Forthcoming Seminars

Wed, 16/02/2011
16:00 		Lars Scheele (University Muenster) Junior Geometric Group Theory Seminar Add to calendar SR2
Slow Ultrafilters and asymptotic cones of proper metric spaces
The construction of the asymptotic cone of a metric space which allows one to capture the "large scale geometry" of that space has been introduced by Gromov and refined by van den Dries and Wilkie in the 1980's. Since then asymptotic cones have mainly been used as important invariants for finitely generated groups, regarded as metric spaces using the word metric. However since the construction of the cone requires non-principal ultrafilters, in many cases the cone itself is very hard to compute and seemingly basic questions about this construction have been open quite some time and only relatively recently been answered. In this talk I want to review the definition of the cone as well as considering iterated cones of metric spaces. I will show that every proper metric space can arise as asymptotic cone of some other proper space and I will answer a question of Drutu and Sapir regarding slow ultrafilters.
Thu, 17/02/2011
12:30 		Yann Brenier (Universite de Nice) OxPDE Lunchtime Seminar Add to calendar Gibson 1st Floor SR
Reconstruction of the early universe: a variational approach taking concentrations into account
The reconstruction of the early universe amounts to recovering the tiny density fluctuations of the early universe (shortly after the "big bang") from the current observation of the matter distribution in the universe. Following Zeldovich, Peebles and, more recently Frisch and collaboratoirs, we use a newtonian gravitational model with time dependent coefficients taking into accont general relativity effects. Due to the (remarkable) convexity of the corresponding action, the reconstruction problem apparently reduces to a straightforward convex minimization problem. Unfortunately, this approach completely ignores the mass concentration effects due to gravitational instabilities. In this lecture, we show a way of modifying the action in order to take concentrations into account. This is obtained through a (questionable) modification of the gravitation model, by substituting the fully nonlinear Monge-Amp`ere equation for the linear Poisson equation. (This is a reasonable approximation in the sense that it makes exact some approximate solutions advocated by Zeldovich for the original gravitational model.) Then the action can be written as a perfect square in which we can input mass concentration effects in a canonical way, based on the theory of gradient flows with convex potentials and somewhat related to the concept of self-dual Lagrangians developped by Ghoussoub. A fully discrete algorithm is introduced for the EUR problem in one space dimension.
Thu, 17/02/2011
13:00 		Ben Davison (University of Oxford) Junior Geometry and Topology Seminar Add to calendar SR1
The geometry and topology of chromatic polynomials
I will talk about a recent paper of Huh, who, building on a wealth of pretty geometry and topology, has given a proof of a conjecture dating back to 1968 regarding the chromatic polynomial (the polynomial that determines how many ways there are of colouring the vertices of a graph with n colours in such a way that no vertices which are joined by an edge have the same colour). I will mainly talk about the way in which a problem that is explicitly a combinatorics problem came to be encoded in algebraic geometry, and give an overview of the geometry and topology that goes into the solution. The talk should be accessible to everyone: no stacks, I promise.
Thu, 17/02/2011
14:00 		Prof Raymond Spiteri (University of Saskatchewan) Computational Mathematics and Applications Add to calendar Gibson Grd floor SR
Stiffness analysis of cardiac cell models
Thu, 17/02/2011
14:30 		Christopher Bowman (Cambridge) Representation Theory Seminar Add to calendar L3
Landrock's Lemma for Cellular and BGG algebras
We show that an adaptation of Landrock's Lemma holds for cellular algebras and BGG algebras. As an application, we show that BGG reciprocity respects Loewy structure.
Thu, 17/02/2011
16:00 		Jan Denef (Leuven) Logic Seminar Add to calendar
Number Theory Seminar Add to calendar
Geometric proof of theorems of Ax-Kochen and Ersov

We will sketch a new proof of the Theorem of Ax and Kochen that any projective hypersurface over the p-adic numbers has a p-adic rational point, if it is given by a homogeneous polynomial with more variables than the square of its degree d, assuming that p is large enough with respect to the degree d. Our proof is purely algebraic geometric and (unlike all previous ones) does not use methods from mathematical logic. It is based on a (small upgrade of a) theorem of Abramovich and Karu about weak toroidalization of morphisms. Our method also yields a new alternative approach to the model theory of henselian valued fields (including the Ax-Kochen-Ersov transfer principle and quantifier elimination).
Thu, 17/02/2011
16:00 		Michel Destrade (National University of Ireland Galway) Differential Equations and Applications Seminar Add to calendar DH 1st floor SR
Acoustics of soft solids
Rubbers and biological soft tissues undergo large isochoric motions in service, and can thus be modelled as nonlinear, incompressible elastic solids. It is easy to enforce incompressibility in the finite (exact) theory of nonlinear elasticity, but not so simple in the weakly nonlinear formulation, where the stress is expanded in successive powers of the strain. In linear and second-order elasticity, incompressibility means that Poisson's ratio is 1/2. Here we show how third- and fourth-order elastic constants behave in the incompressible limit. For applications, we turn to the propagation of elastic waves in soft incompressible solids, a topic of crucial importance in medical imaging (joint work with Ray Ogden, University of Aberdeen).
Thu, 17/02/2011
16:00 		Jan Denef (Leuven) Logic Seminar Add to calendar
Number Theory Seminar Add to calendar 		L3
To Be Announced
Fri, 18/02/2011
14:00 		Prof Ben Simons (University of Cambridge) Mathematical Biology and Ecology Seminar Add to calendar L1
Universal patterns of tissue stem cell fate
Fri, 18/02/2011
14:15 		Mingyu Xu (Chinese Academy of Sciences, Beijing) Nomura Seminar Add to calendar DH 1st floor SR
Reflected BSDE with a constraint and its application
Non-linear backward stochastic differential equations (BSDEs inshort) were firstly introduced by Pardoux and Peng (\cite{PP1990},1990), who proved the existence and uniqueness of the adapted solution, under smooth square integrability assumptions on the coefficient and the terminal condition, and when the coefficient $ g(t,\omega ,y,z) $ is Lipschitz in $ (y,z) $ uniformly in $ (t,\omega) $. From then on, the theory of backward stochastic differential equations (BSDE) has been widely and rapidly developed. And many problems in mathematical finance can be treated as BSDEs. The natural connection between BSDE and partial differential equations (PDE) of parabolic and elliptic types is also important applications. In this talk, we study a new developement of BSDE, BSDE with contraint and reflecting barrier.The existence and uniqueness results are presented and we will give some application of this kind of BSDE at last.
Mon, 21/02/2011
12:00 		James Sparks (Oxford) String Theory Seminar Add to calendar L3
To Be Announced
Mon, 21/02/2011
14:15 		Nitin Nitsure (Tata Institute) Geometry and Analysis Seminar Add to calendar L3
Schematic Harder Narasimhan stratification
The Harder Narasimhan type (in the sense of Gieseker semistability) of a pure-dimensional coherent sheaf on a projective scheme is known to vary semi-continuously in a flat family, which gives the well-known Harder Narasimhan stratification of the parameter scheme of the family, by locally closed subsets. We show that each stratum can be endowed with a natural structure of a locally closed subscheme of the parameter scheme, which enjoys an appropriate universal property. As an application, we deduce that pure-dimensional coherent sheaves of any given Harder Narasimhan type form an Artin algebraic stack. As another application - jointly with L. Brambila-Paz and O. Mata - we describe moduli schemes for certain rank 2 unstable vector bundles on a smooth projective curve, fixing some numerical data.
Mon, 21/02/2011
14:15 		Professor Xu Mingyu (Zhongmin) Stochastic Analysis Seminar Add to calendar Eagle House
To Be Announced
Mon, 21/02/2011
15:45 		Matthias Reitzner Stochastic Analysis Seminar Add to calendar Eagle House
'Poisson-Voronoi approximation and Wiener-Ito-chaos expansions'

Let $X$ be a Poisson point process and $K$ a d-dimensional convex set.
For a point $x \in X$ denote by $v_X(x)$ the Voronoi cell with respect to $X$, and set $$ v_X (K) := \bigcup_{x \in X \cap K } v_X(x) $$ which is the union of all Voronoi cells with center in $K$. We call $v_X(K)$ the Poisson-Voronoi approximation of $K$.
For $K$ a compact convex set the volume difference $V_d(v_X(K))-V_d(K) $ and the symmetric difference $V_d(v_X(K) \triangle K)$ are investigated.
Estimates for the variance and limit theorems are obtained using the chaotic decomposition of these functions in multiple Wiener-Ito integrals
Mon, 21/02/2011
15:45 		Mustafa Korkmaz (METU Ankara) Topology Seminar Add to calendar L3
Curve complexes on nonorientable surfaces

The curve complex on an orientable surface, introduced by William Harvey about 30 years ago, is the abstract simplicial complex whose vertices are isotopy classes of simple close curves. A set of vertices forms a simplex if they can be represented by pairwise disjoint elements. The mapping class group of S acts on this complex in a natural way, inducing a homomorphism from the mapping class group to the group of automorphisms of the curve complex. A remarkable theorem of Nikolai V. Ivanov says that this natural homomorphism is an isomorphism. From this fact, some algebraic properties of the mapping class group has been proved. In the last twenty years, this result has been extended in various directions. In the joint work with Ferihe Atalan, we have proved the corresponding theorem for non-orientable surfaces: the natural map from the mapping class group of a nonorientable surface to the automorphism group of the curve compex is an isomorphism. I will discuss the proof of this theorem and possible applications to the structure of the mapping class groups.
Mon, 21/02/2011
16:00 		James Maynard (Oxford) Junior Number Theory Seminar Add to calendar SR1
The mean square gap between primes
Mon, 21/02/2011
17:00 		Marco Cicalese (Universita die Napoli) Partial Differential Equations Seminar Add to calendar Gibson 1st Floor SR
The isoperimetric inequality in quantitative form
The classical isoperimetric inequality states that, given a set $ E $ in $ R^n $ having the same measure of the unit ball $ B $, the perimeter $ P(E) $ of $ E $ is greater than the perimeter $ P(B) $ of $ B $. Moreover, when the isoperimetric deficit $ D(E)=P(E)-P(B) $ equals 0, than $ E $ coincides (up to a translation) with $ B $. The sharp quantitative form of the isoperimetric inequality states that $ D(E) $ can be bound from below by $ A(E)^2 $, where the Fraenkel asymmetry $ A(E) $ of $ E $ is defined as the minimum of the volume of the symmetric difference between $ E $ and any translation of $ B $. This result, conjectured by Hall in 1990, has been proven in its full generality by Fusco-Maggi-Pratelli (Ann. of Math. 2008) via symmetrization arguments and more recently by Figalli-Maggi-Pratelli (Invent. Math. 2010) through optimal transportation techniques. In this talk I will present a new proof of the sharp quantitative version of the isoperimetric inequality that I have recently obtained in collaboration with G.P.Leonardi (University of Modena e Reggio). The proof relies on a variational method in which a penalization technique is combined with the regularity theory for quasiminimizers of the perimeter. As a further application of this method I will present a positive answer to another conjecture posed by Hall in 1992 concerning the best constant for the quantitative isoperimetric inequality in $ R^2 $ in the small asymmetry regime.

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

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