# Talk

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

## [Obersem. Diff. Geometry/Venue: Math. Center, Endenicher Allee 60] "The Yamabe Invariant of Complex Surfaces"

Posted in
Speaker:
Michael Albanese
Zugehörigkeit:
Université du Québec à Montréal
Datum:
Don, 14/07/2022 - 16:30 - 17:30

Please note the VENUE of this talk:
Math Center, Endenicher Allee 60, Room 0.011, Bonn University.

The Yamabe invariant is a real-valued diffeomorphism invariant coming from Riemannian geometry. Using Seiberg-Witten theory, LeBrun showed that the sign of the Yamabe invariant of a Kähler surface is determined by its Kodaira dimension. We consider the extent to which this remains true when the Kähler hypothesis is removed. This is joint work with Claude LeBrun.

## [Oberseminar Diff. Geometry/Venue: Lipschitz-Saal, Endenicher Allee 60] "Stability of hyperbolic metrics"

Posted in
Speaker:
Frieder Jäckel
Zugehörigkeit:
Universität Bonn
Datum:
Don, 07/07/2022 - 16:30 - 17:30

Please note the VENUE of this talk:
Lipschitz-Saal, Endenicher Allee 60, Math. Center, Bonn University.

We show that if a 3-manifold admits a metric of finite volume
that is almost hyperbolic in a suitable, then there exists a hyperbolic
metric that is close to the given metric in the $C^{2,\alpha}$-topology.
We then discuss an application of this result to the drilling and filling of
hyperbolic 3-manifolds. The talk is based on joint work with Ursula
Hamenstädt.

## Gathertown "meet the speakers" moment (online)

Posted in
Speaker:
Meet: Joana Cirici and Kate Ponto
Datum:
Don, 30/06/2022 - 17:00 - 17:45

## Gathertown "meet the speakers" moment (online)

Posted in
Speaker:
Meet: Lars Hesselholt and Akhil Mathew
Datum:
Mit, 29/06/2022 - 17:00 - 17:45

## Gathertown "meet the speakers" moment (online)

Posted in
Speaker:
Meet: Oscar Randal-Williams and Jenny Wilson
Datum:
Die, 28/06/2022 - 17:00 - 17:45

## The Van Est isomorphism, part II [IMPRS Seminar]

Posted in
Speaker:
Zugehörigkeit:
Universität Bonn
Datum:
Mon, 27/06/2022 - 12:30 - 14:00
Parent event:
IMPRS-seminar on Lie groups

Contact: Christian Kaiser (kaiser@mpim-bonn.mpg.de)

## tba

Posted in
Speaker:
Ivan Horozov
Zugehörigkeit:
MPIM/City University of New York, Bronx
Datum:
Mit, 20/07/2022 - 14:30 - 15:30
Parent event:
Number theory lunch seminar

Contact: Pieter Moree (moree@mpim-bonn.mpg.de)

## On Birch–Swinnerton-Dyer volumes for hypergeometric Calabi-Yau motives

Posted in
Speaker:
Vasily Golyshev
Zugehörigkeit:
IITP, IHES
Datum:
Mit, 22/06/2022 - 14:30 - 15:30
Parent event:
Number theory lunch seminar

Contact: Pieter Moree (moree@mpim-bonn.mpg.de)

We study the arithmetic of rank 4 weight 3 Calabi--Yau
motives in the framework of a broader program that approaches
regulators via differential equations that control them. We
introduce biextension periods for certain hypergeometric
CY motives and compare them numerically to the first derivative
of their $L$--functions at $s=2$, obtaining evidence in favor
of a B-SD-type conjecture.

## The Van Est isomorphism, part I

Posted in
Speaker:
Annika Tarnowsky
Zugehörigkeit:
MPIM
Datum:
Mon, 20/06/2022 - 12:15 - 13:45
Parent event:
IMPRS-seminar on Lie groups

Contact: Christian Kaiser (kaiser@mpim-bonn.mpg.de)

## Symplectic Calabi-Yau 4-manifolds: some recent progress

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Speaker:
Weimin Chen
Zugehörigkeit:
MPIM/University of Massachusetts-Amherst
Datum:
Don, 23/06/2022 - 15:00 - 16:00
Parent event:
MPI-Oberseminar

Contact: Christian Kaiser (kaiser@mpim-bonn.mpg.de)

## Detecting non-permutative elements of $K_1(\text{Var})$ using point counting

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Speaker:
Inna Zakharevich || CA
Zugehörigkeit:
Cornell University
Datum:
Don, 30/06/2022 - 17:45 - 18:30

The Grothendieck ring of varieties is defined to be the free abelian group generated by varieties (over some base field $k$) modulo the relation that for a closed immersion $Y\to X$ there is a relation that $[X] = [Y] + [X \setminus Y]$. This structure can be extended to produce a space whose connected components give the Grothendieck ring of varieties and whose higher homotopy groups represent other geometric invariants of varieties. This structure is compatible with many of the structures on varieties.

## Topological cyclic homology and the Fargues-Fontaine curve

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Speaker:
Lars Hesselholt || GER
Zugehörigkeit:
University of Copenhagen
Datum:
Don, 30/06/2022 - 16:15 - 17:00

I will explain how the Fargues-Fontaine curve appears from localizing invariants, including K-theory and topological cyclic homology, and indicate how the twistor projective line should appear analogously.

## Euler classes, pairings, and duality

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Speaker:
Kate Ponto || CA
Zugehörigkeit:
University of Kentucky
Datum:
Don, 30/06/2022 - 15:00 - 15:45

Classical Morita equivalence defines an Euler class for modules that generalizes the Euler characteristic for spaces. Using this understanding of the Euler class, fundamental structure of the class becomes accessible. Among many choices, in this talk I'll focus on compatibility of the Euler class with a familiar pairing on Hochschild homology since it also allows the exploration for different forms of duality.

## The family signature theorem

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Speaker:
Oscar Randal-Williams || GER
Zugehörigkeit:
University of Cambridge
Datum:
Mit, 29/06/2022 - 17:45 - 18:30

Hirzebruch's signature theorem relates the signature of the intersection form of a manifold with the integral over the manifold of a certain characteristic class, namely the L-class. This was extended to families of smooth manifolds (i.e. smooth fibre bundles) by Atiyah, using the family index theorem for the fibrewise signature operator. In this setting it relates the Chern character of a certain vector bundle constructed from the local system of intersection forms of the fibres, with the fibre integral of the L-class.

## Towards conjectures of Rognes and Church--Farb--Putman

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Speaker:
Jenny Wilson || CA
Zugehörigkeit:
University of Michigan
Datum:
Mit, 29/06/2022 - 16:15 - 17:00

In this talk I will give an overview of two related projects. The first project concerns the high-degree rational cohomology of the special linear group of a number ring $R$. Church--Farb--Putman conjectured that, when $R$ is the integers, these cohomology groups vanish in a range close to the virtual cohomological dimension. The groups $SL_n(R)$ satisfy a twisted analogue of Poincaré duality called virtual Bieri--Eckmann duality, and their rational cohomology groups are governed by $SL_n(R)$-representations called the Steinberg modules.

## Yang-Baxter elements and a new proof of homological stability for the mapping class group of surfaces

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Speaker:
Nathalie Wahl || GER
Zugehörigkeit:
University of Copenhagen
Datum:
Mit, 29/06/2022 - 15:00 - 15:45

A Yang-Baxter element in a monoidal category gives a weak form of braiding. We explain how such an element allows to define a semi-simplicial set whose connectivity rules homological stability for certain automorphism groups in the category, and how this can be used in the category of bimarked surfaces to give a quite direct proof of slope 2/3 stability of the homology of the mapping class groups of surfaces. This is joint work with Oscar Harr and Max Vistrup.

## Syntomic Complexes

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Speaker:
Akhil Mathew || CA
Zugehörigkeit:
University of Chicago
Datum:
Die, 28/06/2022 - 17:45 - 18:30

I will discuss the theory of syntomic complexes (due to Bhatt--Morrow--Scholze and Bhatt--Lurie) and their identification for regular schemes (joint with Bhatt), inspired by some work in topological Hochschild and cyclic homology.

## Weights in homotopy theory

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Speaker:
Joana Cirici || GER
Zugehörigkeit:
Universitat de Barcelona
Datum:
Die, 28/06/2022 - 16:15 - 17:00

Weight decompositions were first introduced in the setting of rational homotopy as a tool to study p-universal spaces. The same notion may be adapted to many other algebraic contexts and, in general, positive and pure weight decompositions have strong homotopical consequences, often related to formality. A main source of weights is algebraic geometry, either via the theory of mixed Hodge structures on de Rham cohomology or the theory of Galois actions in étale cohomology.

## On the $K$-theory of $\mathbb{Z}/p^n$

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Speaker:
Ben Antieau || CA
Zugehörigkeit:
Northwestern University
Datum:
Mon, 27/06/2022 - 16:15 - 17:00

I will report on joint work with Achim Krause and Thomas Nikolaus on an algorithm to compute the higher algebraic $K$-groups of rings such as $\mathbb{Z}/p^n$.

## Artin reciprocity via spheres

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Speaker:
Dustin Clausen || GER
Zugehörigkeit:
University of Copenhagen
Datum:
Mon, 27/06/2022 - 17:30 - 18:15

I will explain a very strange proof of the Artin reciprocity law.  At the heart of it is the construction of a sphere from every locally compact Q-vector space.

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