Abstracts of upcoming talks at the MPIM. For an overview see also the calendar.

## Recent developments in Quantum Topology -- Cancelled --

We will review the basics of quantum topology such as the colored Jones polynomial of a knot, its standard conjectures relating to asymptotics, arithmeticity and modularity, as well as the recent quantum hyperbolic invariants of Kashaev et al, their state-integrals and their structural properties. The course is aimed to be accessible by graduate students and young researchers.

## "What is...?" seminar

## Recent developments in Quantum Topology

We will review the basics of quantum topology such as the colored Jones polynomial of a knot, its standard conjectures relating to asymptotics, arithmeticity and modularity, as well as the recent quantum hyperbolic invariants of Kashaev et al, their state-integrals and their structural properties. The course is aimed to be accessible by graduate students and young researchers.

## On Gromov-Witten invariants of P^1

Okounkov and Pandharipande derived Virasoro constraints for Gromov-Witten theory of P

1. Later and independently, using Teleman reconstruction theorem and its correspondence with topological recursion, Dunin-Barkowski et al. proved that the stationary sector is encoded in the meromorphic forms w_{g,n} computed by the topological recursion for the spectral curve x(z) = z + 1/z, y(z) = \ln z. This statement is equivalent to local Virasoro constraints.## Vertex Operator Algebras and Modular Forms

Time: Tuesdays, 4.30 - 6 pm

Place: MPIM Lecture Hall, Vivatsgasse 7

First lecture: on April 2, 2019, end on July 2

## Moment maps, their quantization and reduction

Given a Lie group acting on a Poisson manifold and a moment map, Marsden-Weinstein reduction allows us to reduce the manifold and the Poisson structure. This reduction procedure extends to invariant star products and quantum moment maps via the BRST approach. On the other hand, invariant Poisson structures (resp. star products) together with corresponding moment maps (resp. quantum moment maps) can be described as (curved) Maurer Cartan elements of certain DGLA's.

## Modular forms and optimization in the Euclidean space

## Arithmetic support and monodromy

In my talk on Arbeitstagung 2017 I introduced a strange series with rational coefficients related to p-curvatures of certain family of algebraic linear differential equations (Heun equations). This series has zero radius of convergence p-adically for any prime p, which seems to be a new phenomenon, and it is extremely hard to calculate (e.g. using first 40000 primes one can get only first 250 coefficients of the series).

## Single-valued integration

This talk was originally inspired by Zagier's construction of single-valued polylogarithms and regulators in the late 80's.

In short, single-valued functions are ubiquitous in mathematics and physics, since well-defined problems have well-defined answers. On the other hand, the solution to such a problem is often given by an integral, which is usually a multi-valued function of its parameters. The reason is that integration is a pairing between differential forms and chains of integration, and the latter are ambiguously defined.

## Hochschild cohomology and deformation quantization of affine toric varieties

For an affine toric variety we give a convex geometric description of the Hodge decomposition of its Hochschild cohomology. Moreover, we show that every Poisson structure on a possibly singular affine toric variety can be quantized in the sense of deformation quantization.

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