Forthcoming Seminars

Thu, 16/10/2008
16:30 		Amit Acharya (Pittsburgh) Differential Equations and Applications Seminar Add to calendar DH 1st floor SR
On the choice of coarse variables for dynamics
Thu, 16/10/2008
17:00 		Kobi Peterzil (Haifa) Logic Seminar Add to calendar L3
Definably compact, connected groups are elementarily equivalent to compact real Lie groups
(joint work with E. Hrushovski and A. Pillay) If G is a definably compact, connected group definable in an o-minimal structure then, as is known, G/Z(G) is semisimple (no infinite normal abelian subgroup). We show, that in every o-minimal expansion of an ordered group: If G is a definably connected central extension of a semisimple group then it is bi-intepretable, over parameters, with the two-sorted structure (G/Z(G), Z(G)). Many corollaries follow for definably connected, definably compact G. Here are two: 1. (G,.) is elementarily equivalent to a compact, connected real Lie group of the same dimension. 2. G can be written as an almost direct product of Z(G) and [G,G], and this last group is definable as well (note that in general [G,G] is a countable union of definable sets, thus not necessarily definable).
Fri, 17/10/2008
11:30 		Dr Alex Lubansky (Engineering Science, Oxford) Industrial and Interdisciplinary Workshops Add to calendar DH 1st floor SR
"Extending filament-based rheometry"
Fri, 17/10/2008
13:30 		Margaret Beck (Brown University, US) OxPDE Lunchtime Seminar Add to calendar Gibson 1st Floor SR
Using global invariant manifolds to understand metastability in Burgers equation with small viscosity
The large-time behavior of solutions to Burgers equation with small viscosity is described using invariant manifolds. In particular, a geometric explanation is provided for a phenomenon known as metastability,which in the present context means that solutions spend a very long time near the family of solutions known as diffusive N-waves before finally converging to a stable self-similar diffusion wave. More precisely, it is shown that in terms of similarity, or scaling, variables in an algebraically weighted $ L^2 $ space, the self-similar diffusion waves correspond to a one-dimensional global center manifold of stationary solutions. Through each of these fixed points there exists a one-dimensional, global, attractive, invariant manifold corresponding to the diffusive N-waves. Thus, metastability corresponds to a fast transient in which solutions approach this “metastable" manifold of diffusive N-waves, followed by a slow decay along this manifold, and, finally, convergence to the self-similar diffusion wave.
Fri, 17/10/2008
14:15 		Ernst Eberlein (Freiburg) Mathematical Finance Seminar Add to calendar DH 1st floor SR
Analysis of valuation formulae and applications to option pricing in Levy models
We discuss the valuation problem for a broad spectrum of derivatives, especially in Levy driven models. The key idea in this approach is to separate from the computational point of view the role of the two ingredients which are the payoff function and the driving process for the underlying quantity. Conditions under which valuation formulae based on Fourier and Laplace transforms hold in a general framework are analyzed. An interesting interplay between the properties of the payoff function and the driving process arises. We also derive the analytically extended characteristic function of the supremum and the infimum processes derived from a Levy process. Putting the different pieces together, we can price lookback and one-touch options in Levy driven models, as well as options on the minimum and maximum of several assets.
Mon, 20/10/2008
12:00 		Ali Chamseddine (American University of Beirut) String Theory Seminar Add to calendar L3
Noncommutative Geometry and the Spectrum of the Dirac operator
Abstract: Noncommutative geometry has been slowly emerging as a new paradigm of geometry which starts from quantum mechanics. One of its key features is that the new geometry is spectral, in agreement with the physical way of measuring distances which is also spectral. I present an overview on the study of the quantum nature of space-time using the tools of noncommutative geometry. In particular we examine the suitability of using the spectral action functional to describe the dynamics of a geometrical theory.
Mon, 20/10/2008
14:15 		Prof. Sergei Levendorskii (Leicester) Stochastic Analysis Seminar Add to calendar Oxford-Man Institute
Wiener-Hopf factorization as a general method for valuation of real and American options
A new general approach to optimal stopping problems in Lévy models, regime switching Lévy models and Lévy models with stochastic volatility and stochastic interest rate is developed. For perpetual options, explicit solutions are found, for options with finite time horizon, time discretization is used, and explicit solutions are derived for resulting sequences of perpetual options. The main building block is the option to abandon a monotone payoff stream. The optimal exercise boundary is found using the operator form of the Wiener-Hopf method, which is standard in analysis, and interpretation of the factors as expected present value operators (EPV-operators) under supremum and infimum processes. Other types of options are reduced to the option to abandon a monotone stream. For regime-switching models, an additional ingredient is an efficient iteration procedure. Lévy models with stochastic volatility and/or stochastic interest rate are reduced to regime switching models using discretization of the state space for additional factors. The efficiency of the method for 2 factor Lévy models with jumps and for 3-factor Heston model with stochastic interest rate is demonstrated. The method is much faster than Monte-Carlo methods and can be a viable alternative to Monte Carlo method as a general method for 2-3 factor models. Joint work of Svetlana Boyarchenko,University of Texas at Austin and Sergei Levendorski\v{i}, University of Leicester
Mon, 20/10/2008
14:15 		Stefan Friedl (Warwick) Topology Seminar Add to calendar L3
"Fibered 3-manifolds and twisted Alexander polynomials"
It is a classical result that the Alexander polynomial of a fibered knot has to be monic. But in general the converse does not hold, i.e. the Alexander polynomial does not detect fibered knots. We will show that the collection of all twisted Alexander polynomials (which are a natural generalization of the ordinary Alexander polynomial) detect fibered 3-manifolds. As a corollary it follows that given a 3-manifold N the product S1 x N is symplectic if and only if N is fibered.
Mon, 20/10/2008
15:30 		Anne Thomas (Cornell) Topology Seminar Add to calendar L3
"Lattices acting on Platonic polygonal complexes and Fuchsian buildings"
A polygonal complex $ X $ is Platonic if its automorphism group $ G $ acts transitively on the flags (vertex, edge, face) in $ X $. Compact examples include the boundaries of Platonic solids.  Noncompact examples $ X $ with nonpositive curvature (in an appropriate sense) and three polygons meeting at each edge were classified by \'Swi\c{a}tkowski, who also determined when the group $ G=Aut(X) $, equipped with the compact-open topology, is nondiscrete.  For example, there is a unique $ X $ with the link of each vertex the Petersen graph, and in this case $ G $ is nondiscrete.  A Fuchsian building is a two-dimensional also determined when the group $ G=Aut(X) $, equipped with the compact-open topology, is nondiscrete.  For example, there is a unique $ X $ with the link of each vertex the Petersen graph, and in this case $ G $ is nondiscrete.  A Fuchsian building is a two-dimensional hyperbolic building.  We study lattices in automorphism groups of Platonic complexes and Fuchsian buildings.  Using similar methods for both cases, we construct uniform and nonuniform lattices in $ G=Aut(X) $.  We also show that for some $ X $ the set of covolumes of lattices in $ G $ is nondiscrete, and that $ G $ admits lattices which are not finitely generated.  In fact our results apply to the larger class of Davis complexes, which includes examples in dimension > 2.
Mon, 20/10/2008
15:45 		Dr. Michael Caruana (Cambridge) Stochastic Analysis Seminar Add to calendar Oxford-Man Institute
Partial Differential Equations driven by rough paths
In this talk, we present an extension of the theory of rough paths to partial differential equations. This allows a robust approach to stochastic partial differential equations, and in particular we can replace Brownian motion by more general Gaussian and Markovian noise. Support theorems and large deviation statements all become easy corollaries of the corresponding statements of the driving process. This is joint work with Peter Friz in Cambridge.
Mon, 20/10/2008
16:45 		Ian Leary (Ohio State; visitin Bristol) Topology Seminar Add to calendar L3
"Simple platonic polygonal complexes."
We classify 2-dimensional polygonal complexes that are simply connected, platonic (in the sense that they admit a flag-transitive group of symmetries) and simple (in the sense that each vertex link is a complete graph).  These are a natural generalization of the 2-skeleta of simple polytopes. Our classification is complete except for some existence questions for complexes made from squares and pentagons. (Joint with Tadeusz Januszkiewicz, Raciel Valle and Roger Vogeler.)
Mon, 20/10/2008
17:00 		Christopher Jones (University of North Carolina & Warwick) Partial Differential Equations Seminar Add to calendar Gibson 1st Floor SR
"Oscillations" and Stability in Multi-Dimensions
Tue, 21/10/2008
12:00 		Prof Jean-Philippe Nicolas (Brest) Relativity Seminar Add to calendar L3
Regularity at space-like and null infinity
Tue, 21/10/2008
14:30 		Roy Meshulam (Technion) Combinatorial Theory Seminar Add to calendar L3
Domination numbers, homology and hypergraph matching
The homological Hall lemma is a topological tool that has recently been used to derive Hall type theorems for systems of disjoint representatives in hypergraphs. After outlining the general method, we.ll describe one such theorem in some detail. The main ingredients in the proof are: 1) A relation between the spectral gap of a graph and the topological connectivity of its flag complex. 2) A new graph domination parameter defined via certain vector representations of the graph. Joint work with R. Aharoni and E. Berger
Tue, 21/10/2008
17:00 		John McKay (Concordia University) Algebra Seminar Add to calendar L2
The sporadic simple groups, past, present and possible future

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

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