# This Week

Here is a selection of seminars that might be of interest to string theorists in Oxford:

On Monday, November 20, at 12:45 in L3, a seminar in
the String Theory series:

Andrew Dancer (Oxford)

Quivers, nonreductive quotients and symplectic duality

On Monday, November 20, at 14:00 in Dennis Sciama Lecture Theatre, a seminar in
the Astrophysics Colloquia series:

Martin Ward (Durham)

TBD

On Monday, November 20, at 14:15 in L5, a seminar in
the Geometry and Analysis series:

Ben Davison (University of Glasgow)

In search of the extended Kac-Moody Lie algebra

*Associated to a finite graph without loops is the Kac-Moody Lie algebra for the Cartan matrix whose off diagonal entries are (minus) the adjacency matrix for the graph. Two famous conjectures of Kac, proved by Hausel, Letellier and Villegas, hint that there may be some larger cohomologically graded algebra associated to the graph (even if there are loops), providing 'higher' Kac moody Lie algebras, or at least their positive halves. Using work with Sven Meinhardt, I will give a geometric construction of the (full) Kac-Moody algebra for a general finite graph, using cohomological DT theory. Along the way we'll see a proof of the positivity conjecture for the modified Kac polynomials of Bozec, Schiffmann and Vasserot counting various types of representations of quivers.*

**Further information:**
On Tuesday, November 21, at 11:30 in BIPAC seminar room, a seminar in
the Cosmology series:

Massimo Meneghetti (Bologna)

Strong lensing by substructures in galaxy clusters

On Tuesday, November 21, at 12:00 in L4, a seminar in
the Quantum Field Theory series:

Alexander Strohmaier (Leeds)

Index Theory for Dirac Operators in Lorentzian Signature and Geometric Scattering

*I will review some classical results on geometric scattering theory for linear hyperbolic evolution equations on globally hyperbolic spacetimes and its relation to particle and charge creation in QFT. I will then show that some index formulae for the scattering matrix can be interpreted as a special case of the Lorentzian analog of the Atyiah-Patodi-Singer index theorem. I will also discuss a local version of this theorem and its relation to anomalies in QFT. (Joint work with C. Baer)*

**Further information:**
On Tuesday, November 21, at 15:45 in L4, a seminar in
the Algebraic Geometry series:

Wenzhe Yang (University of Oxford)

Mirror symmetry, mixed motives and zeta(3)

*In mirror symmetry, the prepotential on the Kahler side has an expansion, the constant term of which is a rational multiple of zeta(3)/(2 pi i)^3 after an integral symplectic transformation. In this talk I will explain the connection between this constant term and the period of a mixed Hodge-Tate structure constructed from the limit MHS at large complex structure limit on the complex side. From Ayoub’s works on nearby cycle functor, there exists an object of Voevodsky’s category of mixed motives such that the mixed Hodge-Tate structure is expected to be a direct summand of the third cohomology of its Hodge realisation. I will present the connections between this constant term and conjecture about how mixed Tate motives sit inside Voevodsky’s category, which will also provide a motivic interpretation to the occurrence of zeta(3) in prepotential.*

**Further information:**
On Thursday at 12:45 in L2, a seminar in
the Strings Junior series:

Johan Henriksson

Higgs bundles

On Thursday at 13:00 in Dalitz Institute, a seminar in
the Dalitz Seminar in Fundamental Physics series:

None (Oxford)

Cancelled

On Thursday at 16:00 in L6, a seminar in
the Number Theory series:

Anna Cadoret (Université Paris 6 (IMJ-PRG))

The fundamental theorem of Weil II (for curves) with ultra product coefficients

*l-adic cohomology was built to provide an etale cohomology with coefficients in a field of characteristic 0. This, via the Grothendieck trace formula, gives a cohomological interpretation of L-functions - a fundamental tool in Deligne's theory of weights developed in Weil II. Instead of l-adic coefficients one can consider coefficients in ultra products of finite fields. I will state the fundamental theorem of Weil II for curves in this setting and explain briefly what are the difficulties to overcome to adjust Deligne's proof. I will then discuss how this ultra product variant of Weil II allows to extend to arbitrary coefficients previous results of Gabber and Hui, Tamagawa and myself for constant $\mathbb{Z}_\ell$-coefficients. For instance, it implies that, in an $E$-rational compatible system of smooth $\overline{\mathbb{Q}}_\ell$-sheaves all what is true for $\overline{\mathbb{Q}}_\ell$-coefficients (semi simplicity, irreducibility, invariant dimensions etc) is true for $\overline{\mathbb{F}}_\ell$-coefficients provided $\ell$ is large enough or that the $\overline{\mathbb{Z}}_\ell$-models are unique with torsion-free cohomology provided $\ell$ is large enough.*

**Further information:**
On Thursday at 16:15 in Dennis Sciama Lecture Theatre, a seminar in
the Theoretical Particle Physics series:

Christophe Grojean (DESY Hamburg)

Assessing the Higgs (self-)couplings

On Friday at 14:00 in Dennis Sciama Lecture Theatre, a seminar in
the Theoretical Physics Colloquia series:

Thordur Jonsson (Iceland)

The dynamical triangulation approach to quantum gravity