Forthcoming Seminars

Mon, 01/02/2010
12:00 		Lionel Mason (Oxford) String Theory Seminar Add to calendar L3
Twistor-Strings, Grassmannians and Leading Singularities
A systematic procedure is derived for obtaining an explicit, L-loop leading singularities of planar N=4 super Yang-Mills scattering amplitudes in twistor space directly from their momentum space channel diagrams. The expressions are given as integrals over the moduli of connected, nodal curves in twistor space whose degree and genus matches expectations from twistor-string theory. We propose that a twistor-string theory for pure N=4 super Yang-Mills, if it exists, is determined by the condition that these leading singularity formulae arise as residues when an unphysical contour for the path integral is used, by analogy with the momentum space leading singularity conjecture. We go on to show that the genus g twistor-string moduli space for g-loop N^{k-2}MHV amplitudes may be mapped into the Grassmannian G(k,n). Restricting to a leading singularity, the image of this map is a 2(n-2)-dimensional subcycle of G(k,n) of exactly the type found from the Grassmannian residue formula of Arkani-Hamed, Cachazo, Cheung and Kaplan. Based on this correspondence and the Grassmannian conjecture, we deduce restrictions on the possible leading singularities of multi-loop N^pMHV amplitudes. In particular, we argue that no new leading singularities can arise beyond 3p loops.
Mon, 01/02/2010
14:15 		Giambattista Giamcomin (University of Paris Diderot) Stochastic Analysis Seminar Add to calendar Eagle House
Scaling Limits and Universality in Disordered Copolimer Models
A copolymer is a chain of repetitive units (monomers) that are almost identical, but they differ in their degree of affinity for certain solvents. This difference leads to striking phenomena when the polymer fluctuates in a non-homogeneous medium, for example made up by two solvents separated by an interface. One may observe, for exmple, the localization of the polymer at the interface between the two solvents. Much of the literature on the subject focuses on the most basic model based on the simple symmetric random walk on the integers, but E. Bolthausen and F. den Hollander (AP 1997) pointed out the convergence of the (rescaled) free energy of such a discrete model toward the free energy of a continuum model, based on Brownian motion, in the limit of weak polymer-solvent coupling. This result is remarkable because it strongly suggests a universal feature for copolymer models. In this work we prove that this is indeed the case. More precisely, we determine the weak coupling limit for a general class of discrete copolymer models, obtaining as limits a one-parameter (alpha in (0,1)) family of continuum models, based on alpha-stable regenerative sets.
Mon, 01/02/2010
14:15 		Nigel Hitchin (Oxford) Geometry and Analysis Seminar Add to calendar L3
Stable Bundles and Polyvector Fields
Mon, 01/02/2010
15:45 		Kurt Johansson (Matematiske Institutionen Stockholm) Stochastic Analysis Seminar Add to calendar Eagle House
Wigner random matrices with weak moment conditions
Abstract: There has in the last year been much progresson the universality problem for the spectra of a Wigner random matrices, i.e.Hermitian or symmetric random matrices with independent elements. I will givesome background on this problem and also discuss what can be said when we onlyassume a few moments of the matrix elements to be finite. 
Mon, 01/02/2010
16:00 		Damiano Testa (Mathematical Institute, Oxford) Junior Number Theory Seminar Add to calendar SR1
Intersections of two cubics and Artin's conjecture
Suppose that $ C $ and $ C' $ are cubic forms in at least 19 variables over a $ p $-adic field $ k $. A special case of a conjecture of Artin is that the forms $ C $ and $ C' $ have a common zero over $ k $. While the conjecture of Artin is false in general, we try to argue that, in this case, it is (almost) correct! This is still work in progress (joint with Heath-Brown), so do not expect a full answer. As a historical note, some cases of Artin's conjecture for certain hypersurfaces are known. Moreover, Jahan analyzed the case of the simultaneous vanishing of a cubic and a quadratic form. The approach we follow is closely based on Jahan's approach, thus there might be some overlap between his talk and this one. My talk will anyway be self-contained, so I will repeat everything that I need that might have already been said in Jahan's talk.
Mon, 01/02/2010
17:00 		Pierre-Gilles Lemarié-Rieusset (Université d'Évry) Partial Differential Equations Seminar Add to calendar Gibson 1st Floor SR
Large homogeneous initial data for the 3D Navier-Stokes equations
Due to the scaling properties of the Navier-Stokes equations, homogeneous initial data may lead to forward self-similar solutions. When the initial data is small enough, it is well known that the formalism of mild solutions (through the Picard-Duhamel formula) give such self-similar solutions. We shall discuss the issue of large initial data, where we can only prove the existence of weak solutions; those solutions may lack self-similarity, due to the fact that we have no results about uniqueness for such weak solutions. We study some tools which may be useful to get a better understanding of those weak solutions.
Tue, 02/02/2010
12:00 		Daniel Litim (Sussex) Quantum Field Theory Seminar Add to calendar L3
Quantum Gravity and the Renormalisation Group
Tue, 02/02/2010
14:15 		Prof. Maisa Roja (University of Chile) Geophysical and Nonlinear Fluid Dynamics Seminar Add to calendar Dobson Room, AOPP
The southern hemisphere westerlies during the last glacial maximum
Tue, 02/02/2010
15:45 		Michael Wemyss (Oxford) Algebraic and Symplectic Geometry Seminar Add to calendar L3
Mutations of Quivers in the Minimal Model Programme
Following work of Bridgeland in the smooth case and Chen in the terminal singularities case, I will explain a proposal that extends the existence of flops for threefolds (and the required derived equivalences) to also cover canonical singularities.  Moreover this technique conjecturally says much more than just the existence of the flop, as it shows how the dual graph changes under the flop and also which curves in the flopped variety contract to points without contracting divisors.  This allows us to continue the Minimal Model Programme on the flopped variety in an easy way, thus producing many varieties birational to the given input.    
Tue, 02/02/2010
16:00 		Richard Wade (Oxford) Junior Geometric Group Theory Seminar Add to calendar SR1
Outer Space
We introduce Outer space, a contractible finite dimensional topological space on which the outer automorphism group of a free group acts 'nicely.' We will explain what 'nicely' is, and provide motivation with comparisons to symmetric spaces, analogous spaces associated to linear groups.
Wed, 03/02/2010
11:30 		David Craven (University of Oxford) Algebra Kinderseminar Add to calendar ChCh, Tom Gate, Room 2
Elliptic Curves and Cryptography
This talk will introduce various aspects of modern cryptography. After introducing RSA and some factoring algorithms, I will move on to how elliptic curves can be used to produce a more complex form of Diffie–Hellman key exchange.
Wed, 03/02/2010
16:00 		Alessandro Sisto (Oxford University) Junior Geometric Group Theory Seminar Add to calendar SR2
TBC
Wed, 03/02/2010
16:00 		Jonathan Zvesper (Computing Laboratory, Oxford) Analytic Topology in Mathematics and Computer Science Add to calendar L3
Arbitrary Levels of belief in Rationality in Strategic Games
TBA
Thu, 04/02/2010
11:00 		Prof. Jean-Marc Ginoux (Université du Sud Génie Mécanique Productique) Applied Dynamical Systems and Inverse Problems Seminar Add to calendar DH 3rd floor SR
Differential Geometry Applied to Dynamical Systems
This work aims to present a new approach called Flow Curvature Method that applies Differential Geometry to Dynamical Systems. Hence, for a trajectory curve, an integral of any n-dimensional dynamical system as a curve in Euclidean n-space, the curvature of the trajectory or the flow may be analytically computed. Then, the location of the points where the curvature of the flow vanishes defines a manifold called flow curvature manifold. Such a manifold being defined from the time derivatives of the velocity vector field, contains information about the dynamics of the system, hence identifying the main features of the system such as fixed points and their stability, local bifurcations of co-dimension one, centre manifold equation, normal forms, linear invariant manifolds (straight lines, planes, hyperplanes). In the case of singularly perturbed systems or slow-fast dynamical systems, the flow curvature manifold directly provides the slow invariant manifold analytical equation associated with such systems. Also, starting from the flow curvature manifold, it will be demonstrated how to find again the corresponding dynamical system, thus solving the inverse problem. Moreover, the concept of curvature of trajectory curves applied to classical dynamical systems such as Lorenz and Rossler models enabled to highlight one-dimensional invariant sets, i.e. curves connecting fixed points which are zero-dimensional invariant sets. Such "connecting curves" provide information about the structure of the attractors and may be interpreted as the skeleton of these attractors. Many examples are given in dimension three and more.
Thu, 04/02/2010
11:00 		Philip Scowcroft (Wesleyan and Oxford) Advanced Logic Class Add to calendar SR2
Some examples of theories lacking the independence property
Thu, 04/02/2010
12:00 		Imran Qureshi (Oxford) Junior Geometry and Topology Seminar Add to calendar SR1
Weighted projective varieties in higher codimension
Many interesting classes of projective varieties can be studied in terms of their graded rings. For weighted projective varieties, this has been done in the past in relatively low codimension. Let $ G $ be a simple and simply connected Lie group and $ P $ be a parabolic subgroup of $ G $, then homogeneous space $ G/P $ is a projective subvariety of $ \mathbb{P}(V) $ for some
$ G $-representation $ V $. I will describe weighted projective analogues of these spaces and give the corresponding Hilbert series formula for this construction. I will also show how one may use such spaces as ambient spaces to construct weighted projective varieties of higher codimension.

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

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