Wed, 18 May 2022

12:45 - 14:00
L4

A pedestrian introduction to the geometry of 3d twisted indices

Andrea Ferrari
(Durham)
Further Information

Please note the unusual time.

Abstract

3d N=4 gauge theories can be studied on a circle times a closed Riemann surface. Their partition functions on this geometry, known as twisted indices, were computed some time ago using supersymmetric localisation on the Coulomb branch. An alternative perspective is to consider the theory as a supersymmetric quantum mechanics on S^1. In this talk I will review this point of view, which unveils interesting connection to topics in geometry such as wall-crossing and symplectic duality of quasi-maps.

Mon, 14 Mar 2022
16:00
Virtual

Amplituhedron-Like Geometries and the Product of Amplitudes

Gabriele Dian
(Durham)
Abstract

The on-shell superspace formulation of N=4 SYM allows the writing of all possible scattering processes in one compact object called the super-amplitude.   Famously, the super-amplitude integrand can be extracted from generalized polyhedra called the amplituhedron. In this talk, I will review this construction and present a natural generalization of the amplituhedron that we proved at tree level and conjectured at loop level to correspond to the product of two parity conjugate superamplitudes. The sum of all parity conjugate amplitudes corresponds to a particular limit of the supercorrelator through the Wilson Loop/Amplitude duality.  I will conclude by discussing this connection from a geometrical point of view. This talk is based on the reference arXiv:2106.09372 .

 

Mon, 03 Feb 2020
12:45
L3

IIB flux non-commutativity and the global structure of field theories

Inaki Garcia-Etxebarria
(Durham)
Abstract

I will discuss the origin of the choice of global structure
--- or equivalently, the choice for which higher p-form symmetries are
present in the theory --- for various (Lagrangian and non-Lagrangian)
field theories in terms of their realization in IIB and M-theory. I
will explain how this choice on the field theory side can be traced
back to the fact that fluxes in string/M-theory do not commute in the
presence of torsion. I will illustrate how these ideas provide a
stringy explanation for the fact that six-dimensional (2,0) and (1,0)
theories generically have a partition vector (as opposed to a partition
function) and explain how this reproduces the classification of N=4
theories provided by Aharony, Seiberg and Tachikawa. Time permitting, I
will also explain how to use these ideas to obtain the algebra of
higher p-form symmetries for 5d SCFTs arising from M-theory at
arbitrary isolated toric singularities, and to classify global forms
for various 4d theories in the presence of duality defects.

Tue, 05 Nov 2019
17:00
C1

Schroedinger operator with non-zero accumulation points of complex eigenvalues

Sabine Boegli
(Durham)
Abstract

We consider Schroedinger operators on the whole Euclidean space or on the half-space, subject to real Robin boundary conditions. I will present the construction of a non-real potential that decays at infinity so that the corresponding Schroedinger operator has infinitely many non-real eigenvalues accumulating at every point of the essential spectrum. This proves that the Lieb-Thirring inequalities, crucial in quantum mechanics for the proof of stability of matter, do no longer hold in the non-selfadjoint case.

Tue, 18 Jun 2019
12:00
L3

Wilson-loop form-factors, a new duality

Dr Paul Heslop
(Durham)
Abstract

We find a new duality for form factors of lightlike Wilson loops in planar N=4 super-Yang-Mills theory. The duality maps a form factor involving an n-sided lightlike polygonal super-Wilson loop together with m external on-shell states, to the same type of object but with the edges of the Wilson loop and the external states swapping roles. This relation can essentially be seen graphically in Lorentz harmonic chiral (LHC) superspace where it is equivalent to planar graph duality. However there are some crucial subtleties with the cancellation of spurious poles due to the gauge fixing. They are resolved by finding the correct formulation of the Wilson loop and by careful analytic continuation from Minkowski to Euclidean space. We illustrate all of these subtleties explicitly in the simplest non-trivial NMHV-like case.

Mon, 11 May 2015

12:00 - 13:00
L5

TBA

Ruth Gregory
(Durham)
Mon, 09 Mar 2015
15:45
L6

Non-arithmetic lattices

John Parker
(Durham)
Abstract

If G is a semi-simple Lie group, it is known that all lattices
are arithmetic unless (up to finite index) G=SO(n,1) or SU(n,1).
Non-arithmetic lattices have been constructed in SO(n,1) for
all n and there are infinitely many non-arithmetic lattices in
SU(1,1). Mostow and Deligne-Mostow constructed 9 commensurability
classes of non-arithmetic lattices in SU(2,1) and a single
example in SU(3,1). The problem is open for n at least 4.
I will survey the history of this problem, and then describe
recent joint work with Martin Deraux and Julien Paupert, where
we construct 10 new commensurability classes of non-arithmetic
lattices in SU(2,1). These are the first examples to be constructed
since the work of Deligne and Mostow in 1986.

Mon, 25 Nov 2013
15:30
L5

Spectral sequences from Khovanov homology

Andrew Lobb
(Durham)
Abstract

There are various Floer-theoretical invariants of links and 3-manifolds

which take the form of homology groups which are the E_infinity page of

spectral sequences starting from Khovanov homology. We shall discuss recent

work, joint with Raphael Zentner, and work in progress, joint with John

Baldwin and Matthew Hedden, in investigating and exploiting these spectral

sequences.

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