Forthcoming events in this series


Tue, 12 Jun 2018

15:00 - 16:15
C2

Subriemannian metrics and the metrizability of parabolic geometries

Prof Jan Slovak
(Brno)
Abstract

We present the linearized metrizability problem in the context of parabolic geometries and subriemannian geometry, generalizing the metrizability problem in projective geometry studied by R. Liouville in 1889. We give a general method for linearizability and a classification of all cases with irreducible defining distribution where this method applies. These tools lead to natural subriemannian metrics on generic distributions of interest in geometric control theory.

Thu, 18 Jun 2015

17:00 - 18:00
L2

TheLMS Hardy Lecture: The famous inverse scattering transform method and its less famous discrete version

Prof Nalini Joshi
(University of Sydney)
Abstract

Abstract: The simplest solutions of integrable systems are special functions that have been known since the time of Newton, Gauss and Euler. These functions satisfy not only differential equations as functions of their independent variable but also difference equations as functions of their parameter(s).  We show how the inverse scattering transform method, which was invented to solve the Korteweg-de Vries equation, can be extended to its discrete version.

S.Butler and N.Joshi, An inverse scattering transform for the lattice potential KdV equation, Inverse Problems 26 (2010) 115012 (28pp)

Tue, 12 Jun 2012
10:30
Gibson 1st Floor SR

The Nekrasov Partition Function

Tim Adamo
(Oxford)
Abstract
Abstract: We'll try to learn something about Nekrasov's conjecture/theorem, which relates an instanton-counting partition function to the Seiberg-Witten prepotential of N=2 SYM theory on R^4. This will entail a review of some salient aspects of N=2 SYM theories, Witten's description of Donaldson invariants in terms of correlation functions in those theories, and the physical and mathematical definition of Nekrasov's partition function. Depending on time, I might talk about computational techniques for the partition function, methods of proof for Nekrasov's conjecture, or the partition function's role in the AGT conjectures.
Tue, 13 Sep 2011
12:00

Secret symmetries of AdS/CFT

Allessandro Torielli
(University of York)
Abstract

We review the representation theory of the integrable model underlying the AdS_5/CFT_4 correspondence. We will discuss short and long multiplets, and their impact on the issue of the universal R-matrix. We will give special emphasis to the role of the so-called 'secret symmetry', which completes the Yangian symmetry of the system to a yet to be understood new type of quantum group.

Fri, 02 May 2008

12:00 - 13:00
L1

Movable algebraic singularities of second-order ordinary differential equations

Dr Galina Filipuk
Abstract

Any nonlinear equation of the form y''=\sum_{n=0}^N a_n(z)y^n

has a (generally branched) solution with leading order behaviour

proportional to

(z-z_0)^{-2/(N-1)} about a point z_0, where the coefficients a_n are analytic at z_0 and a_N(z_0)\ne 0. Jointly with R.G. Halburd we consider the subclass of equations for which each possible leading order term of

this

form corresponds to a one-parameter family of solutions represented near

z_0

by a Laurent series in fractional powers of z-z_0. For this class of

equations we show that the only movable singularities that can be reached

by

analytic continuation along finite-length curves are of the algebraic type

just described. This work generalizes previous results of S. Shimomura.

The only other possible kind of movable singularity that might occur is an

accumulation point of algebraic singularities that can be reached by

analytic continuation along infinitely long paths ending at a finite point

in the complex plane. This behaviour cannot occur for constant coefficient

equations in the class considered. However, an example of R. A. Smith

shows

that such singularities do occur in solutions of a simple autonomous

second-order differential equation outside the class we consider here.

Fri, 25 Apr 2008

12:00 - 13:00
L3

Metricity in projective geometry.

Dr Maciej Dunajski
(Cambridge)
Abstract

Cover a plane with curves, one curve through each point

in each direction. How can you tell whether these curves are

the geodesics of some metric?

This problem gives rise to a certain closed system of partial

differential equations and hence to obstructions to finding such a

metric. It has been an open problem for at least 80 years. Surprisingly

it is harder in two dimensions than in higher dimensions. I shall present

a solution obtained jointly with Robert Bryant and Mike Eastwood.