Forthcoming Seminars

Mon, 24/10/2011
14:15

Justin Sawon (University of North Carolina & Bonn)

Fourier-Mukai transforms and deformations in generalized complex geometry

In this talk I will describe Toda's results on deformations of the category Coh(X) of coherent sheaves on a complex manifold X. They come from deformations of X as a complex manifold, non-commutative deformations, and gerby deformations (which can all be interpreted as deformations of X as a generalized complex manifold). Toda also described how to deform Fourier-Mukai equivalences, and I will present some examples coming from mirror SYZ fibrations.

Mon, 24/10/2011 15:45	Nick Wright (Southampton)	Topology Seminar	L3
	Asymptotic dimension for CAT(0) cube complexes
	In this talk I'll explain how to build CAT(0) cube complexes and construct Lipschitz maps between them. The existence of suitable Lipschitz maps is used to prove that the asymptotic dimension of a CAT(0) cube complex is no more than its dimension.

Mon, 24/10/2011 15:45	Jean-Francois Le Gall (Universite of Paris sud and Institut Universitaire de France)	Stochastic Analysis Seminar	Oxford-Man Institute
	The continuous limit of large random planar maps
	Planar maps are graphs embedded in the plane, considered up to continuous deformation. They have been studied extensively in combinatorics, and they have also significant geometrical applications. Particular cases of planar maps are p-angulations, where each face (meaning each component of the complement of edges) has exactly p adjacent edges. Random planar maps have been used in theoretical physics, where they serve as models of random geometry.Our goal is to discuss the convergence in distribution of rescaled random planar maps viewed as random metric spaces.More precisely, we consider a random planar map M(n) which is uniformly distributed over the set of all p-angulations with n vertices. We equip the set of vertices of M(n) with the graph distance rescaled by the factor n to the power -1/4. Both in the case p=3 and when p>3 is even, we prove that the resulting random metric spaces converge as n tends to infinity to a universal object called the Brownian map. This convergence holds in the sense of the Gromov-Hausdorff distance between compact metric spaces. In the particular case of triangulations (p=3), this solves an open problem stated by Oded Schramm in his 2006 ICM paper. As a key tool, we use bijections between planar maps and various classes of labeled trees

Mon, 24/10/2011 16:00	Sebastian Pancratz	Junior Number Theory Seminar	SR1
	Radix conversion for polynomials
	We describe various approaches to the problem of expressing a polynomial $f(x) = \sum_{i=0}^{m} a_i x^i$ in terms of a different radix $r(x)$ as $f(x) = \sum_{j=0}^{n} b_j(x) r(x)^j$ with $0 \leq \deg(b_j) < \deg(r)$ . Two approaches, the naive repeated division by $r(x)$ and the divide and conquer strategy, are well known. We also describe an approach based on the use of precomputed Newton inverses, which appears to offer significant practical improvements. A potential application of interest to number theorists is the fibration method for point counting, in current implementations of which the runtime is typically dominated by radix conversions.

Mon, 24/10/2011 17:00	Hung Tran (University of California, Berkeley)	Partial Differential Equations Seminar	Gibson 1st Floor SR
	Partial Regularity Results for A Variational Problem for Nematic Liquid Crystal.
	This is a joint work with Craig Evans. We study the partial regularity of minimizers for certain functionals in the calculus of variations, namely the modified Landau-de Gennes energy functional in nematic liquid crystal theory introduced by Ball and Majumdar.

Tue, 25/10/2011 12:00	Dorje C. Brody (Brunel University)	Quantum Field Theory Seminar	L2
	Six-dimensional space-time from quaternionic quantum mechanics
	Quaternionic quantum Hamiltonians describing nonrelativistic spin particles require the ambient physical space to have five dimensions. The quantum dynamics of a spin-1/2 particle system characterised by a generic such Hamiltonian is described. There exists, within the structure of quaternionic quantum mechanics, a canonical reduction to three spatial dimensions upon which standard quantum theory is retrieved. In this dimensional reduction, three of the five dynamical variables oscillate around a cylinder, thus behaving in a quasi one-dimensional manner at large distances. An analogous mechanism exists in the case of octavic Hamiltonians, where the ambient physical space has nine dimensions. Possible experimental tests in search for the signature of extra dimensions at low energies are briefly discussed. (Talk based on joint work with Eva-Maria Graefe, Imperial.)

Tue, 25/10/2011 14:15	Prof. Carl Wunsch (MIT)	Geophysical and Nonlinear Fluid Dynamics Seminar	Dobson Room, AOPP
	Testing Basic Ocean Circulation Dynamics

Tue, 25/10/2011 14:30	Bjarne Toft (University of Southern Denmark)	Combinatorial Theory Seminar	L3
	The board game Hex – history, results, problems
	Hex was discovered independently by Piet Hein in Copenhagen in 1942 and byJohn Nash in Princeton in 1948. The game is interesting because its rules are very simple, yet it is not known how to play best possible. For example, a winning first move for the first player (who does have a winning strategy) is still unknown. The talk will tell the history of the game and give simple proofs for basic results about it. Also the reverse game of HEX,sometimes called REX, will be discussed. New results about REX are under publication in Discrete Mathematics in a paper: How to play Reverse Hex (joint work with Ryan Hayward and Phillip Henderson).

Tue, 25/10/2011 15:00		Advanced Class in Algebra	SR2
	Serre theorem on pro-p groups with cd<2

Tue, 25/10/2011 15:45	Agnes Gadbled (Cambridge)	Algebraic and Symplectic Geometry Seminar	L3
	Exotic monotone Lagrangian tori
	There exist two constructions of families of exotic monotone Lagrangian tori in complex projective spaces and products of spheres, namely the one by Chekanov and Schlenk, and the one via the Lagrangian circle bundle construction of Biran. It was conjectured that these constructions give Hamiltonian isotopic tori. I will explain why this conjecture is true in the complex projective plane and the product of two two-dimensional spheres.

Tue, 25/10/2011 17:00	Andras Zsak (Cambridge)	Functional Analysis Seminar	L3
	Closed ideals of operators on certain classes of Banach spaces

Tue, 25/10/2011 17:00	Dr. S. Goodwin (Birmingham)	Algebra Seminar	L2
	Representations of finite W-algebras in classical type

Wed, 26/10/2011 10:15	Marc Fivel (Grenoble INP)	OCCAM Wednesday Morning Event	OCCAM Common Room (RI2.28)
	3D Discrete Dislocation Dynamics Simulations: A Review of Recent Studies

Wed, 26/10/2011 11:30	Martin Palmer	Algebra Kinderseminar
	Coincidences between characteristic classes of surface bundles (St Hugh's, 80WR18)
	I will begin by defining the notion of a characteristic class of surface bundles, and constructing the MMM (Miller-Morita-Mumford) classes as examples. I will then talk about a recent theorem of Church, Farb, and Thibault which shows that the characteristic numbers associated to certain MMM-classes do not depend on how the total space is fibred as a surface bundle - they depend only on the topology of the total space itself. In particular they don't even depend on the genus of the fibre. Hence there are many 'coincidences' between the characteristic numbers of very different-looking surface bundles. A corollary of this is an obstruction to low-genus fiberings: given a smooth manifold E, the non-vanishing of a certain invariant of E implies that any surface bundle with E as its total space must have a fibre with genus greater than a certain lower bound. Also, following the paper of Church-Farb-Thibault, I will sketch how to construct examples of 4-manifolds which fibre in two distinct ways as a surface bundle over another surface, thus giving concrete examples to which the theorem applies.

Wed, 26/10/2011 15:45	Lars Louder	Junior Geometric Group Theory Seminar	L2
	A user's guide to JSJ decompositions I

Thu, 27/10/2011 11:00	Vincenzo Mantova (Pisa and Oxford)	Advanced Class Logic	SR2
	An involution on Zilber's field

Thu, 27/10/2011 12:00	Heinrich Hartmann	Junior Geometry and Topology Seminar	SR2
	Stability conditions on K3 surfaces
	We will explain Bridgelands results on the stabiltiy manifold of a K3 surface. As an application we will define the stringy Kaehler moduli space of a K3 surface and comment on the mirror symmetry picture.

Thu, 27/10/2011 13:00	Johannes Ruf (OMI)	Mathematical Finance Internal Seminar	DH 1st floor SR
	Hedging Options On Exploding Exchange Rates
	: Recently strict local martingales have been used to model exchange rates. In such models, put-call parity does not hold if one assumes minimal superreplicating costs as contingent claim prices. I will illustrate how put-call parity can be restored by changing the definition of a contingent claim price. More precisely, I will discuss a change of numeraire technique when the underlying is only a local martingale. Then, the new measure is not necessarily equivalent to the old measure. If one now defines the price of a contingent claim as the minimal superreplicating costs under both measures, then put-call parity holds. I will discuss properties of this new pricing operator. To illustrate this techniques, I will discuss the class of "Quadratic Normal Volatility" models, which have drawn much attention in the financial industry due to their analytic tractability and flexibility. This talk is based on joint work with Peter Carr and Travis Fisher.

Thu, 27/10/2011 14:00	Andrzej Skowronski (Torun)	Representation Theory Seminar	L3
	Tame algebras and Tits quadratic forms
	The class of finite dimensional algebras over an algebraically closed field K may be divided into two disjoint subclasses (tame and wild dichotomy). One class consists of the tame algebras for which the indecomposable modules occur, in each dimension d, in a finite number of discrete and a finite number of one-parameter families. The second class is formed by the wild algebras whose representation theory comprises the representation theories of all finite dimensional algebras over K. Hence, the classification of the finite dimensional modules is feasible only for the tame algebras. Frequently, applying deformations and covering techniques, we may reduce the study of modules over tame algebras to that for the corresponding simply connected tame algebras. We shall discuss the problem concerning connection between the tameness of simply connected algebras and the weak nonnegativity of the associated Tits quadratic forms, raised in 1975 by Sheila Brenner.

Thu, 27/10/2011 14:00	Prof Joerg Liesen (Technical University of Berlin)	Computational Mathematics and Applications	Gibson Grd floor SR
	Writing the matrix adjoint as a rational function in the matrix can be interesting
	We will study the question of whether the adjoint of a given matrix can be written as a rational function in the matrix. After showing necessary and sufficient conditions, rational interpolation theory will help to characterize the most important existing cases. Several topics related to our question will be explored. They range from short recurrence Krylov subspace methods to the roots of harmonic polynomials and harmonic rational functions. The latter have recently found interesting applications in astrophysics, which will briefly be discussed as well.