Past Seminars

Thu, 09/05
15:00 		Alejandro Betancourt Junior Geometry and Topology Seminar Add to calendar SR1
A brief survey on Ricci flow
Based on ideas from Eells and Sampson, the Ricci flow was introduced by R. Hamilton in 1982 to try to prove Thurston's Geometrization Conjecture (a path which turned out to be successful). In this talk we will introduce the Ricci flow equation and view it as a modified heat flow. Using this we will prove the basic results on existence and uniqueness, and gain some insight into the evolution of various geometric quantities under Ricci flow. With this results we will proceed to define Perelman's $ \mathcal{F} $ and $ \mathcal{W} $ entropy functionals to view the Ricci flow as a gradient flow. If time permits we will briefly sketch some results from Cheeger and Gromov's compactness theory, which, along with the entropy functionals, alow us to blow up singularities.This is meant to be an introductory talk so I will try to develop as much geometric intuition as possible and stay away from technical calculations.
Thu, 09/05
14:00 		Dr Jennifer Ryan (University of East Anglia) Computational Mathematics and Applications Add to calendar Gibson Grd floor SR
Superconvergence for Discontinuous Galerkin solutions: Making it Useful
The discontinuous Galerkin (DG) method has recently become one of the most widely researched and utilized discretization methodologies for solving problems in science and engineering. It is fundamentally based upon the mathematical framework of variational methods, and provides hope that computationally fast, efficient and robust methods can be constructed for solving real-world problems. By not requiring that the solution to be continuous across element boundaries, DG provides a flexibility that can be exploited both for geometric and solution adaptivity and for parallelization. This freedom comes at a cost. Lack of smoothness across elements can hamper simulation post-processing like feature extraction and visualization. However, these limitations can be overcome by taking advantage of an additional property of DG - that of superconvergence. Superconvergence can aid in addressing the lack of continuity through the development of Smoothness-Increasing Accuracy-Conserving (SIAC) filters. These filters respect the mathematical properties of the data while providing levels of smoothness so that commonly used visualization tools can be used appropriately, accurately, and efficiently. In this talk, the importance of superconvergence in applications such as visualization will be discussed as well as overcoming the mathematical barriers in making superconvergence useful for applications.
Thu, 09/05
14:00 		Christopher Dodd Representation Theory Seminar Add to calendar L3
Modules over Algebraic Quantizations and representation theory
Recently, there has been a great deal of interest in the theory of modules over algebraic quantizations of so-called symplecticresolutions. In this talk I'll discuss some new work -joint, and very much in progress- that open the door to giving a geometric description to certain categories of such modules; generalizing classical theorems of Kashiwara and Bernstein in the case of D-modules on an algebraic variety.
Thu, 09/05
12:01 		Šárka Nečasová (Academy of Sciences of the Czech Republic) OxPDE Lunchtime Seminar Add to calendar Gibson 1st Floor SR
Weak solutions to the barotropic Navier-Stokes system with slip boundary conditions in time dependent domains and incompressible limits
We consider the compressible (barotropic) Navier-Stokes system on time-dependent domains, supplemented with slip boundary conditions. Our approach is based on penalization of the boundary behaviour, viscosity, and the pressure in the weak formulation. Global-in-time weak solutions are obtained. Secondly, we suppose that the characteristic speed of the fluid is domi- nated by the speed of sound and perform the low Mach number limit in the framework of weak solutions. The standard incompressible Navier-Stokes system is identified as the target problem. References:
    [1] E. Feireisl, O. Kreml, S. Nečasová, J. Neustupa, and J. Stebel. Weak solutions to the barotropic NavierStokes system with slip boundary conditions in time dependent domains. J. Differential Equations, 254:125–140, 2013.
    [2] E. Feireisl, O. Kreml, S. Nečasová, J. Neustupa, and J. Stebel. Incompressible limits of fluids excited by moving boundaries. Submitted
Wed, 08/05
16:00 		David Hume (University of Oxford) Junior Geometric Group Theory Seminar Add to calendar SR2
Amenable hyperbolic groups
The integers (while wonderful in many others respects) do not make for fascinating Geometric Group Theory. They are, however, essentially the only infinite finitely generated group which is both hyperbolic and amenable. In the class of locally compact topological groups, the intersection of these two notions is richer, and the major aim of this talk will be to give the structure of a classification of such groups due to Caprace-de Cornulier-Monod-Tessera, beginning with Milnor's proof that any connected Lie group admitting a left-invariant negatively curved Riemannian metric is necessarily soluble.
Wed, 08/05
11:30 		Thomas Wasserman Algebra Kinderseminar Add to calendar Queen's College
Categorification
Categorification is a fancy word for a process that is pretty ubiquitous in mathematics, though it is usually not referred to as "a thing". With the advent of higher category theory it has, however, become "a thing". I will explain what people mean by this "thing" (sneak preview: it involves replacing sets by categories) and hopefully convince you it is not quite as alien as it may seem and maybe even tempt you to let it infect some of your maths. I'll then explain how this fits into the context of higher categories.
Tue, 07/05
17:00 		Garth Dales (Lancaster) Functional Analysis Seminar Add to calendar L3
C(X) as a bidual space
Tue, 07/05
15:45 		Jesse Wolfson (Northwestern) Algebraic and Symplectic Geometry Seminar Add to calendar L3
Descent for n-Bundles
Given a Lie group $ G $, one can construct a principal $ G $-bundle on a manifold $ M $ by taking a cover $ U\to M $, specifying a transition cocycle on the cover, and then descending the trivialized bundle $ U \times G $ along the cocycle. We demonstrate the existence of an analogous construction for local $ n $-bundles for general $ n $. We establish analogues for simplicial Lie groupoids of Moore's results on simplicial groups; these imply that bundles for strict Lie $ n $-groupoids arise from local $ n $-bundles. We conclude by constructing a simple finite dimensional model of the Lie 2-group String($ n $) using cohomological data.
Tue, 07/05
14:30 		Mat Bullimore (Oxford) Twistor Workshop Add to calendar Gibson 1st Floor SR
The GKP string
Tue, 07/05
14:30 		Joel Ouaknine (University of Oxford) Combinatorial Theory Seminar Add to calendar L3
Positivity problems for low-order linear recurrence sequences
We consider two decision problems for linear recurrence sequences(LRS) over the integers, namely the Positivity Problem (are all terms of a given LRS positive?) and the Ultimate Positivity Problem (are all but finitely many terms of a given LRS positive?). We show decidability of both problems for LRS of order 5 or less, and for simple LRS (i.e. whose characteristic polynomial has no repeated roots) of order 9 or less. Moreover, we show by way of hardness that extending the decidability of either problem to LRS of order 6 would entail major breakthroughs in analytic number theory, more precisely in the field of Diophantine approximation of transcendental numbers.This talk is based on a recent paper, available athttp://www.cs.ox.ac.uk/people/joel.ouaknine/publications/positivity13abs.html joint with James Worrell and Matt Daws.
Tue, 07/05
14:15 		Dr Dan Rowlands (Cumulus/PCE Investors) Geophysical and Nonlinear Fluid Dynamics Seminar Add to calendar Dobson Room, AOPP
Using probabilistic weather forecasts for practical decision making: Thoughts from an energy trading perspective
I'm going to make the talk more of a general discussion about weather forecasts and how they are used for practical decision making in energy trading in the first half, then spend the second half focusing on how we think about assessing and using the notion of state dependent predictability in our decision making process.
Tue, 07/05
12:00 		Marshall Slemrod (University of Wisconsin) OxPDE Special Seminar Add to calendar Gibson 1st Floor SR
Higher dimensional isometric embedding
I will present new results on local smooth embedding of Riemannian manifolds of dimension $ n $ into Euclidean space of dimension $ n(n+1)/2 $.  This part of ac joint project with G-Q Chen ( OxPDE), Jeanne Clelland ( Colorado), Dehua Wang ( Pittsburgh), and Deane Yang ( Poly-NYU).
Tue, 07/05
00:00 		Andreas Doring Algebra Seminar Add to calendar L2
Spectral presheaves as generalised (Gelfand) spectra
The spectral presheaf of a nonabelian von Neumann algebra or C*-algebra was introduced as a generalised phase space for a quantum system in the so-called topos approach to quantum theory. Here, it will be shown that the spectral presheaf has many features of a spectrum of a noncommutative operator algebra (and that it can be defined for other classes of algebras as well). The main idea is that the spectrum of a nonabelian algebra may not be a set, but a presheaf or sheaf over the base category of abelian subalgebras. In general, the spectral presheaf has no points, i.e., no global sections. I will show that there is a contravariant functor from unital C*-algebras to their spectral presheaves, and that a C*-algebra is determined up to Jordan *-isomorphisms by its spectral presheaf in many cases. Moreover, time evolution of a quantum system can be described in terms of flows on the spectral presheaf, and commutators show up in a natural way. I will indicate how combining the Jordan and Lie algebra structures may lead to a full reconstruction of nonabelian C*- or von Neumann algebra from its spectral presheaf.
Mon, 06/05
17:00 		Eduard Feireisl (institute of mathematics of the Academy of sciences of the Czech Republic) Partial Differential Equations Seminar Add to calendar Gibson 1st Floor SR
Multiple scales in the dynamics of compressible fluids
We discuss several singular limits for a scaled system of equations (barotropic Navier-Stokes system), where the characteristic numbers become small or “infinite”. In particular, we focus on the situations relevant in certain geophysical models with low Mach, large Rossby and large Reynolds numbers. The limit system is rigorously identified in the framework of weak solutions. The relative entropy inequality and careful analysis of certain oscillatory integrals play crucial role.
Mon, 06/05
14:15 		Nigel Hitchin (Oxford) Geometry and Analysis Seminar Add to calendar L3
Real Higgs bundles and mirror symmetry.
Mon, 06/05
12:00 		Mario Garcia Fernandez (EPFL) String Theory Seminar Add to calendar L3
Torsion-free generalized connections and heterotic supergravity
I will present a new derivation of the equations of motion of Heterotic supergravity using generalized geometry, inspired by the geometric description of 11-dimensional and type II supergravity by Coimbra, Strickland-Constable and Waldram. From a mathematical point of view, this arises from the study of torsion-free generalized connections on a non-exact Courant algebroid. We will find that the freedom provided by the dilaton field in the physical theory can be interpreted as the freedom of choice of Levi-Civita connection in generalized geometry.
Fri, 03/05
17:00 		Mikhail Korobkov (Sobolev Institute of Mathematics, Novosibirsk) Partial Differential Equations Seminar Add to calendar Gibson 1st Floor SR
The Morse-Sard Theorem for $ W^{n,1} $ Sobolev functions on $ \mathbb R^n $ and applications in fluid mechanics
The talk is based on the joint papers [Bourgain J., Korobkov M.V. and Kristensen~J.: Journal fur die reine und angewandte Mathematik (Crelles Journal). DOI: 10.1515/crelle-2013-0002]  and  [Korobkov~M.V., Pileckas~K. and Russo~R.: arXiv:1302.0731, 4 Feb 2013] We establish Luzin $ N $ and Morse–Sard properties for functions from the Sobolev space $ W^{n,1}(\mathbb R^n) $. Using these results we prove that almost all level sets are finite disjoint unions of $ C^1 $-smooth compact manifolds of dimension $ n-1 $. These results remain valid also within the larger space of functions of bounded variation $ BV_n(\mathbb R^n) $. As an application, we study the nonhomogeneous boundary value problem for the Navier–Stokes equations of steady motion of a viscous incompressible fluid in arbitrary bounded multiply connected plane or axially-symmetric spatial domains. We prove that this problem has a solution under the sole necessary condition of zero total flux through the boundary. The problem was formulated by Jean Leray 80 years ago. The proof of the main result uses Bernoulli's law for a weak solution to the Euler equations based on the above-mentioned Morse-Sard property for Sobolev functions.

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

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