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## The Grothendieck-Teichmüller Lie algebra and related subjects

## From quantum invariants of knots to categorification

## Vorlesung Topology of 4-Manifolds

## Higher quantum Airy structures and W-algebras

This is a joint work with Vincent Bouchard, Dmitry Noshchenko and Nitin Chidambaram.

## Good definition of GR and the case of continuous functions on Teichmüller spaces

## The Barycenter method and the Degree Theorem

## A New Northcott Property for the Faltings Height

The Faltings height is a useful invariant for addressing questions in

arithmetic geometry. In his celebrated proof of the Mordell and

Shafarevich conjectures, Faltings shows the Faltings height satisfies a

certain Northcott property, which allows him to deduce his finiteness

statements. In this work we prove a new Northcott property for the

Faltings height. Namely we show, assuming the Colmez Conjecture and the

Artin Conjecture, that there are finitely many CM abelian varieties of a

fixed dimension which have bounded Faltings height. The technique

## Split Lie 2-algebroids and matched pairs of 2-representations

A matched pair of Lie algebroid representations is equivalent to two seemingly different objects; the bicrossproduct Lie algebroid and the double Lie algebroid of the matched pair. In similar manner, a Lie bialgebroid is equivalent to a ‘cotangent double Lie algebroid’, and to a ‘bicrossproduct' Courant algebroid.

## On congruences in Iwasawa theory for supersingular abelian varieties

Generalizing work of Kobayashi, Büyükboduk and Lei have defined modified Selmer groups along the Zp-cyclotomic extension for abelian varieties with good supersingular reduction. We will discuss congruence properties for these Selmer groups.

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## New guests at the MPIM

## Moduli Spaces of Riemann surfaces

## A renormalization program for Dyson–Schwinger equations (part II)

This Minicourse is based on the speaker's monograph "a mathematical perspective on the phenomenology of non-perturbative Quantum Field Theory" (to appear in MPIM preprint series). In this talk I plan to review the fundamental structure of the Connes--Kreimer renormalization Hopf algebra of Feynman diagrams and combinatorial Dyson--Schwinger equations. Then I explain a recent application of infinite graph theory to Quantum Field Theory which leads to build a renormalization machinery for infinite formal expansions of Feynman diagrams.

## A renormalization program for Dyson–Schwinger equations (part I)

This Minicourse is based on the speaker's Monograph "A mathematical perspective on the phenomenology of non-perturbative Quantum Field Theory" (to appear in MPIM preprint series). In this talk I plan to review the fundamental structure of the Connes--Kreimer renormalization Hopf algebra of Feynman diagrams and combinatorial Dyson--Schwinger equations. Then I explain a recent application of infinite graph theory to Quantum Field Theory which leads to build a renormalization machinery for infinite formal expansions of Feynman diagrams.

## Arithmetic of zero-cycles on products of Kummer varieties and K3 surfaces

The following is joint work with Rachel Newton. In the spirit of work by Yongqi Liang, we relate the arithmetic of rational points to that of zero-cycles for the class of Kummer varieties over number fields. In particular, if X is any Kummer variety over a number field k, we show that if the Brauer-Manin obstruction is the only obstruction to the existence of rational points on X over all finite extensions of k, then the Brauer-Manin obstruction is the only obstruction to the existence of a zero-cycle of any odd degree on X.

## Modular tensor categories and 3D TQFT

## From quantum invariants of knots to categorification, II -- cancelled --

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