Forthcoming Seminars

Thu, 21/01/2010
14:30 		Jan Grabowski (Oxford) Representation Theory Seminar Add to calendar L3
Quantizing Grassmannians, Schubert cells and cluster algebras
The quantum Grassmannians and their quantum Schubert cells are well-known and important examples in the study of quantum groups and quantum geometry.  It has been known for some time that their classical counterparts admit cluster algebra structures, which are closely related to positivity properties.  Recently we have shown that in the finite-type cases quantum Grassmannians admit quantum cluster algebra structures, as introduced by Berenstein and Zelevinsky.  We will describe these structures explicitly and also show that they naturally induce quantum cluster algebra structures on the quantum Schubert cells. This is joint work with S. Launois.
Thu, 21/01/2010
16:30 		Jonathan Sherratt (Herriot-Watt University, Edinburgh) Differential Equations and Applications Seminar Add to calendar DH 1st floor SR
Patterns of sources and sinks in the complex Ginzburg-Landau equation
Patterns of sources and sinks in the complex Ginzburg-Landau equation Jonathan Sherratt, Heriot-Watt University The complex Ginzburg-Landau equation is a prototype model for self-oscillatory systems such as binary fluid convection, chemical oscillators, and cyclic predator-prey systems. In one space dimension, many boundary conditions that arise naturally in applications generate wavetrain solutions. In some contexts, the wavetrain is unstable as a solution of the original equation, and it proves necessary to distinguish between two different types of instability, which I will explain: convective and absolute. When the wavetrain is absolutely unstable, the selected wavetrain breaks up into spatiotemporal chaos. But when it is only convectively stable, there is a different behaviour, with bands of wavetrains separated by sharp interfaces known as "sources" and "sinks". These have been studied in great detail as isolated objects, but there has been very little work on patterns of alternating sources and sinks, which is what one typically sees in simulations. I will discuss new results on source-sink patterns, which show that the separation distances between sources and sinks are constrained to a discrete set of possible values, because of a phase-locking condition. I will present results from numerical simulations that confirm the results, and I will briefly discuss applications and the future challenges. The work that I will describe has been done in collaboration with Matthew Smith (Microsoft Research) and Jens Rademacher (CWI, Amsterdam). ——————————
Thu, 21/01/2010
17:00 		Gareth Jones (Manchester) Logic Seminar Add to calendar L3
Counting rational points on certain Pfaffian surfaces.
I'll give a brief survey of what is known about the density of rational points on definable sets in o-minimal expansions of the real field, then discuss improving these results in certain cases.
Fri, 22/01/2010
10:00 		Various (Oxford) Industrial and Interdisciplinary Workshops Add to calendar DH 1st floor SR
Australian Study Group Preview
Each problem to be solved at the study group will be discussed.
Fri, 22/01/2010
11:30 		DH common room coffee at 11:00 and meeting in DHSR3 11:30 Industrial and Interdisciplinary Workshops Add to calendar DH 3rd floor SR
No workshop in this slot due to OCIAM meeting
Fri, 22/01/2010
12:00 		Mat Bullimore (Oxford) Twistor Workshop Add to calendar Gibson 1st Floor SR
BCFW and infrared relations
Fri, 22/01/2010
14:00 		Prof Alain Goriely (OCCAM) Mathematical Biology Seminar Add to calendar L3
The Life of Streptomyces: a Case Study in Microbiomechanics
TBA
Fri, 22/01/2010
14:15 		Bruno Bouchard (University Paris Dauphine) Nomura Seminar Add to calendar DH 1st floor SR
Optimal Control Under Stochastic Target Constraints
Normal 0 false false false EN-GB X-NONE X-NONE MicrosoftInternetExplorer4 /* Style Definitions */ table.MsoNormalTable {mso-style-name:"Table Normal"; mso-tstyle-rowband-size:0; mso-tstyle-colband-size:0; mso-style-noshow:yes; mso-style-priority:99; mso-style-qformat:yes; mso-style-parent:""; mso-padding-alt:0cm 5.4pt 0cm 5.4pt; mso-para-margin:0cm; mso-para-margin-bottom:.0001pt; mso-pagination:widow-orphan; font-size:11.0pt; font-family:"Calibri","sans-serif"; mso-ascii-font-family:Calibri; mso-ascii-theme-font:minor-latin; mso-fareast-font-family:"Times New Roman"; mso-fareast-theme-font:minor-fareast; mso-hansi-font-family:Calibri; mso-hansi-theme-font:minor-latin; mso-bidi-font-family:"Times New Roman"; mso-bidi-theme-font:minor-bidi;} We study a class of Markovian optimal stochastic control problems in which the controlled process $ Z^\nu $ is constrained to satisfy an a.s.~constraint $ Z^\nu(T)\in G\subset \R^{d+1} $ $ \Pas $ at some final time $ T>0 $.  When the set is of the form $ G:=\{(x,y)\in \R^d\x \R~:~g(x,y)\ge 0\} $, with $ g $ non-decreasing in $ y $, we provide a Hamilton-Jacobi-Bellman  characterization of the associated value function. It gives rise to a state constraint problem where the constraint can be expressed in terms of an auxiliary value function $ w $ which characterizes the set $ D:=\{(t,Z^\nu(t))\in [0,T]\x\R^{d+1}~:~Z^\nu(T)\in G\;a.s. $ for some $ \nu\} $. Contrary to standard state constraint problems, the domain $ D $ is not given a-priori and we do not need to impose conditions on its boundary. It is naturally incorporated in the auxiliary value function $ w $ which is itself a viscosity solution of a non-linear parabolic PDE.  Applying ideas recently developed in Bouchard, Elie and Touzi (2008), our general result also allows to consider optimal control problems with moment constraints of the form $ \Esp{g(Z^\nu(T))}\ge 0 $ or $ \Pro{g(Z^\nu(T))\ge 0}\ge p $.
Fri, 22/01/2010
16:30 		Professor Don Zagier (Max-Planck Institut) Colloquia Add to calendar L2
Modular Forms, K-theory and Knots
Many problems from combinatorics, number theory, quantum field theory and topology lead to power series of a special kind called q-hypergeometric series. Sometimes, like in the famous Rogers-Ramanujan identities, these q-series turn out to be modular functions or modular forms. A beautiful conjecture of W. Nahm, inspired by quantum theory, relates this phenomenon to algebraic K-theory. In a different direction, quantum invariants of knots and 3-manifolds also sometimes seem to have modular or near-modular properties, leading to new objects called "quantum modular forms".
Mon, 25/01/2010
12:00 		Yang-Hui He (Oxford) String Theory Seminar Add to calendar L3
Scanning through Heterotic Vacua
We discuss some recent progress in obtaining the exact spectrum of the MSSM from a generalized embedding of the heterotic string. Utilizing current developments in algebraic geometry, especially algorithmic, we search through the landscape of vector bundles over Calabi-Yau manifolds for a special corner wherein such exact models may be found.
Mon, 25/01/2010
14:15 		Samy Tindel (Universite henri Poincare (Nancy)) Stochastic Analysis Seminar Add to calendar Eagle House
On Rough Path Constructions for Fractional Brownian Motion
Abstract: In this talk we will review some recentadvances in order to construct geometric or weakly geometric rough paths abovea multidimensional fractional Brownian motion, with a special emphasis on thecase of a Hurst parameter H<1/4. In this context, the natural piecewiselinear approximation procedure of Coutin and Qian does not converge anymore,and a less physical method has to be adopted. We shall detail some steps ofthis construction for the simplest case of the Levy area. 
Mon, 25/01/2010
15:45 		Andrzej Zuk (Paris) Topology Seminar Add to calendar L3
L^2 Betti numbers of closed manifolds
TBA
Mon, 25/01/2010
15:45 		Anne De Bouard (VMAP) Stochastic Analysis Seminar Add to calendar Eagle House
Stochastic nonlinear Schrodinger equations and modulation of solitary waves
In this talk, we will focus on the asymptotic behavior in time of the solution of a model equation for Bose-Einstein condensation, in the case where the trapping potential varies randomly in time. The model is the so called Gross-Pitaevskii equation, with a quadratic potential with white noise fluctuations in time whose amplitude tends to zero. The initial condition is a standing wave solution of the unperturbed equation We prove that up to times of the order of the inverse squared amplitude the solution decomposes into the sum of a randomly modulatedmodulation parameters. In addition, we show that the first order of the remainder, as the noise amplitude goes to zero, converges to a Gaussian process, whose expected mode amplitudes concentrate on the third eigenmode generated by the Hermite functions, on a certain time scale, as the frequency of the standing wave of the deterministic equation tends to its minimal value.
Mon, 25/01/2010
16:00 		James Maynard (Mathematical Institute Oxford) Junior Number Theory Seminar Add to calendar SR1
The Hardy–Littlewood Conjectures
Mon, 25/01/2010
17:00 		Mikhail Korobkov (Sobolev Institute of Mathematics) Partial Differential Equations Seminar Add to calendar Gibson 1st Floor SR
Properties of the $ C^1 $-smooth functions whose gradient range has topological dimension 1
In the talk we discuss some results of [1]. We apply our previous methods [2] to geometry and to the mappings with bounded distortion. Theorem 1.  Let $ v:\Omega\to\mathbb{R} $ be a $ C^1 $-smooth function on a domain (open connected set) $ \Omega\subset\mathbb{R}^2 $. Suppose
$$ (1)\qquad \operatorname{Int} \nabla v(\Omega)=\emptyset. $$
Then $ \operatorname{meas}\nabla v(\Omega)=0 $. Here $ \operatorname{Int}E $ is the interior of $ {E} $, $ \operatorname{meas} E $ is the Lebesgue measure of $ {E} $. Theorem 1 is a straight consequence of the following two results. Theorem 2 [2].  Let $ v:\Omega\to\mathbb{R} $ be a $ C^1 $-smooth function on a domain $ \Omega\subset\mathbb{R}^2 $. Suppose (1) is fulfilled. Then the graph of $ v $ is a normal developing surface.  Recall that a $ C^1 $-smooth manifold $ S\subset\mathbb{R}^3 $ is called  a normal developing surface [3] if for any $ x_0\in S $ there exists a straight segment $ I\subset S $ (the point $ x_0 $ is an interior point of $ I $) such that the tangent plane to $ S $ is stationary along $ I $. Theorem 3.  The spherical image of any $ C^1 $-smooth normal developing surface $ S\subset\mathbb{R}^3 $ has the area (the Lebesgue measure) zero. Recall that the spherical image of a surface $ S $ is the set $ \{\mathbf{n}(x)\mid x\in S\} $, where $ \mathbf{n}(x) $ is the unit normal vector to $ S $ at the point~$ x $. From Theorems 1–3 and the classical results of A.V. Pogorelov (see [4, Chapter 9]) we obtain the following corollaries Corollary 4. Let the spherical image of a $ C^1 $-smooth surface $ S\subset\mathbb{R}^3 $ have no interior points. Then this surface is a surface of zero extrinsic curvature in the sense of Pogorelov. Corollary 5. Any $ C^1 $-smooth normal developing surface $ S\subset\mathbb{R}^3 $ is a surface of zero extrinsic curvature in the sense of Pogorelov. Theorem 6. Let $ K\subset\mathbb{R}^{2\times 2} $ be a compact set and the topological dimension of $ K $ equals 1. Suppose there exists $ \lambda&gt; 0 $ such that $ \forall A,B\in K, \, \, |A-B|^2\le\lambda\det(A-B). $ Then for any Lipschitz mapping $ f:\Omega\to\mathbb R^2 $ on a domain $ \Omega\subset\mathbb R^2 $ such that $ \nabla f(x)\in K $ a.e. the identity $ \nabla f\equiv\operatorname{const} $ holds. Many partial cases of Theorem 6 (for instance, when $ K=SO(2) $ or $ K $ is a segment) are well-known (see, for example, [5]). The author was supported by the Russian Foundation for Basic Research (project no. 08-01-00531-a).   [1] {Korobkov M.\,V.,} {“Properties of the $ C^1 $-smooth functions whose gradient range has topological dimension~1,” Dokl. Math., to appear.} [2] {Korobkov M.\,V.} {“Properties of the $ C^1 $-smooth functions with nowhere dense gradient range,” Siberian Math. J., 48, No.~6, 1019–1028 (2007).} [3] { Shefel$ {}' $ S.\,Z.,} {“$ C^1 $-Smooth isometric imbeddings,” Siberian Math. J., 15, No.~6, 972–987 (1974).} [4] {Pogorelov A.\,V.,} {Extrinsic geometry of convex surfaces, Translations of Mathematical Monographs. Vol. 35. Providence, R.I.: American Mathematical Society (AMS). VI (1973).} [5] {Müller ~S.,} {Variational Models for Microstructure and Phase Transitions. Max-Planck-Institute for Mathematics in the Sciences. Leipzig (1998) (Lecture Notes, No.~2. http://www.mis.mpg.de/jump/publications.html).}
Tue, 26/01/2010
12:00 		Jerzy Lewandowski (Warsaw) Relativity Seminar Add to calendar L3
Gravity Quantized
Canonical quantization of gravitational field will beconsidered. Examples for which the procedure can be completed (without reducingthe degrees of freedom) will be presented and discussed. The frameworks appliedwill be: Loop Quantum Gravity, relational construction of the Dirac observablesand deparametrization. 
Tue, 26/01/2010
13:00 		Trevor Wood (OCIAM Oxford) Junior Applied Mathematics Seminar Add to calendar DH 1st floor SR
Submarine Hunting and Other Applications of the Mathematics of Tracking
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.
Tue, 26/01/2010
14:00 		Dr Konstantinos Zyglakis (OCCAM (Oxford)) Computational Mathematics and Applications Add to calendar 3WS SR
On the existence of modified equations for stochastic differential equations
In this talk we describe a general framework for deriving modified equations for stochastic differential equations with respect to weak convergence. We will start by quickly recapping of how to derive modified equations in the case of ODEs and describe how these ideas can be generalized in the case of SDEs. Results will be presented for first order methods such as the Euler-Maruyama and the Milstein method. In the case of linear SDEs, using the Gaussianity of the underlying solutions, we will derive a SDE that the numerical method solves exactly in the weak sense. Applications of modified equations in the numerical study of Langevin equations and in the calculation of effective diffusivities will also be discussed.
Tue, 26/01/2010
14:00 		Richard Thomas (Imperial College London) Algebraic and Symplectic Geometry Seminar Add to calendar SR1
(HoRSe seminar) GW/stable pairs on K3 surfaces
The Katz-Klemm-Vafa formula is a conjecture expressing Gromov-Witten invariants of K3 surfaces in terms of modular forms. In genus 0 it reduces to the (proved) Yau-Zaslow formula. I will explain how the correspondence between stable pairs and Gromov-Witten theory for toric 3-folds (proved by Maulik-Oblomkov-Okounkov-Pandharipande), some calculations with stable pairs (due to Kawai-Yoshioka) and some deformation theory lead to a proof of the KKV formula. (This is joint work with Davesh Maulik and Rahul Pandharipande. Only they understand the actual formulae. People who like modular forms are not encouraged to come to this talk.)

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

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