## New guests at the MPIM

## A categorical approach to universal knot invariants

## tba

## Surface systems of links and refined triple linking numbers

A surface system for a link in the 3-sphere is a collection of Seifert surfaces for the components of the links, that intersect one another transversally and in at most triple points. The intersections are thought of as oriented manifolds. Given two links with the same pairwise linking numbers, do they admit homeomorphic surface systems?

## tba

## Topological Twists of Factorization Algebras

The idea of topologically twisting a supersymmetric field theory was introduced in the physics literature in order to generate interesting new examples of topological field theories. The idea is very general, but systematically realising the examples it produces is not always possible using mathematical models for topological field theory (such as Atiyah-Segal's functorial field theory, or the theory of E_n-algebras). In this talk I'll explain what it means to twist a supersymmetric field theory in the factorization algebra framework devel

## New guests at the MPIM

## Harmonic maps between Riemannian manifolds

## Algebraic K-theory of infinite products via Grayson's binary complexes

## BV formalism of T-duality geometry

A BV formalism is not only a fundamental framework of quantum field theory, but also appears in a variety of fields of mathematics and physics as an universal structure. After we prepare BV-geometry and notion of so called NS fluxes and T-duality, we reformulate geometry of T-duality by the BV-AKSZ formalism based on supergeometry. Moreover we explain that extended T-duality recently proposed in physics is also formulated and unified by this formalism.

## Variations of semi-infinite Hodge structures, quantum master equation on cyclic cochains, Feynman transforms and cohomological field theories

## On Cayley and Langlands type correspondences for Higgs bundles

The Hitchin fibration is a natural tool through which one can understand the moduli space of Higgs bundles and its interesting subspaces (branes). After reviewing the type of questions and methods considered in the area, we shall dedicate this talk to the study of certain branes which lie completely inside the singular fibres of the Hitchin fibrations.

## The Khovanov space and generalizations

A quantum knot cohomology is a knot invariant recovering a quantum knot polynomial as its Euler characteristic. Sometimes these cohomologies are the usual singular cohomologies of spaces which are themselves knot invariants. The first example is due to Lipshitz and Sarkar: the Khovanov space. I'll tell you why you might care about this if you're only interested in low-dimensional topology. I'll also sketch the construction, aiming to keep it understandable, and point to some generalizations. No knowledge assumed. This is join

## Formality theorem and Kontsevich-Duflo theorem for Lie pairs

A Lie pair $(L,A)$ consists of a Lie algebroid $L$ together with a Lie subalgebroid $A$. A wide range of geometric situations can be described in terms of Lie pairs including complex manifolds, foliations, and manifolds equipped with Lie algebra actions. We establish the formality theorem for Lie pairs. As an application, we obtain Kontsevich-Duflo type theorems for Lie pairs. In this talk, I'll start with the case of $\mathbf{g}$-manifolds, i.e., smooth manifolds equipped with Lie algebra actions.

## New guests at the MPIM

## On semiconjugate rational functions

Let A and B be rational functions on the Riemann sphere. The function B is

said to be semiconjugate to the function A if there exists a non-constant rational

function X such that A\circ X= X\circ B (*).

The semiconjugacy condition generalises both the classical conjugacy relation and

the commutativity condition. In the talk we present a description of solutions of

functional equaton (*) in terms of orbifolds of non-negative Euler characteristic on

the Riemann sphere, and discuss numerous relations of this equation with complex

dynamics and number theory.

## Exotic Poisson summation formulas on the real line

A crystalline measure is a measure whose support is a discrete closed set,

and whose Fourier transform is also a measure with this property. A

generalized Dirac comb is always crystalline, and all other crystalline

measures are called exotic. I will describe a recent construction of a

continuous family of exotic crystalline measures that uses weakly

holomorphic modular forms on the Hecke group.

The talk is based on a joint work with Maryna Viazovska.