Past Seminars

Mon, 11/03
15:45 		NIKOLAOS ENGLEZOS (University of Piraeus) Stochastic Analysis Seminar Add to calendar Oxford-Man Institute
Random FBSDEs: Burgers SPDEs, Rational Expectations / Consol Rate Models, Control for Large Investors, and Stochastic Viscosity Solutions.
Abstract: Burgers equation is a quasilinear partial differential equation (PDE), proposed in 1930's to model the evolution of turbulent fluid motion, which can be linearized to the heat equation via the celebrated Cole-Hopf transformation. In the first part of the talk, we study in detail general versions of stochastic Burgers equation with random coefficients, in both forward and backward sense. Concerning the former, the Cole-Hopf transformation still applies and we reduce a forward stochastic Burgers equation to a forward stochastic heat equation that can be treated in a “pathwise" manner. In case of deterministic coefficients, we obtain a probabilistic representation of the Cole-Hopf transformation by associating the backward Burgers equation with a system of forward-backward stochastic differential equations (FBSDEs). Returning to random coefficients, we exploit this representation in order to establish a stochastic version of the Cole-Hopf transformation. This generalized transformation allows us to find solutions to a backward stochastic Burgers equation through a backward stochastic heat equation, subject to additional constraints that reflect the presence of randomness in the coefficients. In both settings, forward and backward, stochastic Feynman-Kac formulae are derived for the solutions of the respective stochastic Burgers equations, as well. Finally, an application that illustrates the obtained results is presented to a pricing/hedging problem arising from mathematical finance. In the second part of the talk, we study a class of stochastic saddlepoint systems, represented by fully coupled FBSDEs with infinite horizon, that gives rise to a continuous time rational expectations / consol rate model with random coefficients. Under standard Lipschitz and monotonicity conditions, and by means of the contraction mapping principle, we establish existence, uniqueness and dependence on a parameter of adapted solutions. Making further the connection with quasilinear backward stochastic PDEs (BSPDEs), we are led to the notion of stochastic viscosity solutions. A stochastic maximum principle for the optimal control problem of a large investor is also provided as an application to this framework. This is joint work with N. Frangos, X.- I. Kartala and A. N. Yannacopoulos*
Mon, 11/03
14:15 		SANDIE DAVIE (University of Edinburgh) Stochastic Analysis Seminar Add to calendar Oxford-Man Institute
Pathwise approximation of SDE solutions using coupling
The standard Taylor series approach to the higher-order approximation of vector SDEs requires simulation of iterated stochastic integrals, which is difficult. The talk will describe an approach using methods from optimal transport theory which avoid this difficulty in the case of non-degenerate diffusions, for which one can attain arbitrarily high order pathwise approximation in the Vaserstein 2-metric, using easily generated random variables.
Mon, 11/03
10:00 		Tim Blass (Carnegie Mellon University & OxPDE) Industrial and Interdisciplinary Workshops Add to calendar Gibson 1st Floor SR
Dislocations
Please note the unusual day of the week for this workshop (a Monday) and also the unusual location.
Fri, 08/03
16:00 		Agnes Sulem (INRIA Paris Rocquencourt) Nomura Seminar Add to calendar DH 1st floor SR
A stochastic control approach to robust duality in finance
A celebrated financial application of convex duality theory gives an explicit relation between the following two quantities: (i) The optimal terminal wealth X*(T) := Xφ* (T) of the classical problem to maximise the expected U-utility of the terminal wealth Xφ(T) generated by admissible portfolios φ(t); 0 ≤ t ≤ T in a market with the risky asset price process modeled as a semimartingale; (ii) The optimal scenario dQ*/dP of the dual problem to minimise the expected V -value of dQ/dP over a family of equivalent local martingale measures Q. Here V is the convex dual function of the concave function U. In this talk we consider markets modeled by Itô-Lėvy processes, and we present in a first part a new proof of the above result in this setting, based on the maximum principle in stochastic control theory. An advantage with our approach is that it also gives an explicit relation between the optimal portfolio φ* and the optimal scenario Q*, in terms of backward stochastic differential equations. In a second part we present robust (model uncertainty) versions of the optimization problems in (i) and (ii), and we prove a relation between them. We illustrate the results with explicit examples. The presentation is based on recent joint work with Bernt ¬Oksendal, University of Oslo, Norway.
Fri, 08/03
14:30 		Dr Kody Law (University of Warwick) Mathematical Geoscience Seminar Add to calendar DH 3rd floor SR
Accurate Filtering with 3DVAR for Dissipative Systems
Unstable dynamical systems can be stabilized, and hence the solution recovered from noisy data, provided two conditions hold. First, observe enough of the system: the unstable modes. Second, weight the observed data sufficiently over the model. In this talk I will illustrate this for the 3DVAR filter applied to three dissipative dynamical systems of increasing dimension: the Lorenz 1963 model, the Lorenz 1996 model, and the 2D Navier-Stokes equation.
Fri, 08/03
11:30 		Various (OCCAM) OCCAM Special Seminar Add to calendar OCCAM Common Room (RI2.28)
OCCAM Group Meeting
  • Wonjung Lee - Adaptive approximation of higher order posterior statistics
  • Amy Smith - Multi-scale modelling of fluid transport in the coronary microvasculature
  • Mark Curtis - The Stokes flow around arbitrary slender bodies
Fri, 08/03
09:45 		Nick Hall-Taylor (TBC) Industrial and Interdisciplinary Workshops Add to calendar DH 1st floor SR
Experimental results in two-phase flow
In vertical annular two-phase flow, large amplitude waves ("disturbance waves") are the most significant means by which the liquid is transported by the action of the gas phase. The presentation is of certain experimental results with the intention of defining a conceptual model suitable for possible mathematical interpretation. These large waves have been studied for over 50 years but there has been little corresponding advance in the mathematical understanding of the phenomenon. The aim of the workshop is to discuss what analysis might be possible and how this might contribute to the understanding of the phenomena involved.
Thu, 07/03
17:00 		Jeff Paris (Manchester) Logic Seminar Add to calendar L3
Pure Inductive Logic
I shall give a non-technical survey of Pure Inductive Logic, a branch of Carnap's Inductive Logic which was anticipated early on in that subject but has only recently begun to be developed as an area of Mathematical Logic. My intention is to cover its origins and aims, and to pick out some of the key concepts which have emerged in the last decade or so.
Thu, 07/03
16:00 		Gert Van Der Heijden (UCL London) Industrial and Applied Mathematics Seminar Add to calendar DH 1st floor SR
Theory of equilibria of elastic braids with applications to DNA supercoiling
We formulate a new theory for equilibria of 2-braids, i.e., structures formed by two elastic rods winding around each other in continuous contact and subject to a local interstrand interaction. Unlike in previous work no assumption is made on the shape of the contact curve. The theory is developed in terms of a moving frame of directors attached to one of the strands with one of the directors pointing to the position of the other strand. The constant-distance constraint is automatically satisfied by the introduction of what we call braid strains. The price we pay is that the potential energy involves arclength derivatives of these strains, thus giving rise to a second-order variational problem. The Euler-Lagrange equations for this problem (in Euler-Poincare form) give balance equations for the overall braid force and moment referred to the moving frame as well as differential equations that can be interpreted as effective constitutive relations encoding the effect that the second strand has on the first as the braid deforms under the action of end loads. Hard contact models are used to obtain the normal contact pressure between strands that has to be non-negative for a physically realisable solution without the need for external devices such as clamps or glue to keep the strands together. The theory is first illustrated by a few simple examples and then applied to several problems that require the numerical solution of boundary-value problems. Both open braids and closed braids (links and knots) are considered and current applications to DNA supercoiling are discussed.
Thu, 07/03
16:00 		Emanuel Carneiro (IMPA) Number Theory Seminar Add to calendar L3
Conditional bounds for the Riemann zeta-function via Fourier analysis.
In this talk I will present the best up-to-date bounds for the argument of the Riemann zeta-function on the critical line, assuming the Riemann hypothesis. The method applies to other objects related to the Riemann zeta-function and uses certain special families of functions of exponential type. This is a joint work with Vorrapan Chandee (Montreal) and Micah Milinovich (Mississipi).
Thu, 07/03
15:00 		Benjamin Volk Junior Geometry and Topology Seminar Add to calendar SR1
An introduction to Orbifold Bordism
This talk will give a quick and dirty introduction to orbifold bordism. We will start by briefly recalling some basic properties and definitions of orbifolds and sketch (very roughly) how orbifolds can be defined in the language of $ C^\infty $-stacks due to Joyce (after introducing these). We will then review classical bordism theory for manifolds (in some nonstandard way) and discuss which definitions and results generalize to the orbifold case. A word of warning: this talk is intended to be an introduction and wants to give an overview over the subject, so it is likely that we will be sloppy here and there.
Thu, 07/03
14:00 		Ana Paula Santana (University of Coimbra) Representation Theory Seminar Add to calendar L3
Borel- Schur algebras and resolutions of Weyl modules
Using the Borel-Schur algebra, we construct explicit characteristic-free resolutions for Weyl modules for the general linear group. These resolutions provide an answer to the problem, posed in the 80's by A. Akin and D. A. Buchsbaum, of constructing finite explicit and universal resolutions of Weyl modules by direct sums of divided powers. Next we apply the Schur functor to these resolutions and prove a conjecture of Boltje and Hartmann on resolutions of co-Specht modules. This is joint work with I. Yudin.
Thu, 07/03
14:00 		Dr Philip Knight (University of Strathclyde) Computational Mathematics and Applications Add to calendar Rutherford Appleton Laboratory, nr Didcot
The How and Why of Balancing

We consider the problem of taking a matrix A and finding diagonal matrices D and E such that the rows and columns of B = DAE satisfy some specific constraints. Examples of constraints are that

* the row and column sums of B should all equal one;
* the norms of the rows and columns of B should all be equal;
* the row and column sums of B should take values specified by vectors p and q.

Simple iterative algorithms for solving these problems have been known for nearly a century. We provide a simple framework for describing these algorithms that allow us to develop robust convergence results and describe a straightforward approach to accelerate the rate of convergence.

We describe some of the diverse applications of balancing with examples from preconditioning, clustering, network analysis and psephology.

This is joint work with Kerem Akartunali (Strathclyde), Daniel Ruiz (ENSEEIHT, Toulouse) and Bora Ucar (ENS, Lyon).
Thu, 07/03
12:00 		Marc Briane (Université de Rennes) OxPDE Lunchtime Seminar Add to calendar Gibson 1st Floor SR
Characterisation of electric fields in periodic composites
This is work done in collaboration with G.W. Milton and A. Treibergs (University of Utah). Our purpose is to characterise, among all the regular periodic gradient fields, the ones which are isotropically realisable electric fields, namely solutions of a conduction equation with a suitable isotropic conductivity. In any dimension a sufficient condition of realisability is that the gradient field does not vanish. This condition is also necessary in dimension two but not in dimension three. However, when the conductivity also needs to be periodic, the previous condition is shown to be not sufficient. Then, using the associated gradient flow a necessary and sufficient condition for the isotropic realisability in the torus is established and illustrated by several examples. The realisability of the matrix gradient fields and the less regular laminate fields is also investigated.
Wed, 06/03
16:00 		Henry Bradford (University of Oxford) Junior Geometric Group Theory Seminar Add to calendar SR2
From Riches to RAAGs: Special Cube Complexes and the Virtual Haken Theorem (Part 2)
I will outline Bergeron-Wise’s proof that the Virtual Haken Conjecture follows from Wise’s Conjecture on virtual specialness of non-positively curved cube complexes. If time permits, I will sketch some highlights from the proof of Wise’s Conjecture due to Agol and based on the Weak Separation Theorem of Agol-Groves-Manning.
Wed, 06/03
10:30 		Emily Cliff -- Queen's Lecture C Algebra Kinderseminar Add to calendar Queen's College
Factorization structures and the study of G-bundles
We'll provide some motivation for the appearance of factorization algebras in physics, before discussing the definition of a factorization monoid. We'll then review the definition of a principal G-bundle and show how a factorization monoid can help us understand the moduli stack Bun_G of principal G-bundles.
Wed, 06/03
10:15 		Prof. Michael Mackey (McGill) OCCAM Wednesday Morning Event Add to calendar OCCAM Common Room (RI2.28)
Using mathematics to understand, treat, and avoid hematological disease
In this talk aimed at a general audience I will discuss the ways in which we have used mathematical models of the regulation of haematopoiesis (blood cell production) to understand haematological diseases, and suggest successful treatment strategies for these diseases. At the end I will talk about our current work on tailoring chemotherapy so that it has less damaging effects on the haematopoietic system and, consequently, improve the quality of life for patients being treated for a variety of tumours.
Tue, 05/03
17:00 		Prof Iain Gordon (Edinburgh) Algebra Seminar Add to calendar L2
"Galois problems in Schubert Calculus, and related problems"
I will discuss some recent developments in Schubert calculus and a potential relation to classical combinatorics for symmetric groups and possible extensions to complex reflection groups.
Tue, 05/03
17:00 		Olivia Constantin (Kent) Functional Analysis Seminar Add to calendar L3
Carleson embeddings and integration operators of Volterra type on Fock spaces
We consider spaces of entire functions that are $ p $-integrable with respect to a radial weight. Such spaces are usually called Fock spaces, and a classical example is provided by the Gaussian weight. It turns out that a function belongs to some Fock space if and only if its derivative belongs to a Fock space with a (possibly) different weight. Furthermore, we characterize the Borel measures $ \mu $ for which a Fock space is continuously embedded in $ L^q(\mu0) $ with $ q>0 $. We then illustrate the applicability of these results to the study of properties such as boundedness, compactness, Schatten class membership and the invariant subspaces of integration operators of Volterra type acting on Fock spaces. (joint work with Jose Angel Pelaez)

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

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