Women at the intersection of mathematics and theoretical physics

9 Apr 2018, 09:30 → 12 Apr 2018, 15:00 Europe/Berlin

SR 4a / 4b (DESY Hamburg)

The primary goals of the workshop will be to promote the visibility of women in our field and to stimulate interactions across the borders of mathematics and theoretical physics.

Monday 9 April

1 Welcome

Speaker: Joachim Mnich

2 Analytic conformal bootstrap

In this talk I will introduce the conformal bootstrap framework. I will first discuss how it can be useful to constrain CFT data and then I will present how it can be applied to find analytic solutions to crossing equations. If time permits, I will discuss an application to the case of superconformal field theories.

Speaker: Agnese Bissi

11:30 Coffee break

3 Four Tales of Mathematical Physics

What does it mean for a partial differential equation (PDE) or system of PDEs to be integrable? Is there a way to measure how “nonintegrable” a model might be? We shall discuss four results in fluid dynamics and gravitation aimed at answering these questions. Our discussion will reveal rich interconnections between nonlinear waves, astrophysics, combinatorics, geometric analysis, and algebraic geometry.

Speaker: Shabnam BEHESHTI (Queen Mary)

13:15 Lunch

4 Gauge/Gravity Duality: Foundations and applications

Based on the AdS/CFT correspondence, gauge/gravity duality provides a new relation between quantum field theories on flat space and gravity theories. In addition to its intrinsic interest and its implications for the nature of gravity, this new duality provides a new approach to calculating observables in strongly coupled quantum field theories, for which there is no standard calculation method. We explain the foundations of gauge/gravity duality and present some recent applications to both particle and condensed matter physics.

Speaker: Johanna Erdmenger (Max Planck-Institut fuer Physik)

15:45 Coffee break

5 Round table discussion

Tuesday 10 April

6 Manifolds and Topological Quantum Field Theory

Manifolds (and cobordisms) are at the very heart of topological quantum field theory (TQFT). We will survey how the study of TQFT from a topological point of view has led to a renaissance of manifold theory, and vice versa how a reinterpretation of classical manifold theory has led to deep insight in TQFT.

Speaker: Ulrike Tillmann

10:45 Coffee break

7 Seiberg-like dualities in 4D and 3D via branes

Speaker: Susanne Reffert

12:30 Lunch

8 Black Holes & Number Theory: how to bootstrap a black hole via modular forms

In the language of statistical physics, an extremal black hole is a zero temperature system with a huge amount of residual entropy. Understanding which class of counting formulas can account for a large degeneracy will undoubtedly unveil interesting properties of quantum gravity. In this talk I will discuss the application of Siegel modular forms to black hole entropy counting. The role of the Igusa cusp form in the D1D5P system is well-known in string theory, and its transformation properties are what allow precision microstate counting in this case. We implement this counting for other Siegel modular and paramodular forms, and we show that they could serve as candidates for other gravitational systems.

Speaker: Alejandra Castro (University of Amsterdam)

15:15 Coffee break

9 Short talk and round table discussion

Speaker: Jan Louis (Hamburg University)

Wednesday 11 April

10 Mathematical structures in quantum field theory: from axioms to Feynman graphs and back

In this talk I will give a pedagogical introduction into perturbative algebraic quantum field theory (pAQFT) and briefly sketch the recent results. The pAQFT framework is a mathematically rigorous formalism that allows to prove structural results in quantum field theory (QFT). It combines the axiomatic framework of algebraic QFT with perturbative methods that involve for example expansion into Feynman graphs. On the mathematical side, the pAQFT formalism combines methods of functional analysis, geometry and homological algebra, creating numerous opportunities for interdisciplinary research.

Speaker: Kasia Rejzner

11:40 Coffee break

11 On the generalisation of the AGT correspondence for non-Lagrangian class S theories

Speaker: Ioana Coman (DESY)

13:10 Lunch

Statistical Equilibrium in Group Field Theory Quantum Gravity

Formulating statistical equilibrium in background independent settings, where the standard notions of time and energy are absent, is an open issue. This is even more so in non-perturbative quantum gravity contexts which are not based on the usual geometrical spacetime, which then is an emergent structure. In this talk, I will clarify the different characterisations of Gibbs statistical equilibrium, focussing on those crucial for background independent (such as, time-less) systems. I will then present the relevant basics of the group field theory formalism for quantum gravity, whose fundamental quanta are non-spatiotemporal ‘atoms’ or building blocks of space, organised in a Fock space along with its quantum statistical mechanics. Based on this, one can construct Gibbs states encoding different notions of equilibrium. In this talk, I will present one such example of a non-standard Gibbs state based on a geometric volume operator, which supports condensation to a low-spin phase.

Convener: Isha Kotecha

Representations of certain non-rational W-algebras

Convener: Ana Kontrec

Thursday 12 April

12 N=2 super Yang-Mills theory in Projective superspace

Speaker: Ariunzul Davgadorj

10:45 Coffee break

13 From topological field theories to “higher” algebra.. and back?

We will start this talk with an introduction to the Atiyah-Segal approach to topological field theories. This will be a recollection from Ulrike Tillmann’s talk. We will then take a different direction and see how this approach led to developments of so-called higher algebra and higher categories in mathematics. We will see how a classification of so called "fully extended” topological field theories leads to studying algebraic “dualizability” conditions, generalizing a finite dimensional vector space and its dual. The study of these conditions has lead to many interesting connections to different fields of mathematics, e.g. in representation theory.

Speaker: Claudia Scheimbauer

12:30 Lunch