GRK-Seminar Wintersem. 2024/25

RTG Seminar Winter term 2024

The Thursday morning seminar (10:15-11:45 in WSC-N-U-3.05) will be the “Research Training Group Seminar” where members of the RTG (PhD students, post-docs,…) present their results. Sometimes, we also have speakers from other places. Depending on the number of speakers and on the proposed topic, a speaker could use one or two sessions.

31.10.2024	Carolina Tamborini	Non-tautological double cover cycles
7.11.2024	Andreas Pieper	Newton meets Torelli
14.11.2024	Sebastian Bartling	Some remarks on Brauer groups of proper and smooth Deligne-Mumford stacks over the integers.
21.11.2024	Pietro Gigli	tba
28.11.2024	reserved	general assembly
5.12.2024	Robert Franz	tba
12.12.2024	N. N.	tba
19.12.2024	Pietro Gigli	tba
9.1.2025	Thiago Solovera y Nery	tba
16.1.2025	Maximilian Hauck	Syntomic cohomology and stacks in p-adic geometry
23.1.2025	Lukas Bröring	tba
30.1.2025	Giorgio Navone	tba

Abstracts

Carolina Tamborini: Non-tautological double cover cycles.

After an introduction on moduli spaces of curves and their tautological rings, I will discuss joint works together with V. Arena, S. Canning, E. Clader, R. Haburcak, A.Q. Li, and S.C. Mok and with D. Faro on the construction of many new non-tautological algebraic cohomology classes arising from double cover cycles, generalising previous work by Graber-Pandharipande and van Zelm.

Andreas Pieper: Newton meets Torelli.

The Newton stratification is a natural refinement of the $f$-number stratification of the moduli space $\mathcal{A}_g$ in characteristic $p>0$. In the beginning of the talk I will define the stratification and discuss its properties. The main part will be about the restriction of the Newton-stratification to the Torelli locus. Here much less is known; despite numerous contributions there is no complete (even conjectural) picture of questions regarding non-emptiness, dimensions, or the closure relation.
I will report on work in progress that shows that all the Newton strata on $\mathcal{M}_4$ are not empty and have the expected dimension.

Sebastian Bartling: Some remarks on Brauer groups of proper and smooth Deligne-Mumford stacks over the integers.

Class field theory implies that $Br(Spec(\mathbb{Z}))=0$. One might wonder whether $Br(X)=0$ for any DM-stack $X\rightarrow Spec(\mathbb{Z})$ that is proper and smooth. I want to explain that $Br(X)$ is always finite, give conditions when $Br(X)=0$ and explain that for the moduli stack of stable genus $g$ curves with $n$ marked points, we have $Br(\overline{\mathcal{M}}_{g,n,\mathbb{Z}})=0$ for $(g,n)=(1,1),(1,2),(2,0),(3,0)$, any $g$ greater or equal than 4. This is joint work with Kazuhiro Ito.