# Talk

Talks and seminars, possibly part of a conference or series.

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

Posted in
Speaker:
Pedro Tamaroff
Affiliation:
Trinity College Dublin
Date:
Tue, 2021-03-16 14:00 - 15:30

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

## Differential bimodular forms with given residues

Posted in
Speaker:
Nina Sakharova
Affiliation:
Higher School of Economics Moscow/MPIM
Date:
Wed, 2021-03-10 14:30 - 15:30
Parent event:
Number theory lunch seminar

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

Posted in
Speaker:
Jiakun Pan
Affiliation:
Texas A&M University, College of Science/MPIM
Date:
Wed, 2021-03-03 14:30 - 15:30
Parent event:
Number theory lunch seminar

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.

Posted in
Speaker:
Affiliation:
Universität Göttingen/MPIM
Date:
Mon, 2021-03-01 14:30 - 15:00
Parent event:
MPIM Topology Seminar

Meeting ID: 916 5855 1117
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

Posted in
Speaker:
Johnny Nicholson
Affiliation:
University College London/MPIM
Date:
Mon, 2021-03-01 14:00 - 14:30
Parent event:
MPIM Topology Seminar

Meeting ID: 916 5855 1117
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

Posted in
Speaker:
Nikdelan Younes
Affiliation:
MPIM
Date:
Wed, 2021-02-24 14:30 - 15:30
Parent event:
Number theory lunch seminar

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

Posted in
Speaker:
Jean-Louis Colliot-Thélène
Affiliation:
CNRS et Université Paris-Saclay
Date:
Tue, 2021-03-02 14:00 - 15:30

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

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

Posted in
Speaker:
Alessandro Giacchetto
Affiliation:
MPIM
Date:
Thu, 2021-02-18 10:00 - 11:30

Meeting ID: 997 9940 1217

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

## Geometry of integrable systems

Posted in
Speaker:
Campbell Wheeler
Affiliation:
MPIM
Date:
Thu, 2021-02-11 14:15 - 15:45

Meeting ID: 997 9940 1217

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

## IMPRS seminar on various topics: Integrable systems

Posted in
Organiser(s):
Christian Kaiser
Date:
Thu, 2021-02-11 14:15 - 14:45

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

Posted in
Speaker:
Marco Golla
Affiliation:
Nantes
Date:
Mon, 2021-02-22 14:00 - 15:00
Parent event:
MPIM Topology Seminar

Meeting ID: 916 5855 1117
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

Posted in
Speaker:
Marco Marengon
Affiliation:
MPIM
Date:
Mon, 2021-02-15 14:00 - 15:00
Parent event:
MPIM Topology Seminar

Meeting ID: 916 5855 1117
Contact: Aru Ray and Tobias Barthel.

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

Posted in
Speaker:
Arunima Ray
Affiliation:
MPIM
Date:
Mon, 2021-02-08 14:00 - 15:00
Parent event:
MPIM Topology Seminar
Meeting ID: 916 5855 1117

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

Posted in
Speaker:
Daniel Gulotta
Affiliation:
MPIM
Date:
Wed, 2021-02-17 14:30 - 15:30
Parent event:
Number theory lunch seminar

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

Posted in
Speaker:
Andreas Mono
Affiliation:
Universität zu Köln
Date:
Wed, 2021-02-10 14:30 - 15:30
Parent event:
Number theory lunch seminar

Zoom Meeting ID: 919 6497 4060
For password see the email or contact Pieter Moree (moree@mpim...).

## Pseudoisotopies and surfaces in 4-manifolds

Posted in
Speaker:
Oliver Singh
Affiliation:
Durham University
Date:
Mon, 2021-02-01 14:00 - 14:20
Parent event:
MPIM Topology Seminar

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

Posted in
Speaker:
Bryce Kerr
Affiliation:
MPIM
Date:
Wed, 2021-02-03 14:30 - 15:30
Parent event:
Number theory lunch seminar

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

Posted in
Speaker:
Bernando Uribe
Affiliation:
MPIM
Date:
Mon, 2021-01-25 14:30 - 14:50
Parent event:
MPIM Topology Seminar

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

Posted in
Speaker:
Carmen Rovi
Affiliation:
Ruprecht-Karls-Universität Heidelberg/MPIM
Date:
Mon, 2021-01-25 14:00 - 14:20
Parent event:
MPIM Topology Seminar

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

Posted in
Speaker:
Mingjia Zhang
Affiliation:
Universität Bonn/MPIM
Date:
Thu, 2021-02-04 14:15 - 15:45

Meeting ID: 997 9940 1217
For passcode contact Christian Kaiser (kaiser@mpim...)

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