Thu, 26 Jan 2012

16:00 - 17:00
DH 1st floor SR

Modelling the Transition from Channel-Veins to PSBs in the Early Stage of Fatigue Tests

Yichao Zhu
(Oxford)
Abstract

Understanding the fatigue of metals under cyclic loads is crucial for some fields in mechanical engineering, such as the design of wheels of high speed trains and aero-plane engines. Experimentally it has been found that metal fatigue induced by cyclic loads is closely related to a ladder shape pattern of dislocations known as a persistent slip band (PSB). In this talk, a quantitative description for the formation of PSBs is proposed from two angles: 1. the motion of a single dislocation analised by using asymptotic expansions and numerical simulations; 2. the collective behaviour of a large number of dislocations analised by using a method of multiple scales.

Mon, 14 Nov 2011
14:15
L3

Invariants for non-reductive group actions

Gergely Berczi
(Oxford)
Abstract

Translation actions appear all over geometry, so it is not surprising that there are many cases of moduli problems which involve non-reductive group actions, where Mumford’s geometric invariant theory does not apply. One example is that of jets of holomorphic map germs from the complex line to a projective variety, which is a central object in global singularity theory. I will explain how to construct this moduli space using the test curve model of Morin singularities and how this can be generalized to study the quotient of projective varieties by a wide class of non-reductive groups. In particular, this gives information about the invariant ring. This is joint work with Frances Kirwan.

Thu, 01 Dec 2011

15:00 - 16:00
L3

Uniformizing Bun(G) by the affine Grassmannian

Kobi Kremnitzer
(Oxford)
Abstract

I'll present the work of Gaitsgory arXiv:1108.1741. In it he uses Beilinson-Drinfeld factorization techniques in order to uniformize the moduli stack of G-bundles on a curve. The main difference with the gauge theoretic technique is that the the affine Grassmannian is far from being contractible but the fibers of the map to Bun(G) are contractible.

Tue, 22 Nov 2011

14:30 - 15:30
L3

Structure and the Fourier transform

Tom Sanders
(Oxford)
Abstract

We shall discuss how the algebra norm can be used to identify structure in groups. No prior familiarity with the area will be assumed.

Thu, 20 Oct 2011
11:00
SR2

"Motivic Integration and counting conjugacy classes in algebraic groups over number fields"

Jamshid Derakhshan
(Oxford)
Abstract

This is joint work with Uri Onn. We use motivic integration to get the growth rate of the sequence consisting of the number of conjugacy classes in quotients of G(O) by congruence subgroups, where $G$ is suitable algebraic group over the rationals and $O$ the ring of integers of a number field.

The proof uses tools from the work of Nir Avni on representation growth of arithmetic groups and results of Cluckers and Loeser on motivic rationality and motivic specialization.

Mon, 07 Nov 2011
15:45
L3

Right-angled Artin groups and their automorphisms

Ric Wade
(Oxford)
Abstract

Automorphisms of right-angled Artin groups interpolate between $Out(F_n)$ and $GL_n(\mathbb{Z})$. An active area of current research is to extend properties that hold for both the above groups to $Out(A_\Gamma)$ for a general RAAG. After a short survey on the state of the art, we will describe our recent contribution to this program: a study of how higher-rank lattices can act on RAAGs that builds on the work of Margulis in the free abelian case, and of Bridson and the author in the free group case.

Mon, 21 Nov 2011

12:00 - 13:00
L3

Gravity duals of supersymmetric gauge theories on curved manifolds

James Sparks
(Oxford)
Abstract

In just the last year it has been realized that one can define supersymmetric gauge theories on non-trivial compact curved manifolds, coupled to a background R-symmetry gauge field, and moreover that expectation values of certain BPS operators reduce to finite matrix integrals via a form of localization. I will argue that a general approach to this topic is provided by the gauge/gravity correspondence. In particular, I will present several examples of supersymmetric gauge theories on different 1-parameter deformations of the three-sphere, which have a large N limit, together with their gravity duals (which are solutions to Einstein-Maxwell theory). The Euclidean gravitational partition function precisely matches a large N matrix model evaluation of the field theory partition function, as an exact \emph{function} of the deformation parameter.

Mon, 14 Nov 2011

12:00 - 13:00
L3

Scattering and Sequestering of Blow-Up Moduli in Local String Models

Lukas Witkowski
(Oxford)
Abstract

I will study the sequestering of blow-up fields through a CFT in a toroidal orbifold setting. In particular, I will examine the disk correlator between orbifold blow-up moduli and matter Yukawa couplings. Blow-up moduli appear as twist fields on the worldsheet which introduce a monodromy

condition for the coordinate field X. Thus I will focus on how the presence of twist field affects

the CFT calculation of disk correlators. Further, I will explain how the results are relevant to

suppressing soft terms to scales parametrically below the gravitino mass. Last, I want to explore the

relevance of our calculation for the case of smooth Calabi-Yaus.

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