Forthcoming Seminars
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Mon, 26/04/2010 12:00 |
Yang-Hui He (Oxford) |
String Theory Seminar  |
L3 |
| We investigate certain arithmetic properties of field theories. In particular, we study the vacuum structure of supersymmetric gauge theories as algebraic varieties over number fields of finite characteristic. Parallel to the Plethystic Programme of counting the spectrum of operators from the complex geometry, we investigate the Hasse-Weil zeta functions and the associated Dirichlet expansions. We find curious dualities wherein the geometrical properties and asymptotic behaviour of one gauge theory is governed by the number theoretic nature of another. | |||
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Mon, 26/04/2010 12:30 |
Yong-Kum Cho (Chung-Ang University) |
OxPDE Lunchtime Seminar |
Gibson 1st Floor SR |
| In this talk we consider the Boltzmann equation arising in gas dynamics with long-range interactions. Mathematically, it involves bilinear singular integral operators known as collision operators with non-cutoff collision kernels. As for the associated Cauchy problem, we develop a theory of weak solutions and present some of its a priori estimates related with physical quantities including the energy and moments. | |||
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Mon, 26/04/2010 13:00 |
Nicholas Touikan (UQÀM) |
Junior Geometric Group Theory Seminar |
SR1 |
| Take a group G and split it as the fundamental group of a graph of groups, then take the vertex groups and split them as fundamental groups of graphs of groups etc. If at some point you end up with a collection of unsplittable groups, then you have a hierarchy. Haken showed that for any 3-manifold M with an incompressible surface S, one can cut M along S and and then find other incompressible surfaces in M and cut again, and repeating this process one eventually obtains a collection of balls. Analogously, Delzant and Potyagailo showed that for any finitely presented group without 2-torsion and a certain sensible class E of subgroups of G, G admits a hierarchy where the edge groups of the splittings lie in E. I really like their proof and I will present it. | |||
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Mon, 26/04/2010 14:15 |
Franco Flandoli |
Stochastic Analysis Seminar |
Eagle House |
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Mon, 26/04/2010 14:15 |
David Calderbank (Bath) |
Geometry and Analysis Seminar |
L3 |
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Mon, 26/04/2010 15:45 |
David Ayala (Copenhagen) |
Topology Seminar |
L3 |
| The talk will begin with a brief account of the construction of string topology operations. I will point out some mysteries with the formulation of these operations, such as the role of (moduli) of surfaces, and pose some questions. The remainder of the talk will address these issues. In particular, I will sketch some ideas for a higher-dimensional version of string topology. For instance, (1) I will describe an E_{d+1} algebra structure on the (shifted) homology of the free mapping space H_*(Map(S^d,M^n)) and (2) I will outline how to obtain operations H_*(Map(P,M)) -> H_*(Map(Q,M)) indexes by a moduli space of zero-surgery data on a smooth d-manifold P with resulting surgered manifold Q. | |||
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Mon, 26/04/2010 15:45 |
Olasunkanmi Obanubi (Imperial College London) |
Stochastic Analysis Seminar |
Eagle House |
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Mon, 26/04/2010 17:00 |
Norman Dancer (University of Sydney) |
Partial Differential Equations Seminar |
Gibson 1st Floor SR |
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Tue, 27/04/2010 15:45 |
Jonny Evans (Cambridge) |
Algebraic and Symplectic Geometry Seminar |
L3 |
| Lagrangian submanifolds are an important class of objects in symplectic geometry. They arise in diverse settings: as vanishing cycles in complex algebraic geometry, as invariant sets in integrable systems, as Heegaard tori in Heegaard-Floer theory and of course as "branes" in the A-model of mirror symmetry. We ask the difficult question: when are two Lagrangian submanifolds isotopic? Restricting to the simplest case of Lagrangian spheres in rational surfaces we will give examples where this question has a complete answer. We will also give some very pictorial examples (due to Seidel) illustrating how two Lagrangians can fail to be isotopic. | |||
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Tue, 27/04/2010 17:00 |
Andrei Marcus (Cluj) |
Algebra Seminar |
L2 |
| The topic of this talk is the representation theory of Hopf-Galois extensions. We consider the following questions. Let H be a Hopf algebra, and A, B right H-comodule algebras. Assume that A and B are faithfully flat H-Galois extensions. 1. If A and B are Morita equivalent, does it follow that the subalgebras A^coH and B^coH of H-coinvariant elements are also Morita equivalent? 2. Conversely, if A^coH and B^coH are Morita equivalent, when does it follow that A and B are Morita equivalent? As an application, we investigate H-Morita autoequivalences of the H-Galois extension A, introduce the concept of H-Picard group, and we establish an exact sequence linking the H-Picard group of A and the Picard group of A^coH.(joint work with Stefaan Caenepeel) | |||
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Wed, 28/04/2010 11:30 |
Ivan Reilly (Auckland) |
Analytic Topology in Mathematics and Computer Science |
L3 |
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Wed, 28/04/2010 11:30 |
David Craven (University of Oxford) |
Algebra Kinderseminar |
ChCh, Tom Gate, Room 2 |
| There are two competing notions for a normal subsystem of a (saturated) fusion system. A recent theorem of mine shows how the two notions are related. In this talk I will discuss normal subsystems and their properties, and give some ideas on why this might be useful or interesting. | |||
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Wed, 28/04/2010 14:00 |
Istvan Juhasz (Budapest) |
Analytic Topology in Mathematics and Computer Science |
L3 |
| tba | |||
-compactness and PCF |
Thu, 29/04/2010 12:00 |
Maria Buzano (Oxford) |
Junior Geometry and Topology Seminar |
SR1 |
| The aim of this talk is to get a feel for the Ricci flow. The Ricci flow was introduced by Hamilton in 1982 and was later used by Perelman to prove the Poincaré conjecture. We will introduce the notions of Ricci flow and Ricci soliton, giving simple examples in low dimension. We will also discuss briefly other types of geometric flows one can consider. | |||
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Thu, 29/04/2010 12:30 |
Dmitri Vassiliev (University College, London) |
OxPDE Lunchtime Seminar |
Gibson 1st Floor SR |
| We consider a 3-dimensional elastic continuum whose material points can experience no displacements, only rotations. This framework is a special case of the Cosserat theory of elasticity. Rotations of material points of the continuum are described mathematically by attaching to each geometric point an orthonormal basis which gives a field of orthonormal bases called the coframe. As the dynamical variables (unknowns) of our theory we choose the coframe and a density. In the first part of the talk we write down the general dynamic variational functional of our problem. In doing this we follow the logic of classical linear elasticity with displacements replaced by rotations and strain replaced by torsion. The corresponding Euler-Lagrange equations turn out to be nonlinear, with the source of this nonlinearity being purely geometric: unlike displacements, rotations in 3D do not commute. In the second part of the talk we present a class of explicit solutions of our Euler-Lagrange equations. We call these solutions plane waves. We identify two types of plane waves and calculate their velocities. In the third part of the talk we consider a particular case of our theory when only one of the three rotational elastic moduli, that corresponding to axial torsion, is nonzero. We examine this case in detail and seek solutions which oscillate harmonically in time but depend on the space coordinates in an arbitrary manner (this is a far more general setting than with plane waves). We show [1] that our second order nonlinear Euler-Lagrange equations are equivalent to a pair of linear first order massless Dirac equations. The crucial element of the proof is the observation that our Lagrangian admits a factorisation. [1] Olga Chervova and Dmitri Vassiliev, "The stationary Weyl equation and Cosserat elasticity", preprint http://arxiv.org/abs/1001.4726 | |||
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Thu, 29/04/2010 13:00 |
Zhongmin Qian (Oxford) |
Mathematical Finance Internal Seminar |
DH 1st floor SR |
| This talk I present a study of BSDEs with non-linear terms of quadratic growth by using Girsanov's theorem. In particular we are able to establish a non-linear version of the Cameron-Martin formula, which can be for example used to obtain gradient estimates for some non-linear parabolic equations. | |||
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Thu, 29/04/2010 14:00 |
Prof Dominique Orban (Ecole Polytechnique de Montréal and GERAD) |
Computational Mathematics and Applications |
Rutherford Appleton Laboratory, nr Didcot |
| Interior-point methods for linear and convex quadratic programming require the solution of a sequence of symmetric indefinite linear systems which are used to derive search directions. Safeguards are typically required in order to handle free variables or rank-deficient Jacobians. We propose a consistent framework and accompanying theoretical justification for regularizing these linear systems. Our approach is akin to the proximal method of multipliers and can be interpreted as a simultaneous proximal-point regularization of the primal and dual problems. The regularization is termed "exact" to emphasize that, although the problems are regularized, the algorithm recovers a solution of the original problem. Numerical results will be presented. If time permits we will illustrate current research on a matrix-free implementation. This is joint work with Michael Friedlander, University of British Columbia, Canada | |||
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Thu, 29/04/2010 14:30 |
Armin Shalile (Oxford) |
Representation Theory Seminar |
L3 |
| We define Brauer characters for Brauer algebras which share many of the features of Brauer characters defined for finite groups. Since notions such as conjugacy classes and orders of elements are not a priori meaningful for Brauer algebras, we show which structure replaces the conjugacy classes and determine eigenvalues associated to these. | |||
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Thu, 29/04/2010 16:30 |
Alain Goriely (University of Oxford) |
Differential Equations and Applications Seminar |
DH 1st floor SR |
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Thu, 29/04/2010 17:00 |
Franz-Viktor Kuhlmann (Saskatoon) |
Logic Seminar |
L3 |
| Elimination of wild ramification is used in the structure theory of valued function fields, with applications in areas such as local uniformization (i.e., local resolution of singularities) and the model theory of valued fields. I will give a survey on the role that Artin-Schreier extensions play in the elimination of wild ramification, and corresponding main theorems on the structure of valued function fields. I will show what these results tell us about local uniformization. I have shown that local uniformization is always possible after a separable extension of the function field of the algebraic variety (separable "alteration"). This was extended to the arithmetic case in joint work with Hagen Knaf. Recently, Michael Temkin has proved local uniformization by purely inseparable alteration. Further, I will describe a classification of Artin-Schreier extensions with non-trivial defect. It can be used to improve one of the above mentioned main theorems ("Henselian Rationality"). This could be a key for a purely valuation theoretical proof of Temkin's result. On the other hand, the classification shows that separable alteration and purely inseparable alteration are just two ways to eliminate the critical defects. So the existence of these two seamingly "orthogonal" local uniformization results does not necessarily indicate that local uniformization without alteration is possible. | |||
