Wednesday
8 November, 2023

14:00

U2200

Riccardo Pengo (Leibniz Universität Hannover)
Standard conjectures in Arakelov geometry: from the projective space to Grassmannians

16:00

U2200

Manuel Hoff (U Bielefeld)
(G, mu)displays and RapoportZink spaces

Wednesday
6 December, 2023

14:1515:15

U2200

Léonard PilleSchneider (U Regensburg)
Continuity of families of MongeAmpère measures

16:1517:15

U2200

Enrica Mazzon (U Regensburg)
A nonarchimedean approach to the SYZ conjecture

Wednesday
20 December, 2023

14:00

U2200

Paul Kiefer(U Bielefeld)
Injectivity of the KudlaMillsonLift in genus 2

16:00

U2200

Jens Funke (Durham U)
Indefinite theta series via incomplete theta integrals

Wednesday
17 January, 2024

14:00

U2200

Timo Richarz(TU Darmstadt)
Nonnormality of Schubert varieties

16:00

U2200

Thibaud van den Hove (TU Darmstadt)
Motivic Satake equivalences and central motives

Wednesday
31 January, 2024

16:00

U2200

Claudia Fevola (INRIA Saclay)
KP solutions from nodal curves, and the Schottky problem

17:00

U2200

Andreas Gross (Goethe Universität Frankfurt am Main)
Tropicalizing Psi Classes
[Abstract]
Tropical curves are piecewise linear objects arising as
degenerations of algebraic curves. The close connection between
algebraic curves and their tropical limits persists when considering
moduli. This exhibits certain spaces of tropical curves as the
tropicalizations of the moduli spaces of stable curves. It is,
however, still unclear which properties of the algebraic moduli spaces
of curves are reflected in their tropical counterparts.
In work with Renzo Cavalieri and Hannah Markwig we defined, in a
purely tropical way, tropical psi classes in arbitrary genus. They are
operational cocycles on a stack of tropical curves, which enjoy
several properties that we know from their algebraic ancestors. We
also computed two examples in genus one and gave a tropical
explanation for the psi class on the moduli space of 1marked stable
genus1 curves to be 1/24 times a point.
In my talk, I will report on joint work in progress with Renzo
Cavalieri, where we explore the missing piece in the story: the link
to algebraic geometry. I will explain how to obtain, if we are lucky,
a family of tropical curves from a family of algebraic curves.
Naturally, there also is a correspondencetype theorem that equates
algebraic and tropical intersection products with psi classes, thus
showing that the tropical computations done with Cavalieri and Markwig
faithfully reflect the algebraic world.

Wednesday
14 February, 2024

14:00

V2200

Jan Vonk (U Leiden)
Around the class number one problem

16:00

V2200

Domenico Valloni (EPFL Lausanne)
Noether problem in mixed characteristic

Wednesday
15 May, 2024

14:30

H4

Fumiaki Suzuki (Hanover)
Noninjectivity of the cycle class map in continuous ladic cohomology

16:00

H4

Fabio Bernasconi (Neuchatel)
On the failure of the Frobeniusstable version of the GrauertRiemenschneider theorem

Wednesday
29 May, 2024

14:00

H4

Anneloes Viergever (U Hannover)
Motivic DonaldsonThomas invariants in low degrees for the threedimensional projective space.
[Abstract]
Suppose that we would like to count ideal sheaves with zerodimensional support of a given length on a smooth projective toric complex threefold with an action of the 3dimensional torus on it. One could try to do this by doing intersection theory on a suitable moduli space, i.e. the Hilbert scheme of points on our threefold. However, these Hilbert schemes might have all sorts of bad singularities. One way to remedy this issue, is to use virtual fundamental classes, introduced by BehrendFantechi. The degrees of those classes  which are integers  are called DonaldsonThomas invariants. Maulik, Nekrasov, Pandharipande and Okounkov have computed the generating series of these DonaldsonThomas invariants in terms of a power of the MacMahon function.
Levine has introduced a motivic analogue of virtual fundamental classes, of which the degrees land in the Witt ring of the base field when the scheme has an orientation in some sense. By another result of Levine, there is such an orientation for the threedimensional projective space, so that one can define its motivic DonaldsonThomas invariants. If we take the base field to be the real numbers, the degrees of these classes are again integers. We discuss a computation of the first three motivic DonaldsonThomas invariants for the threedimensional projective space, and a conjecture for an analogue of the formula of Maulik, Nekrasov, Pandharipande and Okounkov in this setting.

16:00

H4

Nils Scheithauer (TU Darmstadt)
Reflective modular varieties and their cusps

Wednesday
12 June, 2024

14:15

H4

Clémentine LemariéRieusset (U DuisburgEssen)
Motivic Linking
[Abstract]
In classical knot theory and in real algebraic knot theory, one can associate to an oriented link with two components (i.e. two disjoint oriented knots) its linking number: an integer which counts how many times one of the components turns around the other component. In this talk, I will present motivic counterparts, over a perfect field F, to the linking number, which describe how two (nice) disjoint oriented closed Fsubschemes of an ambient Fscheme can be intertwined, i.e. linked together. These counterparts, called quadratic linking degrees, take values in the Witt group of F, in the GrothendieckWitt group of F or in the first MilnorWitt Ktheory group of F and can be computed in a similar way to the classical case, by replacing the singular complex with the RostSchmid complex. There will be several examples, some of which will feature affine planes minus the origin in the affine fourspace minus the origin (the setting closest to classical knot theory) as well as other motivic spheres, and some of which will feature projective lines in the projective threespace (the setting closest to real algebraic knot theory).

15:45

H4

Sara Mehidi (Utrecht University)
The Logarithmic Jacobian and extension of torsors over families of degenerating curves
[Abstract]
The problem of extending fppf torsors has been largely encountered in the literature, without giving a satisfactory solution in the classical setting. Given a torsor on the smooth locus of a family of nodal curves, the question consists in extending each of the structural group and the total space of the torsor above the family. It turns out that adding a log structure to the family of nodal curves allows to enlarge the category of classical (fppf) torsors to what is called log torsors. In particular, this provides a new framework for studying the aforementioned problem.
On the other hand, Molcho and Wise constructed the log Picard group, a canonical compactification of the Picard group of families of nodal curves that is smooth, proper and possesses a group structure, but which can only be represented in the category of logarithmic spaces. Afterwards, it was shown that the restriction of this log Picard group to the degree zero log line bundles  which gives the socalled Logarithmic Jacobian is in fact the log Néron model of the Jacobian of the smooth locus. In this talk, I will show that the Logarithmic Jacobian classifies finite log torsors over families of nodal curves, generalizing the classical situation for smooth curves. Then, we will see that the Néron property of the Log Jacobian allows to get a result on extending fppf torsors into log torsors over families of nodal curves. This is a joint work with Thibault Poiret.

Wednesday
3 July, 2024

14:1515:15

H4

Andreas Mihatsch (University of Bonn)
Generating series of complex multiplication cycles

15:4516:45

H4

Joahnnes Sprang (U DuisburgEssen)
Irrationality and linear independence of padic zeta values

Wednesday
10 July, 2024

14:1515:15

H4

Sebastián Olano (University of Toronto)
Singularities of Secant Varieties from a Hodge theoretic perspective

15:4516:45

H4

Guido Kings (University of Regensburg)
Deligne’s conjecture for algebraic Hecke characters

Wednesday
17 July, 2024

14:15

H4

Steven Charlton (MPIM Bonn)
Goncharov's programme, and depth reductions of multiple polylogarithms (in weight 6)
[Abstract]
Abstract: Multiple polylogarithms Li_{k_1,\ldots,k_d}(x_1,\ldots,x_d) are a class of multivariable special functions appearing in connection with Ktheory, hyperbolic geometry, values of zeta functions/Lfunctions/Mahler measures, mixed Tate motives, and in highenergy physics.
One of the main challenges in the study of multiple polylogarithms resolves around understanding how on many variables a multiple polylogarithm function (or `interesting' combinations thereof) actually depend (``the depth''), as for example Li_{1,1} can already be expressed via Li_2. Goncharov gave a conjectural criterion (``the Depth Conjecture'') for determining this, using the motivic coproduct, as part of his programme to investigate Zagier's Polylogarithm Conjecture on values of the Dedekind zeta function \zeta_F(m).
I will give an overview of multiple polylogarithms, Goncharov's Depth Conjecture, and its implications. I will try to discuss what is currently known, including recent results in weight 6, and what we are still trying to investigate.

15:45

H4

Xiaolei Zhao (UCSB)
Moduli of stable objects on Fano threefolds

Wednesday
23 October, 2024

14:15

TBD

Danylo Radchenko (U Lille)
TBD

15:45

TBD

TBD
TBD
