Forthcoming Seminars

Mon, 31/05/2010
14:15 		Mark Andrea de Cataldo (Stony Brook) Geometry and Analysis Seminar Add to calendar L3
Topology of Hitchin systems and Hodge theory of character varieties
Mon, 31/05/2010
16:00 		James Maynard (University of Oxford) Junior Number Theory Seminar Add to calendar SR1
Looking at Elliptic L-functions via Modular Symbols
We have seen that L-functions of elliptic curves of conductor N coincide exactly with L-functions of weight 2 newforms of level N from the Modularity Theorem. We will show how, using modular symbols, we can explicitly compute bases of newforms of a given level, and thus investigate L-functions of an elliptic curve of given conductor. In particular, such calculations allow us to numerically test the Birch-Swinnerton-Dyer conjecture.
Mon, 31/05/2010
17:00 		James Glimm (SUNY at Stony Brook) Partial Differential Equations Seminar Add to calendar Gibson 1st Floor SR
Mathematical, Numerical and Physical Principles for Turbulent Mixing
Numerical approximation of fluid equations are reviewed. We identify numerical mass diffusion as a characteristic problem in most simulation codes. This fact is illustrated by an analysis of fluid mixing flows. In these flows, numerical mass diffusion has the effect of over regularizing the solution. Simple mathematical theories explain this difficulty. A number of startling conclusions have recently been observed, related to numerical mass diffusion. For a flow accelerated by multiple shock waves, we observe an interface between the two fluids proportional to Delta x-1, that is occupying a constant fraction of the available mesh degrees of freedom. This result suggests
  • (a) nonconvergence for the unregularized mathematical problem or
  • (b) nonuniqueness of the limit if it exists, or
  • (c) limiting solutions only in the very weak form of a space time dependent probability distribution.
The cure for the pathology (a), (b) is a regularized solution, in other words inclusion of all physical regularizing effects, such as viscosity and physical mass diffusion. We do not regard (c) as a pathology, but an inherent feature of the equations. In other words, the amount and type of regularization of an unstable flow is of central importance. Too much regularization, with a numerical origin, is bad, and too little, with respect to the physics, is also bad. For systems of equations, the balance of regularization between the distinct equations in the system is of central importance. At the level of numerical modeling, the implication from this insight is to compute solutions of the Navier-Stokes, not the Euler equations. Resolution requirements for realistic problems make this solution impractical in most cases. Thus subgrid transport processes must be modeled, and for this we use dynamic models of the turbulence modeling community. In the process we combine and extend ideas of the capturing community (sharp interfaces or numerically steep gradients) with conventional turbulence models, usually applied to problems relatively smooth at a grid level. The numerical strategy is verified with a careful study of a 2D Richtmyer-Meshkov unstable turbulent mixing problem. We obtain converged solutions for such molecular level mixing quantities as a chemical reaction rate. The strategy is validated (comparison to laboratory experiments) through the study of 3D Rayleigh-Taylor unstable flows.
Tue, 01/06/2010
13:15 		Sara-Jane Dunn (Oxford) Junior Applied Mathematics Seminar Add to calendar DH 1st floor SR
Towards a Colonic Crypt Model with a Realistic, Deformable Geometry

Colorectal cancer (CRC) is one of the leading causes of cancer-related death worldwide, demanding a response from scientists and clinicians to understand its aetiology and develop effective treatment. CRC is thought to originate via genetic alterations that cause disruption to the cellular dynamics of the crypts of Lieberkűhn, test-tube shaped glands located in both the small and large intestine, which are lined with a monolayer of epithelial cells. It is believed that during colorectal carcinogenesis, dysplastic crypts accumulate mutations that destabilise cell-cell contacts, resulting in crypt buckling and fission. Once weakened, the corrupted structure allows mutated cells to migrate to neighbouring crypts, to break through to the underlying tissue and so aid the growth and malignancy of a tumour. To provide further insight into the tissue-level effects of these genetic mutations, a multi-scale model of the crypt with a realistic, deformable geometry is required. This talk concerns the progress and development of such a model, and its usefulness as a predictive tool to further the understanding of interactions across spatial scales within the context of colorectal cancer.
Tue, 01/06/2010
14:00 		Denis-Charles Cisinski (Paris 13) Algebraic and Symplectic Geometry Seminar Add to calendar L2
(HoRSe seminar) Motivic sheaves over excellent schemes
Starting from Morel and Voevodsky's stable homotopy theory of schemes, one defines, for each noetherian scheme of finite dimension $ X $, the triangulated category $ DM(X) $ of motives over $ X $ (with rational coefficients). These categories satisfy all the the expected functorialities (Grothendieck's six operations), from which one deduces that $ DM $ also satisfies cohomological proper descent. Together with Gabber's weak local uniformisation theorem, this allows to prove other expected properties (e.g. finiteness theorems, duality theorems), at least for motivic sheaves over excellent schemes.
Tue, 01/06/2010
14:15 		Prof. Herbert Huppert FRS (University of Cambridge) Geophysical and Nonlinear Fluid Dynamics Seminar Add to calendar Dobson Room, AOPP
Climate mitigation by carbon dioxide sequestration
Tue, 01/06/2010
14:30 		Tom Sanders (Cambridge) Combinatorial Theory Seminar Add to calendar L3
Subspaces in sumsets: a problem of Bourgain and Green
Suppose that $ A \subset \mathbb F_2^n $ has density $ \Omega(1) $. How large a subspace is $ A+A:=\{a+a’:a,a’ \in A\} $ guaranteed to contain? We discuss this problem and how the the result changes as the density approaches $ 1/2 $.
Tue, 01/06/2010
15:45 		Denis-Charles Cisinski (Paris 13) Algebraic and Symplectic Geometry Seminar Add to calendar L3
(HoRSe seminar) Realizations of motives
A categorification of cycle class maps consists to define realization functors from constructible motivic sheaves to other categories of coefficients (e.g. constructible $ l $-adic sheaves), which are compatible with the six operations. Given a field $ k $, we will describe a systematic construction, which associates, to any cohomology theory $ E $, represented in $ DM(k) $, a triangulated category of constructible $ E $-modules $ D(X,E) $, for $ X $ of finite type over $ k $, endowed with a realization functor from the triangulated category of constructible motivic sheaves over $ X $. In the case $ E $ is either algebraic de Rham cohomology (with $ char(k)=0 $), or $ E $ is $ l $-adic cohomology, one recovers in this way the triangulated categories of $ D $-modules or of $ l $-adic sheaves. In the case $ E $ is rigid cohomology (with $ char(k)=p>0 $), this construction provides a nice system of $ p $-adic coefficients which is closed under the six operations.
Tue, 01/06/2010
17:00 		Peter Jorgensen (Newcastle) Algebra Seminar Add to calendar L2
The cluster category of Dynkin type $ A_\infty $
   The cluster category of Dynkin type $ A_\infty $ is a ubiquitous object with interesting properties, some of which will be explained in this talk.
   Let us denote the category by $ \mathcal{D} $. Then $ \mathcal{D} $ is a 2-Calabi-Yau triangulated category which can be defined in a standard way as an orbit category, but it is also the compact derived category $ D^c(C^{∗}(S^2;k)) $ of the singular cochain algebra $ C^*(S^2;k) $ of the 2-sphere $ S^{2} $. There is also a “universal” definition: $ \mathcal{D} $ is the algebraic triangulated category generated by a 2-spherical object. It was proved by Keller, Yang, and Zhou that there is a unique such category.
  Just like cluster categories of finite quivers, $ \mathcal{D} $ has many cluster tilting subcategories, with the crucial difference that in $ \mathcal{D} $, the cluster tilting subcategories have infinitely many indecomposable objects, so do not correspond to cluster tilting objects.
   The talk will show how the cluster tilting subcategories have a rich combinatorial structure: They can be parametrised by “triangulations of the $ \infty $-gon”. These are certain maximal collections of non-crossing arcs between non-neighbouring integers.
  This will be used to show how to obtain a subcategory of $ \mathcal{D} $ which has all the properties of a cluster tilting subcategory, except that it is not functorially finite. There will also be remarks on how $ \mathcal{D} $ generalises the situation from Dynkin type $ A_n $ , and how triangulations of the $ \infty $-gon are new and interesting combinatorial objects.
Wed, 02/06/2010
10:10 		Rob Style (Oxford) OCCAM Wednesday Morning Event Add to calendar OCCAM Common Room (RI2.28)
The Theory and Applications of the Premelting Phenomenon in Ice
Wed, 02/06/2010
11:30 		Amaia Zugadi Reizabal (Euskal Herriko Unibertsitatea) Algebra Kinderseminar Add to calendar ChCh, Tom Gate, Room 2
The Gupta–Sidki group: some old and new results
Thu, 03/06/2010
12:00 		Oscar Randal-Williams (Oxford) Junior Geometry and Topology Seminar Add to calendar SR1
Cohomology of moduli spaces
I will discuss what is known about the cohomology of several moduli spaces coming from algebraic and differential geometry. These are: moduli spaces of non-singular curves (= Riemann surfaces) $ M_g $, moduli spaces of nodal curves $ \overline{M}_g $, moduli spaces of holomorphic line bundles on curves $ Hol_g^k \to M_g $, and the universal Picard varieties $ Pic^k_g \to M_g $. I will construct characteristic classes on these spaces, talk about their homological stability, and try to explain why the constructed classes are the only stable ones. If there is time I will also talk about the Picard groups of these moduli spaces. Much of this work is due to other people, but some is joint with J. Ebert.
Thu, 03/06/2010
14:00 		Dr Garth Wells (University of Cambridge) Computational Mathematics and Applications Add to calendar 3WS SR
Automated computational modelling
Thu, 03/06/2010
16:00 		Tony Scholl (Cambridge) Number Theory Seminar Add to calendar L3
Hypersurfaces and the Weil conjectures
Thu, 03/06/2010
16:30 		Alexander Movchan (University of Liverpool) Differential Equations and Applications Seminar Add to calendar DH 1st floor SR
Structured media with defects: asymptotic models and localisation
Bloch Floquet waves are considered in structured media. Such waves are dispersive and the dispersion diagrams contain stop bands. For an example of a harmonic lattice, we discuss dynamic band gap Green’s functions characterised by exponential localisation. This is followed by simple models of exponentially localised defect modes. Asymptotic models involving uniform asymptotic approximations of physical fields in structured media are compared with homogenisation approximations.
Thu, 03/06/2010
17:00 		Andreas Doering (Oxford) Logic Seminar Add to calendar L3
Topos Quantum Logic
Standard quantum logic, as intitiated by Birkhoff and von Neumann, suffers from severe problems which relate quite directly to interpretational issues in the foundations of quantum theory. In this talk, I will present some aspects of the so-called topos approach to quantum theory, as initiated by Isham and Butterfield, which aims at a mathematical reformulation of quantum theory and provides a new, well-behaved form of quantum logic that is based upon the internal logic of a certain (pre)sheaf topos.

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

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