14th Seminar on Conformal Field Theory

The speakers of the 14th Seminar on Conformal Field Theory are Alexandra Zvonareva (University of Stuttgart), Sergei Gukov (Caltech) and Boris Pioline (Sorbonne, Paris). It takes place on November 25, 2022, at the FAU in Erlangen.


Time Speaker Title
14:00 – 15:00 Sergei Gukov Fermionic forms in logarithmic CFTs and quivers
15:15 – 16:15 Alexandra Zvonareva Derived equivalences and derived categories of Brauer graph algebras
Coffee break
17:00 – 18:00 Boris Pioline Modular bootstrap for BPS indices on Calabi-Yau threefolds

The seminar will take place at the Department of Mathematics, Cauerstr. 11, Erlangen, in room 04.363.

After the seminar there is a joint dinner.

Abstracts of the talks

Alexandra Zvonareva: Derived equivalences and derived categories of Brauer graph algebras

In this talk, I will explain the classification of Brauer graph algebras up to derived equivalence. These algebras first appeared in representation theory of finite groups and can be defined for any suitably decorated graph on an oriented surface. The classification relies on the connection between Brauer graph algebras and partially wrapped Fukaya categories associated to surfaces with boundary. One of the main tools we used to obtain this classification is enlarging the class of Brauer graph algebras to include some A-infinity categories. This is based on joint work with Sebastian Opper.

Boris Pioline: Modular bootstrap for BPS indices on Calabi-Yau threefolds

Unlike in cases with maximal or half-maximal supersymmetry, the spectrum
of BPS states in type II string theory compactified on a Calabi-Yau
threefold with generic SU(3) holonomy remains partially understood.
Mathematically, the BPS indices coincide with the generalized
Donaldson-Thomas invariants associated to the derived category of
coherent sheaves, but they are rarely known explicitly. String dualities
indicate that suitable generating series of rank 0 Donaldson-Thomas
invariants counting D4-D2-D0 bound states should transform as
vector-valued mock modular forms, in a very precise sense. I will spell
out and test these predictions in the case of one-modulus compact
Calabi-Yau threefolds such as the quintic hypersurface in $P^4$, where
the polar terms can (at least in principle) be computed from
higher-genus Gopakumar-Vafa invariants, using recent mathematical
results by S. Feyzbakhsh and R. Thomas.

Sergei Gukov: Fermionic forms in logarithmic CFTs and quivers

The representation theory of quantum groups is closely related to the representation theory of vertex algebras. In this relation, generally referred to as the Kazhdan-Lusztig correspondence, fermionic forms provide a natural link between the two sides relating graded dimensions of VOA representations to the braiding data. Fermionic forms were extensively studied in rational VOAs during 80s and early 90s, and then in logarithmic VOAs from mid-90s and early 2000s till present day. More recently, the same structure was independently discovered in a completely different kind of representation theory that has to do with enumerative geometry and curve counting, namely in quiver representations. In this talk, I will review both lines of development and establish a precise link between them. One benefit of building a bridge between quivers and vertex algebras is that it sheds a new light on fermionic forms and provides a simple general method of writing the fermionic forms in much larger families than traditional methods allow.