SR
	Wigner-Dyson conjecture on random matrices and Erdos-Renyi graphs
	Random matrices were introduced by E. Wigner to model the excitation spectrum of large nuclei. The central idea is based on the hypothesis that the local statistics of the excitation spectrum for a large complicated system is universal. Dyson Brownian motion is the flow of eigenvalues of random matrices when each matrix element performs independent Brownian motions. In this lecture, we will explain the connection between the universality of random matrices and the approach to local equilibrium of Dyson Brownian motion. The main tools in our approach are the logarithmic Sobolev inequality and entropy flow. The method will be applied to the adjacency matrices of Erdos-Renyi graphs.

Wed, 15/06/2011 13:30	Lawrence C Evans (University of California)	OxPDE Special Seminar	Gibson 1st Floor SR
	Entropy regularization for weak KAM theory
	I will discuss two of my papers that develop PDE methods for weak KAM theory, in the context of a singular variational problem that can be interpreted as a regularization of Mather's variational principle by an entropy term. This is, sort of, a statistical mechanics approach to the problem. I will show how the Euler-Lagrange PDE yield approximate changes to action-angle variables for the corresponding Hamiltonian dynamics.

Wed, 15/06/2011 16:00	Martin Palmer (University of Oxford)	Junior Geometric Group Theory Seminar	SR1
	Cutting and pasting...
	... for Torelli groups of surfaces.

Wed, 15/06/2011 16:00	Dr Henk Bruin (University of Surrey)	Analytic Topology in Mathematics and Computer Science	L3
	Ingram's Conjecture and homeomorphisms of unimodal inverse limit spaces

Thu, 16/06/2011 10:45	Oxford / Cambridge Meeting 15th Biennial Event	Differential Equations and Applications Seminar	L1
	Woolly Owl - host Oxford
	15th Biennial OXFORD / CAMBRIDGE MEETING PROGRAMME FOR THE ‘WOOLLY OWL TROPHY’ Invited Judges John Harper (Victoria University of Wellington, NZ) Arash Yavari (Georgia Tech, Atlanta, USA) Sharon Stephen (University of Birmingham, UK) 10:45 Morning Coffee The Maths Inst Common Room

Thu, 16/06/2011 13:00	Christoph Reisinger	Mathematical Finance Internal Seminar	DH 1st floor SR
	Hedging one's bets by high-dimensional stochastic control
	The first half of this seminar will discuss the hedging problem faced by a large sports betting agent who has to risk-manage an unwanted position in a bet on the simultaneous outcome of multiple football matches, by trading in moderately liquid simple bets on individual results. The resulting mathematical framework is that of a coupled system of multi-dimensional HJB equations. This leads to the wider question of the numerical approximation of such problems. Dynamic programming with PDEs, while very accurate in low dimensions, becomes practically intractable as the dimensionality increases. Monte Carlo methods, while robust for computing linear expectations in high dimensions, are not per se well suited to dynamic programming. This leaves high-dimensional stochastic control problems to be considered computationally infeasible in general. In the second half of the seminar, we will outline ongoing work in this area by sparse grid techniques and asymptotic expansions, the former exploiting smoothness of the value function, the latter a fast decay in the importance of principal components. We hope to instigate a discussion of other possible approaches including e.g. BSDEs.

Thu, 16/06/2011 14:00	none	Computational Mathematics and Applications	Gibson Grd floor SR
	none
	there will be no seminar in this week.

Thu, 16/06/2011 14:30	Delphine Dupont (Oxford)	Representation Theory Seminar	L3
	The category of perverse sheaves on smooth toric varieties
	The category of perverse sheaves, Perv_X, on a stratified space X plays an important role in the Intersection cohomology of Goresky-MacPherson and on the theory of D-modules. It is defined as a subcategory of the derived category of sheaves. Hence a usual complaint is that there are not very concrete objects. A lot of work has been done to describe Perv_X more explicitly. Hence many methods had been develop to describe Perv_X as a category of quiver representations. An important property of perverse sheaves is that they can be viewed as a stack, it means that a perverse sheaf can be defined up to isomorphism from the data of perverse sheaves on an open cover of X plus some glueing data. In this talk we show how the theory of stacks and more precisely the notion of constructible stacks can be used in order to glue a description due to Galligo, Granger and Maisonobe of the category Perv_X when X is C^n stratified by a normal crossing stratification. Thanks to this we will obtain a description of Perv_X on smooth toric varieties stratified by the torus action.

Thu, 16/06/2011
17:00

Rizos Sklinos (Leeds)

Logic Seminar

"Some model theory of the free group".

After Sela and Kharlampovich-Myasnikov independently proved that non abelian free groups share the same common theory model theoretic interest for the subject arose.

In this talk I will present a survey of results around this theory starting with basic model theoretic properties mostly coming from the connectedness of the free group (Poizat).

Then I will sketch our proof with C.Perin for the homogeneity of non abelian free groups and I will give several applications, the most important being the description of forking independence.

In the last part I will discuss a list of open problems, that fit in the context of geometric stability theory, together with some ideas/partial answers to them.