Forthcoming Seminars

Mon, 12/10/2009
12:00 		Marni Sheppeard (Oxford) String Theory Seminar Add to calendar L3
CANCELLED
Mon, 12/10/2009
14:15 		Alice Guionnet (Ecole Normale Superieure, Lyons) Stochastic Analysis Seminar Add to calendar Oxford-Man Institute
The Single Ring Theorum
Mon, 12/10/2009
15:45 		Iain Aitchison (Melbourne) Topology Seminar Add to calendar L3
A concept of genus for finitely presented groups
Mon, 12/10/2009
15:45 		Arnaud Doucet (University of British Columbia and Institute of Statistical Mathematics) Stochastic Analysis Seminar Add to calendar Eagle House
Forward Smoothing using Sequential Monte Carlo with Application
Mon, 12/10/2009
16:00 		Dr Damiano Testa (The Mathematical Institute, Oxford) Junior Number Theory Seminar Add to calendar SR1
The Mordell-Weil group of elliptic curves over function fields
Mon, 12/10/2009
17:00 		Benoît Perthame (Universite Pierre & Marie Curie) Partial Differential Equations Seminar Add to calendar Gibson 1st Floor SR
Adaptive evolution and concentrations in parabolic PDE
Living systems are subject to constant evolution through the two processes of mutations and selection, a principle discovered by C. Darwin. In a very simple, general and idealized description, their environment can be considered as a nutrient shared by all the population. This alllows certain individuals, characterized by a 'phenotypical trait', to expand faster because they are better adapted to use the environment. This leads to select the 'best fitted trait' in the population (singular point of the system). On the other hand, the new-born individuals undergo small variation of the trait under the effect of genetic mutations. In these circumstances, is it possible to describe the dynamical evolution of the current trait? We will give a mathematical model of such dynamics, based on parabolic equations, and show that an asymptotic method allows us to formalize precisely the concepts of monomorphic or polymorphic population. Then, we can describe the evolution of the 'fittest trait' and eventually to compute various forms of branching points which represent the cohabitation of two different populations. The concepts are based on the asymptotic analysis of the above mentioned parabolic equations once appropriately rescaled. This leads to concentrations of the solutions and the difficulty is to evaluate the weight and position of the moving Dirac masses that desribe the population. We will show that a new type of Hamilton-Jacobi equation, with constraints, naturally describes this asymptotic. Some additional theoretical questions as uniqueness for the limiting H.-J. equation will also be addressed. This work is based on collaborations with O. Diekmann, P.-E. Jabin, S. Mischler, S. Cuadrado, J. Carrillo, S. Genieys, M. Gauduchon, S. Mirahimmi and G. Barles.
Tue, 13/10/2009
12:00 		Prof E T Newman (University of Pittsburgh) Relativity Seminar Add to calendar L3
Non-Expanding Horizons, Shear-Free Congruences and H-spaces
Tue, 13/10/2009
14:15 		Dr Pavel Berloff (London) Geophysical and Nonlinear Fluid Dynamics Seminar Add to calendar Dobson Room, AOPP
On formation of multiple zonal jets in the oceans
Tue, 13/10/2009
14:30 		Louigi Addario-Berry (McGill) Combinatorial Theory Seminar Add to calendar L3
Prim's algorithm and self-organized criticality, in the complete graph
Let $ G=(V,E) $ be a graph with weights $ \{w_e : e \in E\} $, and assume all weights are distinct. If $ G $ is finite, then the well-known Prim's algorithm constructs its minimum spanning tree in the following manner. Starting from a single vertex $ v $, add the smallest weight edge connecting $ v $ to any other vertex. More generally, at each step add the smallest weight edge joining some vertex that has already been "explored" (connected by an edge) to some unexplored vertex. If $ G $ is infinite, however, Prim's algorithm does not necessarily construct a spanning tree (consider, for example, the case when the underlying graph is the two-dimensional lattice $ {\mathbb Z}^2 $, all weights on horizontal edges are strictly less than $ 1/2 $ and all weights on vertical edges are strictly greater than $ 1/2 $). The behavior of Prim's algorithm for *random* edge weights is an interesting and challenging object of study, even when the underlying graph is extremely simple. This line of research was initiated by McDiarmid, Johnson and Stone (1996), in the case when the underlying graph is the complete graph $ K_n $. Recently Angel et. al. (2006) have studied Prim's algorithm on regular trees with uniform random edge weights. We study Prim's algorithm on $ K_n $ and on its infinitary analogue Aldous' Poisson-weighted infinite tree. Along the way, we uncover two new descriptions of the Poisson IIC, the critical Poisson Galton-Watson tree conditioned to survive forever. Joint work with Simon Griffiths and Ross Kang.
Tue, 13/10/2009
15:45 		Matt Kerr (Durham) Algebraic and Symplectic Geometry Seminar Add to calendar L3
A Tour of Normal Functions and Algebraic Cycles
Associated to a pencil of algebraic curves with singular fibres is a bundle of Jacobians (which are abelian varieties off the discriminant locus of the family and semiabelian varieties over it). Normal functions, which are holomorphic sections of such a Jacobian bundle, were introduced by Poincare and used by Lefschetz to prove the Hodge Conjecture (HC) on algebraic surfaces. By a recent result of Griffiths and Green, an appropriate generalization of these normal functions remains at the center of efforts to establish the HC more generally and understand its implications. (Furthermore, the nature of the zero-loci of these normal functions is related to the Bloch-Beilinson conjectures on filtrations on Chow groups.) Abel-Jacobi maps give the connection between algebraic cycles and normal functions. In this talk, we shall discuss the limits and singularities of Abel-Jacobi maps for cycles on degenerating families of algebraic varieties. These two features are strongly connected with the issue of graphing admissible normal functions in a Neron model, properly generalizing Poincare's notion of normal functions. Some of these issues will be passed over rather lightly; our main intention is to give some simple examples of limits of AJ maps and stress their connection with higher algebraic K-theory. A very new theme in homological mirror symmetry concerns what the mirror of a normal function should be; in work of Morrison and Walcher, the mirror is related to counting holomorphic disks in a CY 3-fold bounding on a Lagrangian. Along slightly different lines, we shall briefly describe a surprising application of "higher" normal functions to growth of enumerative (Gromov-Witten) invariants in the context of local mirror symmetry.
Tue, 13/10/2009
17:00 		Ilya Spitkovsky (William & Mary College) Functional Analysis Seminar Add to calendar L3
Current state of the almost periodic factorization problem: a survey
Tue, 13/10/2009
17:00 		Aner Shalev (Jerusalem) Algebra Seminar Add to calendar L2
Quantitative representation theory and some applications
Wed, 14/10/2009
10:10 		Dr Kamel Bentahar (OCCAM (Oxford)) Seminar Add to calendar OCCAM Common Room (RI2.28)
Analytic Factorisation of Integers? A review of classical methods and a proposal for a new paradigm
Wed, 14/10/2009
11:30 		Algebra Kinderseminar Add to calendar
NO SEMINAR
Thu, 15/10/2009
11:00 		V.Solanki (Oxford) Advanced Logic Class Add to calendar SR2
Zariski geometry from Quantum harmonic oscillator
Thu, 15/10/2009
12:00 		Dirk Schlueter (Oxford) Junior Geometry and Topology Seminar Add to calendar SR1
The Hodge Conjecture
Thu, 15/10/2009
13:00 		Sergey Nadtochiy (OMI) Mathematical Finance Internal Seminar Add to calendar DH 1st floor SR
MARKET MODELS FOR EUROPEAN OPTIONS: DYNAMIC LOCAL VOLATILITY AND DYNAMIC LOCAL LE´VY MEASURE
Most financial models introduced for the purpose of pricing and hedging derivatives concentrate on the dynamics of the underlying stocks, or underlying instruments on which the derivatives are written. However, as certain types of derivatives became liquid, it appeared reasonable to model their prices directly and use these market models to price or hedge exotic derivatives. This framework was originally advocated by Heath, Jarrow and Morton for the Treasury bond markets. We discuss the characterization of arbitrage free dynamic stochastic models for the markets with infinite number of European Call options as the liquid derivatives. Subject to our assumptions on the presence of jumps in the underlying, the option prices are represented either through local volatility or through local L´evy measure. Each of the latter ones is then given dynamics through an Itˆo stochastic process in infinite dimensional space. The main thrust of our work is to characterize absence of arbitrage in this framework and address the issue of construction of the arbitrage-free models.
Thu, 15/10/2009
14:00 		Timothy Logvinenko (Liverpool) Algebraic and Symplectic Geometry Seminar Add to calendar DH 3rd floor SR
(COW seminar) Reid's recipe and derived categories
We give a three dimensional generalization of the classical McKay correspondence construction by Gonzales-Sprinberg and Verdier. This boils down to computing for the Bridgeland-King-Reid derived category equivalence the images of twists of the point sheaf at the origin of C^3 by irreducible representations of G. For abelian G the answer turns out to be closely linked to a piece of toric combinatorics known as Reid's recipe.
Thu, 15/10/2009
14:00 		Prof. Gitta Kutyniok (University of Osnabruck) Computational Mathematics and Applications Add to calendar 3WS SR
Sparsity, $ \ell_1 $ Minimization, and the Geometric Separation Problem
During the last two years, sparsity has become a key concept in various areas of applied mathematics, computer science, and electrical engineering. Sparsity methodologies explore the fundamental fact that many types of data/signals can be represented by only a few non-vanishing coefficients when choosing a suitable basis or, more generally, a frame. If signals possess such a sparse representation, they can in general be recovered from few measurements using $ \ell_1 $ minimization techniques. One application of this novel methodology is the geometric separation of data, which is composed of two (or more) geometrically distinct constituents – for instance, pointlike and curvelike structures in astronomical imaging of galaxies. Although it seems impossible to extract those components – as there are two unknowns for every datum – suggestive empirical results using sparsity considerations have already been obtained. In this talk we will first give an introduction into the concept of sparse representations and sparse recovery. Then we will develop a very general theoretical approach to the problem of geometric separation based on these methodologies by introducing novel ideas such as geometric clustering of coefficients. Finally, we will apply our results to the situation of separation of pointlike and curvelike structures in astronomical imaging of galaxies, where a deliberately overcomplete representation made of wavelets (suited to pointlike structures) and curvelets/shearlets (suited to curvelike structures) will be chosen. The decomposition principle is to minimize the $ \ell_1 $ norm of the frame coefficients. Our theoretical results, which are based on microlocal analysis considerations, show that at all sufficiently fine scales, nearly-perfect separation is indeed achieved. This is joint work with David Donoho (Stanford University).

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

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