Forthcoming Seminars

Mon, 23/05/2011
15:45 		Matteo Casserini (joint work with Gechun Liang) (ETH Zurich) Stochastic Analysis Seminar Add to calendar Oxford-Man Institute
Fully coupled systems of functional differential equations and applications
Recently, Liang, Lyons and Qian developed a new methodology for the study of backward stochastic differential equations (BSDEs) on general filtered probability spaces. Their approach is based on the analysis of a particular class of functional differential equations, where the driver of the equation does not depend only on the present, but also on the terminal value of the solution. The purpose of this work is to study fully coupled systems of forward functional differential equations, which are related to a broad class of fully coupled forward-backward stochastic dynamics with respect to general filtrations. In particular, these systems of functional differential equations have a more homogeneous structure with respect to the underlying forward-backward problems, allowing to partly avoid the conflicting nature between the forward and backward components. Another advantage of the approach is that its generality allows to consider many other types of forward-backward equations not treated in the classical literature: this is shown with the help of several examples, which have interesting applications to mathematical finance and are related to parabolic integro-partial differential equations. In the second part of the talk, we introduce a numerical scheme for the approximation of decoupled systems, based on a time discretization combined with a local iteration approach.
Mon, 23/05/2011
15:45 		Remi Coulon (MPI Bonn) Topology Seminar Add to calendar L3
Examples of aspherical hyperbolic simplicial complexes. An application of small cancellation for rotation families of groups
The goal of this talk is to construct new examples of hyperbolic aspherical complexes. More precisely, given an aspherical simplicial complex P and a subcomplex Q of P, we are looking for conditions under which the complex obtained by attaching a cone of base Q on P remains aspherical. If Q is a set of loops of a 2-dimensional complex, J.H.C. Whitehead proved that this new complex is aspherical if and only if the elements of the fundamental group of P represented by Q do not satisfy any identity. To deal with higher dimensional subcomplexes we use small cancellation theory and extend the geometric point of view developed by T. Delzant and M. Gromov to rotation families of groups. In particular we obtain hyperbolic aspherical complexes obtained by attaching a cone over the "real part" of a hyperbolic complex manifold.
Mon, 23/05/2011
17:00 		Didier Bresch (Savoie University) Partial Differential Equations Seminar Add to calendar Gibson 1st Floor SR
Well posedness and derivations of some multi-fluid systems
In this talk, we will present some recent mathematical features around two-fluid models. Such systems may be encountoured for instance to model internal waves, violent aerated flows, oil-and-gas mixtures. Depending on the context, the models used for simulation may greatly differ. However averaged models share the same structure. Here, we address the question whether available mathematical results in the case of a single fluid governed by the compressible barotropic equations for single flow may be extended to two phase model and discuss derivations of well-known multi-fluid models from single fluid systems by homogeneization (assuming for instance highly oscillating density). We focus on existence of local existence of strong solutions, loss of hyperbolicity, global existence of weak solutions, invariant regions, Young measure characterization.
Mon, 23/05/2011
17:00 		Marco Avellaneda (Courant Institute, NYU) Nomura Seminar Add to calendar Oxford-Man Institute
Options on Leveraged ETFs

Leveraged ETFs are funds that target a multiple of the daily return of a reference asset; eg UYG (Proshares) targets twice the daily return of XLF (Financial SPDR) and SKF targets minus twice the daily return of XLF.

 It is well known that these leveraged funds have exposure to realized volatility. In particular, the relation between the leveraged and the unleveraged funds over a given time-horizon (larger than 1 day) is uncertain and will depend on the realized volatility. This talk examines this phenomenon theoretically and empirically first, and then uses this to price options on leveraged ETFs in terms of the prices of options on the underlying ETF. The resulting model allows to model the volatility skews of the leveraged and unleveraged funds in relation to each other and therefore suggest an arbitrage relation that could prove useful for traders and risk-managers.
Tue, 24/05/2011
12:00 		Stephen Casey (DAMTP) Relativity Seminar Add to calendar L3
Projective, Optical and Path Geometries
Tue, 24/05/2011
14:15 		Prof Costis Skiadas (NorthwesternUniversity) Nomura Seminar Add to calendar Oxford-Man Institute
Scale-Invariant Asset Pricing Theory and Ambiguity Aversion
Tue, 24/05/2011
14:30 		Angelika Steger (ETH Zurich) Combinatorial Theory Seminar Add to calendar L3
The degree distribution of random planar graphs
A random planar graph $ P_n $ is a graph drawn uniformly at random from the class of all (labelled) planar graphs on $ n $ vertices. In this talk we show that with probability $ 1-o(1) $ the number of vertices of degree $ k $ in $ P_n $ is very close to a quantity $ d_k n $ that we determine explicitly. Here $ k=k(n) \le c \log n $. In the talk our main emphasis will be on the techniques for proving such results. (Joint work with Kosta Panagiotou.)
Tue, 24/05/2011
17:00 		Prof. V. Bavula (Sheffield) Algebra Seminar Add to calendar L2
“An analogue of the Conjecture of Dixmier is true for the algebra of polynomial integro-differential operators”

In 1968, Dixmier posed six problems for the algebra of polynomial

  differential operators, i.e. the Weyl algebra. In 1975, Joseph

solved the third and sixth problems and, in 2005, I solved the

  fifth problem and gave a positive solution to the fourth problem

  but only for homogeneous differential operators. The remaining three problems are still open. The first problem/conjecture of Dixmier (which is equivalent to the Jacobian Conjecture as was shown in 2005-07 by Tsuchimito, Belov and Kontsevich) claims that the Weyl algebra `behaves'

like a finite field. The first problem/conjecture of

  Dixmier:   is it true that an algebra endomorphism of the Weyl

  algebra an automorphism? In 2010, I proved that this question has

  an affirmative answer for the algebra of polynomial

  integro-differential operators. In my talk, I will explain the main

  ideas, the structure of the proof and recent progress on the first problem/conjecture of Dixmier.

 
Wed, 25/05/2011
11:30 		Chris Gill (University of Oxford) Algebra Kinderseminar Add to calendar ChCh, Tom Gate, Room 2
On the Brauer construction and p-Kostka numbers
Wed, 25/05/2011
12:45 		Dr Umut Cetin (London School of Economics) Nomura Seminar Add to calendar Oxford-Man Institute
Explicit construction of a dynamic Bessel bridge of dimension 3
Given a deterministically time-changed Brownian motion Z starting from 1, whose time-change V (t) satisfies V (t) > t for all t > 0, we perform an explicit construction of a process X which is Brownian motion in its own filtration and that hits zero for the first time at V (S), where S := inf {t > 0 : Z_t = 0}. We also provide the semimartingale decomposition of X under the filtration jointly generated by X and Z. Our construction relies on a combination of enlargement of filtration and filtering techniques. The resulting process X may be viewed as the analogue of a 3-dimensional Bessel bridge starting from 1 at time 0 and ending at 0 at the random time V (S). We call this a dynamic Bessel bridge since S is not known at time 0 but is slowly revealed in time by observing Z. Our study is motivated by insider trading models with default risk. (this is a joint work with Luciano Campi and Albina Danilova)
Wed, 25/05/2011
16:00 		Maria Buzano (University of Oxford) Junior Geometric Group Theory Seminar Add to calendar SR1
Homogeneous Einstein metrics and the graph theorem.
First of all, we are going to recall some basic facts and definitions about homogeneous Riemannian manifolds. Then we are going to talk about existence and non-existence of invariant Einstein metrics on compact homogeneous manifolds. In this context, we have that it is possible to associate to every homogeneous space a graph. Then, the graph theorem of Bohm, Wang and Ziller gives an existence result of invariant Einstein metrics on a compact homogeneous space, based on properties of its graph. We are going to discuss this theorem and sketch its proof.
Thu, 26/05/2011
11:00 		B.Zilber (Oxford) Advanced Class Logic Add to calendar L3
"On CIT and the Pila-Wilkie method"
Thu, 26/05/2011
12:30 		Fabrice Planchon (Universite de Nice (France)) OxPDE Lunchtime Seminar Add to calendar Gibson 1st Floor SR
Going beyond Serrin's endpoint regularity criterion for Navier-Stokes
Solutions which are time-bounded in L^3 up to time T can be continued past this time, by a landmark result of Escauriaza-Seregin-Sverak, extending Serrin's criterion. On the other hand, the local Cauchy theory holds up to solutions in BMO^-1; we aim at describing how one can obtain intermediate regularity results, assuming a priori bounds in negative regularity Besov spaces. This is joint work with J.-Y. Chemin, Isabelle Gallagher and Gabriel Koch.
Thu, 26/05/2011
13:00 		Jan Obloj Mathematical Finance Internal Seminar Add to calendar DH 1st floor SR
How do we build a math-finance setup when we do not have a probability space but we do have market prices?
In this talk I want to ask how to create a coherent mathematical framework for pricing and hedging which starts with the information available in the market and does not assume a given probabilistic setup. This calls for re-definition of notions of arbitrage and trading and, subsequently, for a “probability-free first fundamental theorem of asset pricing". The new setup should also link with a classical approach if our uncertainty about the model vanishes and we are convinced a particular probabilistic structure holds. I explore some recent results but, predominantly, I present the resulting open questions and problems. It is an “internal talk" which does not necessarily present one paper but rather wants to engage into a discussion. Ideas for the talk come in particular from joint works with Alex Cox and Mark Davis.
Thu, 26/05/2011
14:00 		Dr Jens-Peter Zemke (Hamburg-Harburg University of Technology) Computational Mathematics and Applications Add to calendar Gibson Grd floor SR
IDR – A New Class of Krylov Subspace Solvers: Benefits and Drawbacks

This talk is about the Induced Dimension Reduction (IDR) methods developed by Peter Sonneveld and, more recently, Martin van Gijzen. We sketch the history, outline the underlying principle, and give a few details about different points of view on this class of Krylov subspace methods. If time permits, we briefly outline some recent developments in this field and the benefits and drawbacks of these and IDR methods in general.
Thu, 26/05/2011
16:00 		David Loeffler (Warwick) Number Theory Seminar Add to calendar L3
Iwasawa theory for modular forms

he Iwasawa theory of elliptic curves over the rationals, and more
generally of modular forms, has mostly been studied with the
assumption that the form is "ordinary" at p -- i.e. that the Hecke
eigenvalue is a p-adic unit. When this is the case, the dual of the
p-Selmer group over the cyclotomic tower is a torsion module over the
Iwasawa algebra, and it is known in most cases (by work of Kato and
Skinner-Urban) that the characteristic ideal of this module is
generated by the p-adic L-function of the modular form.

I'll talk about the supersingular (good non-ordinary) case, where
things are slightly more complicated: the dual Selmer group has
positive rank, so its characteristic ideal is zero; and the p-adic
L-function is unbounded and hence doesn't lie in the Iwasawa algebra.
Under the rather restrictive hypothesis that the Hecke eigenvalue is
actually zero, Kobayashi, Pollack and Lei have shown how to decompose
the L-function as a linear combination of Iwasawa functions and
explicit "logarithm-like" series, and to modify the definition of the
Selmer group correspondingly, in order to formulate a main conjecture
(and prove one inclusion). I will describe joint work with Antonio Lei
and Sarah Zerbes where we extend this to general supersingular modular
forms, using methods from p-adic Hodge theory. Our work also gives
rise to new phenomena in the ordinary case: a somewhat mysterious
second Selmer group and L-function, which is related to the
"critical-slope L-function" studied by Pollack-Stevens and Bellaiche.

Thu, 26/05/2011
16:00 		Demetrios Papageorgiou (Imperial College London) Differential Equations and Applications Seminar Add to calendar DH 1st floor SR
Electrified multi-fluid film flows
Flows involving immiscible liquids are encountered in a variety of industrial and natural processes. Recent applications in micro- and nano-fluidics have led to a significant scientific effort whose aim (among other aspects) is to enable theoretical predictions of the spatiotemporal dynamics of the interface(s) separating different flowing liquids. In such applications the scale of the system is small, and forces such as surface tension or externally imposed electrostatic forces compete and can, in many cases, surpass those of gravity and inertia. This talk will begin with a brief survey of applications where electrohydrodynamics have been used experimentally in micro-lithography, and experiments will be presented that demonstrate the use of electric fields in producing controlled encapsulated droplet formation in microchannels. The main thrust of the talk will be theoretical and will mostly focus on the paradigm problem of the dynamics of electrified falling liquid films over topographically structured substrates. Evolution equations will be developed asymptotically and their solutions will be compared to direct simulations in order to identify their practicality. The equations are rich mathematically and yield novel examples of dissipative evolutionary systems with additional effects (typically these are pseudo-differential operators) due to dispersion and external fields. The models will be analysed (we have rigorous results concerning global existence of solutions, the existence of dissipative dynamics and an absorbing set, and analyticity), and accurate numerical solutions will be presented to describe the large time dynamics. It is found that electric fields and topography can be used to control the flow.Time permitting, I will present some recent results on transitions between convective to absolute instabilities for film flows over periodic topography.
Thu, 26/05/2011
17:00 		Enrique Casanovas (Barcelona) Logic Seminar Add to calendar L3
"Stability classes of partial types"
"We will talk on stability, simplicity, nip, etc of partial types. We will review some known results and we will discuss some open problems."

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

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