Past Seminars
|
Mon, 21/05 17:00 |
Claude Bardos (Paris VII Denis Diderot) |
Partial Differential Equations Seminar  |
Gibson 1st Floor SR |
|
Recent results (starting with Scheffer and
Shnirelman and continuing with De Lellis and Szekelhyhidi ) underline
the importance of considering solutions of the incompressible Euler
equations as limits of solutions of more physical examples like
Navier-Stokes or Boltzmann. |
|||
|
Mon, 21/05 16:00 |
Daniel Kotzen |
Junior Number Theory Seminar |
SR1 |
|
Mon, 21/05 15:45 |
Cornelia Drutu (Oxford) |
Topology Seminar |
L3 |
| In Riemannian geometry there are several notions of rank defined for non-positively curved manifolds and with natural extensions for groups acting on non-positively curved spaces. The talk shall explain how various notions of rank behave for mapping class groups of surfaces. This is joint work with J. Behrstock. | |||
|
Mon, 21/05 15:45 |
DEJAN VELUSCEK (ETH Zurich) |
Stochastic Analysis Seminar |
Oxford-Man Institute |
| We will give a quick overview of the semigroup perspective on splitting schemes for S(P)DEs which present a robust, "easy to implement" numerical method for calculating the expected value of a certain payoff of a stochastic process driven by a S(P)DE. Having a high numerical order of convergence enables us to replace the Monte Carlo integration technique by alternative, faster techniques. The numerical order of splitting schemes for S(P)DEs is bounded by 2. The technique of combining several splittings using linear combinations which kills some additional terms in the error expansion and thus raises the order of the numerical method is called the extrapolation. In the presentation we will focus on a special extrapolation of the Lie-Trotter splitting: the symmetrically weighted sequential splitting, and its subsequent extrapolations. Using the semigroup technique their convergence will be investigated. At the end several applications to the S(P)DEs will be given. | |||
|
Mon, 21/05 14:15 |
CHRISTIAN BAYER (University of Vienna) |
Stochastic Analysis Seminar |
Oxford-Man Institute |
| Based on ideas from rough path analysis and operator splitting, the Kusuoka-Lyons-Victoir scheme provides a family of higher order methods for the weak approximation of stochastic differential equations. Out of this family, the Ninomiya-Victoir method is especially simple to implement and to adjust to various different models. We give some examples of models used in financial engineering and comment on the performance of the Ninomiya-Victoir scheme and some modifications when applied to these models. | |||
|
Mon, 21/05 14:15 |
Andre Neves (Imperial College) |
Geometry and Analysis Seminar |
L3 |
|
Mon, 21/05 12:00 |
Chris Hull (Imperial College London) |
String Theory Seminar |
L3 |
| String theory on a torus requires the introduction of dual coordinates conjugate to string winding number. This leads to physics and novel geometry in a doubled space. This will be compared to generalized geometry, which doubles the tangent space but not the manifold. For a d-torus, string theory can be formulated in terms of an infinite tower of fields depending on both the d torus coordinates and the d dual coordinates. This talk focuses on a finite subsector consisting of a metric and B-field (both d x d matrices) and a dilaton all depending on the 2d doubled torus coordinates. The double field theory is constructed and found to have a novel symmetry that reduces to diffeomorphisms and anti-symmetric tensor gauge transformations in certain circumstances. It also has manifest T-duality symmetry which provides a generalisation of the usual Buscher rules to backgrounds without isometries. The theory has a real dependence on the full doubled geometry: the dual dimensions are not auxiliary. It is concluded that the doubled geometry is physical and dynamical. | |||
|
Fri, 18/05 14:30 |
Dr. Hilmar Gudmundsson (British Antarctic Survey, Cambridge) |
Mathematical Geoscience Seminar |
DH 3rd floor SR |
| Inverse methods are frequently used in geosciences to estimate model parameters from indirect measurements. A common inverse problem encountered when modelling the flow of large ice masses such as the Greenland and the Antarctic ice sheets is the determination of basal conditions from surface data. I will present an overview over some of the inverse methods currently used to tackle this problem and in particular discuss the use of Bayesian inverse methods in this context. Examples of the use of adjoint methods for large-scale optimisation problems that arise, for example, in flow modelling of West-Antarctica will be given. | |||
|
Fri, 18/05 14:15 |
Prof Martin Schweizer (ETH Zurich) |
Nomura Seminar |
DH 1st floor SR |
| Absence of arbitrage is a highly desirable feature in mathematical models of financial markets. In its pure form (whether as NFLVR or as the existence of a variant of an equivalent martingale measure R), it is qualitative and therefore robust towards equivalent changes of the underlying reference probability (the "real-world" measure P). But what happens if we look at more quantitative versions of absence of arbitrage, where we impose for instance some integrability on the density dR/dP? To which extent is such a property robust towards changes of P? We discuss these uestions and present some recent results. The talk is based on joint work with Tahir Choulli (University of Alberta, Edmonton). | |||
|
Fri, 18/05 00:00 |
Mathematical Biology and Ecology Seminar |
||
|
Thu, 17/05 17:00 |
*Cancelled* |
Logic Seminar |
L3 |
|
Thu, 17/05 17:00 |
Jose A Scheinkman (Theodore Wells '29 Professor of Economics at Princeton) |
Nomura Lecture |
Martin Wood Lecture |
| In this lecture I will exploit a model of asset prices where speculators overconfidence is a source of heterogeneous beliefs and arbitrage is limited. In the model, asset buyers are the most positive investors, but prices exceed their optimistic valuation because the owner of an asset has the option of reselling it in the future to an even more optimistic buyer. The value of this resale option can be identified as a bubble. I will focus on assets with a fixed terminal date, as is often the case with credit instruments. I will show that the size of a bubble satisfies a Partial Differential Equation that is similar to the equation satisfied by an American option and use the PDE to evaluate the impact of parameters such as interest rates or a “Tobin tax” on the size of the bubble and on trading volume. | |||
|
Thu, 17/05 16:00 |
Gavin Brown (Manchester) |
Industrial and Applied Mathematics Seminar |
DH 1st floor SR |
| Feature Selection is a ubiquitous problem in across data mining, bioinformatics, and pattern recognition, known variously as variable selection, dimensionality reduction, and others. Methods based on information theory have tremendously popular over the past decade, with dozens of 'novel' algorithms, and hundreds of applications published in domains across the spectrum of science/engineering. In this work, we asked the question 'what are the implicit underlying statistical assumptions of feature selection methods based on mutual information?' The main result I will present is a unifying probabilistic framework for information theoretic feature selection, bringing almost two decades of research on heuristic methods under a single theoretical interpretation. | |||
|
Thu, 17/05 16:00 |
Anish Ghosh (UEA) |
Number Theory Seminar |
L3 |
|
Thu, 17/05 14:00 |
Dr Mike Botchev (University of Twente) |
Computational Mathematics and Applications |
Gibson Grd floor SR |
| Exponential time integrators are a powerful tool for numerical solution of time dependent problems. The actions of the matrix functions on vectors, necessary for exponential integrators, can be efficiently computed by different elegant numerical techniques, such as Krylov subspaces. Unfortunately, in some situations the additional work required by exponential integrators per time step is not paid off because the time step can not be increased too much due to the accuracy restrictions. To get around this problem, we propose the so-called time-stepping-free approach. This approach works for linear ordinary differential equation (ODE) systems where the time dependent part forms a small-dimensional subspace. In this case the time dependence can be projected out by block Krylov methods onto the small, projected ODE system. Thus, there is just one block Krylov subspace involved and there are no time steps. We refer to this method as EBK, exponential block Krylov method. The accuracy of EBK is determined by the Krylov subspace error and the solution accuracy in the projected ODE system. EBK works for well for linear systems, its extension to nonlinear problems is an open problem and we discuss possible ways for such an extension. | |||
|
Thu, 17/05 13:00 |
Jan Witte |
Mathematical Finance Internal Seminar |
DH 1st floor SR |
| Min-Max equations, also called Isaacs equations, arise from many applications, eg in game theory or mathematical finance. For their numerical solution, they are often discretised by finite difference methods, and, in a second step, one is then faced with a non-linear discrete system. We discuss how upper and lower bounds for the solution to the discretised min-max equation can easily be computed. | |||
|
Thu, 17/05 12:30 |
Gianluca Crippa (Universität Basel) |
OxPDE Lunchtime Seminar |
Gibson 1st Floor SR |
|
In this seminar I will present two results regarding the uniqueness (and further properties) for the two-dimensional continuity equation
and the ordinary differential equation in the case when the vector field is bounded, divergence free and satisfies additional conditions on its distributional curl. Such settings appear in a very natural way in various situations, for instance when considering two-dimensional incompressible fluids. I will in particular describe the following two cases: (1) The vector field is time-independent and its curl is a (locally finite) measure (without any sign condition). (2) The vector field is time-dependent and its curl belongs to L^1. Based on joint works with: Giovanni Alberti (Universita' di Pisa), Stefano Bianchini (SISSA Trieste), Francois Bouchut (CNRS & Universite' Paris-Est-Marne-la-Vallee) and Camillo De Lellis (Universitaet Zuerich). |
|||
|
Thu, 17/05 12:00 |
Markus Röser |
Junior Geometry and Topology Seminar |
L3 |
|
In this talk our aim is to explain why there exist hyperkähler metrics on the cotangent bundles and on coadjoint orbits of complex Lie groups. The key observation is that both the cotangent bundle of $G^\mathbb C$ and complex coadjoint orbits can be constructed as hyperkähler quotients in an infinite-dimensional setting: They may be identified with certain moduli spaces of solutions to Nahm's equations, which is a system of non-linear ODEs arising in gauge theory. In the first half we will describe the hyperkähler quotient construction, which can be viewed as a version of the Marsden-Weinstein symplectic quotient for complex symplectic manifolds. We will then introduce Nahm's equations and explain how their moduli spaces of solutions may be related to the above Lie theoretic objects. |
|||
|
Wed, 16/05 11:30 |
Martin Bridson |
Algebra Kinderseminar |
|
|
Tue, 15/05 17:00 |
Aner Shalev (Jerusalem) |
Algebra Seminar |
L2 |
| In recent years there has been extensive interest in word maps on groups, and various results were obtained, with emphasis on simple groups. We shall focus on some new results on word maps for more general families of finite and infinite groups. | |||
