Forthcoming Seminars

Mon, 15/02/2010
14:15 		Antoine Ayache (University of Lille) Stochastic Analysis Seminar Add to calendar Eagle House
Fractional Stockastic Fields and Wavelet Methods
Abstract: The goal of this talk is to discuss threeproblems on fractional and related stochastic fields, in which wavelet methodshave turned out to be quite useful.  The first problemconsists in constructing optimal random series representations of Lévyfractional Brownian field; by optimal we mean that the tails of the seriesconverge to zero as fast as possible i.e. at the same rate as the l-numbers.Note in passing that there are close connections between the l-numbers of aGaussian field and its small balls probabilities behavior.  The secondproblem concerns a uniform result on the local Hölder regularity (the pointwiseHölder exponent) of multifractional Brownian motion; by uniform we mean thatthe result is satisfied on an event with probability 1 which does not depend onthe location.  The third problemconsists in showing that multivariate multifractional Brownian motion satisfiesthe local nondeterminism property. Roughly speaking, this property, which wasintroduced by Berman, means that the increments are asymtotically independentand it allows to extend to general Gaussian fields many results on the localtimes of Brownian motion. 
Mon, 15/02/2010
14:15 		Spiro Karigiannis (Waterloo University) Geometry and Analysis Seminar Add to calendar L3
Curvature of the Moduli Space of G2 Metrics
Mon, 15/02/2010
15:45 		Sigurd Assing (University of Warwick) Stochastic Analysis Seminar Add to calendar Eagle House
THE BEHAVIOR OF THE CURRENT FLUCTUATION FIELD IN WEAKLY ASYMMETRIC EXCLUSION
We consider the time average of the (renormalized) current fluctuation field in one-dimensional weakly asymmetric simple exclusion. The asymmetry is chosen to be weak enough such that the density fluctuation field still converges in law with respect to diffusive scaling. Remark that the density fluctuation field would evolve on a slower time scale if the asymmetry is too strong and that then the current fluctuations would have something to do with the Tracy-Widom distribution. However, the asymmetry is also chosen to be strong enough such that the density fluctuation field does not converge in law to an infinite-dimensional Ornstein-Uhlenbeck process, that is something non-trivial is happening. We will, at first, motivate why studying the time average of the current fluctuation field helps to understand the structure of this non-trivial scaling limit of the density fluctuation field and, second, show how one can replace the current fluctuation field by a certain functional of the density fluctuation field under the time average. The latter result provides further evidence for the common belief that the scaling limit of the density fluctuation field approximates the solution of a Burgers-type equation
Mon, 15/02/2010
15:45 		Jeff Giansiracusa (Swansea and Oxford) Topology Seminar Add to calendar L3
Operads, formality, and diffeomorphisms of handlebodies
Mon, 15/02/2010
16:00 		TBA (Mathematical Institute, Oxford) Junior Number Theory Seminar Add to calendar SR1
To Be Announced
Mon, 15/02/2010
17:00 		Bianca Stroffolini (University of Naples) Partial Differential Equations Seminar Add to calendar Gibson 1st Floor SR
Regularity results for functionals with general growth
In this talk I will present some results on functionals with general growth, obtained in collaboration with L. Diening and A. Verde. Let $ \phi $ be a convex, $ C^1 $-function and consider the functional:
$$ (1)\qquad \mathcal{F}(\bf u)=\int_{\Omega} \phi (|\nabla \bf u|) \,dx $$
where $ \Omega\subset \mathbb{R}^n $ is a bounded open set and $ \bf u: \Omega \to \mathbb{R}^N $. The associated Euler Lagrange system is
$$ -\mbox{div} (\phi' (|\nabla\bf u|)\frac{\nabla\bf u}{|\nabla\bf u|} )=0 $$
In a fundamental paper K.~Uhlenbeck proved everywhere $ C^{1,\alpha} $-regularity for local minimizers of the $ p $-growth functional with $ p\ge 2 $. Later on a large number of generalizations have been made. The case $ 1 {\bf Theorem.} Let $\bfu\in W^{1,\phi}_{\loc}(\Omega)$ be a local minimizer of (1), where $\phi$ satisfies suitable assumptions. Then $\bfV(\nabla \bfu)$ and $\nabla \bfu$ are locally $\alpha$ -Hölder continuous for some $\alpha>0$ . We present a unified approach to the superquadratic and subquadratic $p$ -growth, also considering more general functions than the powers. As an application, we prove Lipschitz regularity for local minimizers of asymptotically convex functionals in a $C^2$ sense.
Tue, 16/02/2010
14:30 		Vadim Lozin (Warwick) Combinatorial Theory Seminar Add to calendar L3
Boundary properties of graphs
The notion of a boundary graph property is a relaxation of that of a minimal property. Several fundamental results in graph theory have been obtained in terms of identifying minimal properties. For instance, Robertson and Seymour showed that there is a unique minimal minor-closed property with unbounded tree-width (the planar graphs), while Balogh, Bollobás and Weinreich identified nine minimal hereditary properties of labeled graphs with the factorial speed of growth. However, there are situations where the notion of minimal property is not applicable. A typical example of this type is given by graphs of large girth. It is known that for each particular value of k, the graphs of girth at least k are of unbounded tree-width and their speed of growth is superfactorial, while the limit property of this sequence (i.e., the acyclic graphs) has bounded tree-width and its speed of growth is factorial. To overcome this difficulty, the notion of boundary properties of graphs has been recently introduced. In the present talk, we use this notion in order to identify some classes of graphs which are well-quasi-ordered with respect to the induced subgraph relation.
Tue, 16/02/2010
15:45 		Martijn Kool (Oxford) Algebraic and Symplectic Geometry Seminar Add to calendar L3
Moduli Spaces of Sheaves on Toric Varieties
Extending work of Klyachko, we give a combinatorial description of pure equivariant sheaves on a nonsingular projective toric variety X and use this description to construct moduli spaces of such sheaves. These moduli spaces are explicit and combinatorial in nature. Subsequently, we consider the moduli space M of all Gieseker stable sheaves on X and describe its fixed point locus in terms of the moduli spaces of pure equivariant sheaves on X. As an application, we compute generating functions of Euler characteristics of M in case X is a toric surface. In the torsion free case, one finds examples of new as well as known generating functions. In the pure dimension 1 case using a conjecture of Sheldon Katz, one obtains examples of genus zero Gopakumar-Vafa invariants of the canonical bundle of X.
Tue, 16/02/2010
16:00 		Anne Thomas (Oxford) Junior Geometric Group Theory Seminar Add to calendar SR1
Coxeter groups and rigidity
Tue, 16/02/2010
17:00 		Charles Batty (Oxford) Functional Analysis Seminar Add to calendar L3
Quasi-hyperbolic operators
Tue, 16/02/2010
17:00 		John Duncan (Cambridge) Algebra Seminar Add to calendar L2
Monstrous moonshine and black holes
   In 1939 Rademacher derived a conditionally convergent series expression for the modular j-invariant, and used this expression—the first Rademacher sum—to verify its modular invariance. We may attach Rademacher sums to other discrete groups of isometries of the hyperbolic plane, and we may ask how the automorphy of the resulting functions reflects the geometry of the group in question.
   In the case of a group that defines a genus zero quotient of the hyperbolic plane the relationship is particularly striking. On the other hand, of the common features of the groups that arise in monstrous moonshine, the genus zero property is perhaps the most elusive. We will illustrate how Rademacher sums elucidate this phenomena by using them to formulate a characterization of the discrete groups of monstrous moonshine.
  A physical interpretation of the Rademacher sums comes into view when we consider black holes in the context of three dimensional quantum gravity. This observation, together with the application of Rademacher sums to moonshine, amounts to a new connection between moonshine, number theory and physics, and furnishes applications in all three fields.
Wed, 17/02/2010
10:10 		Kostas Zygalakis OCCAM Wednesday Morning Event Add to calendar OCCAM Common Room (RI2.28)
Reaction- Rate Theory Fifty Years after Kramers
Wed, 17/02/2010
11:30 		George Wellen (Bradfield College) Algebra Kinderseminar Add to calendar ChCh, Tom Gate, Room 2
$ \pi $
Thu, 18/02/2010
11:00 		Trevor Wood (Oxford) Applied Dynamical Systems and Inverse Problems Seminar Add to calendar DH 3rd floor SR
Submarine Hunting and Other Applications of the Mathematics of Tracking. (NOTE Change of speaker and topic)
The background for the multitarget tracking problem is presented along with a new framework for solution using the theory of random finite sets. A range of applications are presented including submarine tracking with active SONAR, classifying underwater entities from audio signals and extracting cell trajectories from biological data.
Thu, 18/02/2010
12:00 		Laura Schaposnik (Oxford) Junior Geometry and Topology Seminar Add to calendar SR1
Monodromy of Higgs bundles
We will consider the monodromy action on mod 2 cohomology for SL(2) Hitchin systems. We will study Copeland's approach to the subject and use his results to compute the monodromy action on mod 2 cohomology. An interpretation of our results in terms of geometric properties of fixed points of a natural involution on the moduli space is given.
Thu, 18/02/2010
14:00 		Dr. Alison Ramage (University of Strathclyde) Computational Mathematics and Applications Add to calendar 3WS SR
Saddle point problems in liquid crystal modelling
Saddle-point problems occur frequently in liquid crystal modelling. For example, they arise whenever Lagrange multipliers are used for the pointwise-unit-vector constraints in director modelling, or in both general director and order tensor models when an electric field is present that stems from a constant voltage. Furthermore, in a director model with associated constraints and Lagrange multipliers, together with a coupled electric-field interaction, a particular ”double” saddle-point structure arises. This talk will focus on a simple example of this type and discuss appropriate numerical solution schemes. This is joint work with Eugene C. Gartland, Jr., Department of Mathematical Sciences, Kent State University.

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

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