# Trimester Seminar

Date: every Monday, 10:00-11:00 (unless stated otherwise)**Venue:** HIM lecture hall, Poppelsdorfer Allee 45

Organizers: Wojciech Dybalski, Gerald Höhn, Sven Meinhardt, Nuno Romão, Jacopo Stoppa

Monday, September 10, 10:00-11:00

Yoh Tanimoto: Construction of integrable QFT through endomorphisms of chiral CFT

Monday, September 17, 10:00-11:00

Lotte Hollands: Introduction to vortex counting

Monday, September 24, 10:00-11:00

Sven Meinhardt: An introduction to BPS invariants arising from Calabi-Yau 3-categories

Monday, October 1, 13:30-14:30

Nils Scheithauer: Discriminant forms and their automorphisms

Abstract: Let D be a discriminant form, i.e. a finite abelian group with a nondegenerate quadratic form. We prove a version of Witt's Theorem for D, show that the orthogonal group O(D) is generated by reflections and describe the orbits of O(D) on D. Finally we give formulas for the orbit lengths.

Monday, October 8, 13:30-14:30

Dennis Eriksson: Quillen bundles and vortex metrics

Monday, October 15, 10:00-11:00

Katarzyna Rejzner: Local gauge invariance in perturbative algebraic quantum field theory

Monday, October 22, 10:00-11:00

Miranda Cheng: Umbral Moonshine: a status report

Monday, October 29, 10:00-11:00

Jacopo Stoppa: Some geometry of wall-crossing formulae

Monday, November 5, 10:00-11:00

Andreas Ott: Gauged vortices in symplectic topology

Friday, November 16, 10:00-11:00

Jochen Zahn: The renormalized locally covariant Dirac field

Abstract: I present a generalization of the framework of the generally covariant locality principle, such that gauge backgrounds and gauge transformations are treated on equal footing with gravitational backgrounds and isometric embeddings. For a corresponding Dirac field theory (charged under a gauge group and in the presence of a background gauge field), I introduce nonlinear fields (Wick powers) and discuss the current and the stress-energy tensor. Depending on the time, I will sketch the construction of time-ordered products, or how the framework may be useful for the description of Yang-Mills theories.

Monday, November 19, 10:00-11:00

Nils Carqueville: Orbifold completion

Monday, November 26, 10:00-11:00

Nuno Romao: Some geometry of the vortex equations

Monday, December 3, 10:00-11:00

Jan Schlemmer: Thermal aspects of quantum field theory

Abstract: In this talk I will speak about questions arising when rigorously studying physical systems modeled by quantum field theories at "finite temperatures''. Starting from a notion of thermal equilibrium suitable for infinitely extended systems I will sketch a framework which allows the treatment of spatially varying temperature and finish with some remarks about thermal equilibrium in interacting field theories obtained by deformation of free theories.

Thursday, December 6, 15:00-16:00

Thorsten Weist: On the Euler charateristic of Kronecker moduli spaces

Monday, December 10, 10:00-11:00

David Ridout: Modular Properties of Fractional Level WZW Models

Abstract: The modular properties of fractional level WZW models and, in particular, the application of the Verlinde formula, have a long and checkered history in conformal field theory. Such theories were postulated in the late eighties as a means of generalising the GKO-coset construction of the unitary minimal models to their non-unitary cousins. Unfortunately, while their modular properties appeared satisfactory, the Verlinde formula (which is supposed to give the dimensions of certain vector spaces) always gave a few negative integers in addition to the expected non-negative ones. This notorious problem is referred to in textbooks as suggesting that fractional level theories are "intrinsically sick".

Luckily, the formalism of logarithmic conformal field theory has led to a radically new approach to this issue. We will survey the shift in paradigm that has recently been shown to cure the fractional level theories based on affine sl(2) of all sickness. If time permits, we will then discuss (with examples) a selection of the beautiful mathematics that has been used to finally resolve this long-standing problem.

Wednesday, December 12, 11:15-12:15

Simon Wood: M(p_{+},p_{-}) the extended W-algebra of sl_{2} type at rational level

Abstract: I will be talking about a family of chiral algebras that arise in logarithmic CFT, which I will call extended W-algebras of sl_{2} type at rational level or just M(p_{+},p_{-}) for short. These algebras are commonly referred to as the W(p_{+},p_{-}) triplet algebras. However over the course of the talk I hope to convince the audience that "extended W-algebras of sl_{2} type at rational levels" is a more fitting name than triplet algebras. I will present new methods for constructing these algebras by means of screening operators acting on a free field theory. These new screening operator methods used in the construction of these algebras make a lot of previously inaccessible calculations very easy. I will show how they can be used to prove that these algebras satisfy Zhu's c_{2} cofiniteness condition and classify all irreducible representations.

Monday, December 17, 10:00-11:00

Mario Garcia Fernandez: On a modular interpretation of S^{N}(CP^{1})//SL(2,C) via cosmic strings

Tuesday, December 18, 10:00-11:00

Daniel Plencner: Generalized orbifolds of Landau-Ginzburg models

Abstract: Orbifolding a 2-dimensional quantum field theory by a symmetry group admits an elegant description in terms of defect lines and their junction fields. This perspective offers a natural generalization of the concept of an orbifold. In this talk I will focus on the case of Landau-Ginzburg models. After a review of the description of defects in terms of matrix factorizations, I will discuss bulk-boundary correlators in LG orbifolds and give a simple proof of the Cardy condition.