Talk

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.

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.

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

Meeting ID: 997 9940 1217

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

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.

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

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.

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.