## Poincaré-Birkhoff-Witt theorems: homotopical and effective computational methods for universal envelopes

https://hu-berlin.zoom.us/j/61339297016

## Differential bimodular forms with given residues

This talk will be about the construction of the modular forms in two variables, which are the representatives of the smooth cohomology classes of the modular surfaces. Namely, it will be considered the case of the complement to the Hecke curve (the graph of a Hecke correspondence) on the product of two standard modular curves $Y_0(1)^2$.

## The $L^4$-norm problems for newform Eisenstein series

Let $E$ be an Eisenstein series of primitive nebentypus mod $N$. We reduce

the regularized $L^4$-norm of $E$ to an average of automorphic $L$-functions, for all large $N$. The result is the level aspect analogue of the work by Djanković and Khan for classical Eisenstein series. With this reduction, we can see two new problems: how to estimate this sum, and what should be the Random Wave Conjecture for the fourth moment of the truncated newform Eisenstein series. I will also show the progress on solving the two problems.

## Operads and "horizontal" product for modular operads

Meeting ID: 916 5855 1117

Password: as before.

Contact: Aru Ray and Tobias Barthel.

Classical Operads serve as an abstraction of the family of composable functions. One of the straightforward generalizations suggests replacing the combinatorial structure of directed trees with more general "stable" graphs. This leads to the notion of modular operads. Algebras over modular operads found their applications in mathematical physics, namely various string field theories.

## 4-manifolds and exotic group presentations

Meeting ID: 916 5855 1117

Password: as before.

Contact: Aru Ray and Tobias Barthel.

Two presentations for a group G which have the same deficiency are called exotic if the corresponding presentation complexes are not homotopy equivalent. It was not until the 1970s that the first examples of exotic presentations were found. In the 1980s, Kreck and Schafer went on to use these exotic presentations to construct the first and only known examples of smooth closed 4-manifolds which are stably diffeomorphic but not homotopy equivalent.

## Modular vector fields and Calabi-Yau modular forms

This talk will mostly be concentrated on more general ideas, skipping proofs and technical details, to introduce my recent works on constructing a "modern" generalization of the "classical" theory of modular forms. More precisely, I will introduce a certain moduli space $T$ arising from a special family of Calabi-Yau (CY) varieties. There exists a unique vector field $R$ on $T$, called modular vector field, that satisfies a certain equation involving the Gauss-Manin connection.

## Hilbert's irreducibility theorem and jumps in the rank of the Mordell-Weil group

https://hu-berlin.zoom.us/j/61339297016

## Integrable systems and Hurwitz theory (Please note the change of time!)

Meeting ID: 997 9940 1217

Contact: Christian Kaiser (kaiser@mpim...)

## Geometry of integrable systems

Meeting ID: 997 9940 1217

Contact: Christian Kaiser (kaiser@mpim...)

## 3-manifolds that bound no definite 4-manifold

Meeting ID: 916 5855 1117

Password: as before.

Contact: Aru Ray and Tobias Barthel.

All 3-manifolds bound 4-manifolds, and many constructions of 3-manifolds automatically come with a 4-manifold bounding it. Often times these 4-manifolds have definite intersection form. Using Heegaard Floer correction terms and an analysis of short characteristic covectors in bimodular lattices, we give an obstruction for a 3-manifold to bound a definite 4-manifold, and produce some concrete examples. This is joint work with Kyle Larson.

## Gauge-theoretic obstructions to bounding definite 4-manifolds

Meeting ID: 916 5855 1117

Password: as before.

Contact: Aru Ray and Tobias Barthel.

## 3- and 4-manifolds via knots and links

Password: as before.

## Vanishing theorems for Shimura varieties at unipotent level and Galois representations

Zoom Meeting ID: 919 6497 4060

For password see the email or contact Pieter Moree (moree@mpim...).

## On small divisor functions and a construction of polar harmonic Maass forms

Zoom Meeting ID: 919 6497 4060

For password see the email or contact Pieter Moree (moree@mpim...).

## Pseudoisotopies and surfaces in 4-manifolds

I will talk about pseudo-isotopy, a notion important for understanding self-homeomorphisms (or diffeomorphisms) of manifolds up to isotopy.

Pseudo-isotopies of manifolds in dimensions >=5 were understood in the 70s by work of Cerf for simply connected manifolds, and by Hatcher and Wagoner in the non-simply connected case, using invariants from algebraic K-theory. Quinn later proved Cerf’s result in dimension 4, leading to a classification of self-homeomorphisms of simply connected

4-manifolds up to isotopy.

## New estimates for cubic Weyl sums with short summation

In this talk I will describe some ideas which give a new bound

for exponential sums over cubic polynomials with short summation. I will

provide a brief overview of the role of cubic exponential sums in number

theory, indicate how ideas of Enflo may be developed to make progress on

the problem of improving Weyl's estimate and conclude with some ideas for

further developments.

## Equivariant bordism, multiplicative gerbes and topological electronic structures of crystals

In this talk I will give a short presentation of who I am and the main mathematics subjects that have interested me.

## Cut and paste invariants of manifolds via algebraic K-theory

Recent work of Campbell and Zakharevich has focused on building machinery for studying scissors congruence problems via algebraic K-theory. Their main application was the study of the Grothendieck ring of varieties. In this talk, I will present an application of their framework to the study of cut and paste invariants of manifolds. In particular, I will talk about the construction of a spectrum that recovers the classical "cut and paste" groups for manifolds on \pi_0.

## Beauville decomposition: proof via Fourier-Mukai

Meeting ID: 997 9940 1217

For passcode contact Christian Kaiser (kaiser@mpim...)

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