Alternatively have a look at the program.

## Categorification of Chern characters

The Chern character is a central construction with incarnations in algebraic topology, representation

theory and algebraic geometry. It is an important tool to probe $K$-theory, which is notoriously hard

to compute. In my talk, I will explain, what the categorification of the Chern character is and how we

can use it to show that certain classical constructions in algebraic geometry are of non-commutative

origin. The category of motives plays the role of $K$-theory in the categorified picture. The categorification

## Large $N$ limits from a BV perspective

Starting with 't Hooft, physicists have used a ribbon graph expansion to understand certain integrals over spaces

of $N \times N$ matrices in the large $N$ limit. This expansion can be deduced from the Feynman diagram

expansion, which relies on the nice structure of moments of a Gaussian measure. We provide a homological

perspective on this situation: the Batalin-Vilkovisky formalism (which we will outline) provides a homological

approach to computing moments, and the Loday-Quillen-Tsygan theorem (which we will explain) gives a

## From classical Weierstraß elliptic functions to quantum invariants

I will talk about a joint work with Si Li on the computation of higher genus B-model for elliptic curves.

I will first formulate the Feynman amplitudes in the higher genus B-model (Kodaira-Spencer theory)

in terms of cohomological parings. Then I will discuss properties of the Feynman amplitudes, including

the origin of their quasi-modularity, the geometric Interpretation of their modular completions, etc.

Finally I explain the implication of the cohomological reformation in renormalization.

## M-Theory, 3 Manifolds and certain SL(2,Z) representations

The M-theory perspective, more specifically the 3d-3d correspondence, leads to interesting predictions for the structure of the Witten-Reshetikhin-Turaev invariants of 3-manifolds and superconformal indices of the 3d SCFTs arising from compactifying five-branes on 3-manifolds. Especially, one expects SL(2,Z) representations to play an important role.

## On the Hodge-GUE correspondence

We discuss the recent Hodge--GUE correspondence conjecture on an explicit

relationship between special cubic Hodge integrals over the moduli space of stable

algebraic curves and enumeration of ribbon graphs with even valencies. We sketch

a proof of this conjecture based on the Virasoro constraints. We also discuss the

conjectural relationship between the cubic Hodge integrals satisfying the local

Calabi--Yau condition and the Bogoyavlensky--Toda hierarchy (*aka* fractional

KdV). The talk is based on a series of joint works with B. Dubrovin, S.-Q. Liu

## Exact results for class $S_k$

We will introduce a large class of $\mathcal{N}=1$ superconformal theories, called

$S_k$, which is obtained from Gaiotto's $\mathcal{N}=2$ class $S$ via orbifolding. We

will study the Coulomb branch of the theories in the class by

constructing and analyzing their spectral curves. Using our experience

from the $\mathcal{N}=2$ \textsc{agt} correspondence we will search for a 2d/4d relations

(\textsc{agt}${}_{k}$) for the $\mathcal{N}=1$ theories of class $S_k$. From the curves we will

identify the 2d \textsc{cft} symmetry algebra and its representations, namely

## Geometric recipe for superpotentials

Nekrasov, Rosly and Shatashvili observed that the generating function of a certain space

of ${\rm SL}(2)$ opers has a physical interpretation as the effective twisted superpotential

for a four-dimensional $\mathcal{N}=2$ quantum field theory. In this talk we describe the

ingredients needed to generalise this observation to higher rank. Important ingredients are

spectral networks generated by Strebel differentials and the abelianization method. As an

example we find the twisted superpotential for the $E_6$ Minahan-Nemeschansky theory.

## Tropical Hurwitz and GW numbers

Tropical geometry has been proved successful to study various types of enumerative

numbers, including Gromov-Witten invariants for toric surfaces and Hurwitz numbers

with at most two special points. In my talk I will try to give an overview on

some showcase results, recent developments (counting "real'' curves) and relations

to other approaches.

## Group actions on quiver varieties and application to branes

We study two types of actions on King's moduli spaces of quiver representations over a

field $k$, and we decompose their fixed loci using group cohomology in order to give

modular interpretations of the components. The first type of action arises by considering

finite groups of quiver automorphisms. The second is the absolute Galois group of a

perfect field $k$ acting on the points of this quiver moduli space valued in an algebraic

closure of $k$; the fixed locus is the set of $k$-rational points, which we decompose

## Line defects in $\mathcal{N}=2$ QFT and framed quivers

I will discuss a certain class of line defects in four dimensional supersymmetric theories

with $\mathcal{N}=2$. Many properties of these operators can be rephrased in terms of

quiver representation theory. In particular one can study BPS invariants of a new kind, the

so-called framed BPS states, which correspond to bound states of ordinary BPS states with

the defect. Such invariants determine the IR vev of line operators. I will discuss how these

invariants arise from framed quivers. Time permitting I will also discuss a formalism to study

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