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## MPI-Oberseminar

The Oberseminar is a very long running seminar at MPI (‘Ober‘ standing for 'upper'). Its idea is that the guests of the MPI speak in this seminar (hopefully early in their stay) and get the chance to explain their work to the other guests.

## Friedrich Hirzebruch Lecture

The annual Friedrich Hirzebruch Lecture is a series of lectures started in 2007 on the occasion of the 80th birthday of Prof. Friedrich Hirzebruch. The lectures address a general audience and aim at illustrating the relation between mathematics and art, society and other fields.

## From Rational points to étale homotopy fixed points

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

## 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 $Y_0(1)^2$.

## Embeddings of manifolds in Euclidean space and Feynman diagrams

The spaces of embeddings of manifolds M in R^{n} are classical objects in topology. I will discuss the computation of their rational homotopy type, for fairly general M, based on recent joint work with B. Fresse and V. Turchin. The answer can be formulated in terms of combinatorial (Feynman) diagrams.

## 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.

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

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

## 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.

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