The Bielefeld Algebraic and Arithmetic Geometry Seminar WS2025/2

Welcome to the website of the Bielefeld Algebraic and Arithmetic Geometry Seminar! For more information, please contact one of the organizers: Claudia Alfes, Ana Botero, Lennart Gehrmann, Fabian Hebestreit, Eike Lau, Michael Spiess, Charles Vial, and Thomas Zink.

Talks

Wednesday 22 October, 2025
14:15	TBA	TBA TBA [Abstract] TBA
15:45	TBA	TBA TBA [Abstract] TBA
Wednesday 5 November, 2025
14:15	H15	Grzegorz Kapustka (Jagiellonian U) Derived equivalence of hyperkahler fourfolds [Abstract] We present conditions under which two K3^[2] type manifolds are derived equivalent.
15:45	H15	Michal Kapustka (Polish Academy of Sciences) Periods of double EPW sextics and double EPW cubes [Abstract] Double EPW sextics and double EPW cubes are two families of polarised hyperkaehler manifolds arising from the same data, namely Lagrangian subspaces in the third exterior power of a six dimensional vector space. We will discuss relations between Hodge structures of pairs of these manifolds corresponding to the same Lagrangian subspace. As a consequence we shall describe both compared varieties as moduli spaces of objects on the same K3 category: the Kuznetsov component of an associated Gushel-Mukai fourfold. This is joint work with G. Kapustka, A. Kuznetsov, G. Mongardi.
Wednesday 19 November, 2025
14:15	TBA	TBA TBA [Abstract] TBA
15:45	TBA	TBA TBA [Abstract] TBA
Wednesday 3 December, 2025
14:15	V2-205	Felipe Angel (IMPA) The linked projective space [Abstract] Linked projective spaces are quiver Grassmanians of constant dimension one of certain quiver representations, called linked nets, over special class of quivers, called Zn-quivers. They were recently introduced by Esteves, Vital and Santos, as a tool for describing schematic limits of families of divisors. They are subschemes of products of projective spaces of the same dimension. It is an open question whether they are degenerations of the (small) diagonal. We show that linked projective spaces share many geometric and combinatorial features with the special fiber of a well-studied class of degenerations of the diagonal, namely Mustafin varieties. In particular, we show that linked projective spaces are normal crossings schemes and have the chow class of the diagonal.
15:45	V2-205	Eduardo Esteves (IMPA) Limit canonical series [Abstract] For every family of smooth curves degenerating to a fixed stable curve on the Deligne-Mumford boundary of the moduli space of curves, the canonical linear series of Abelian differentials degenerates to a collection of linear series on the stable curve. As the degenerating family varies, so does the resulting collection. In this way, each stable curve in the moduli space is associated with infinitely many such collections of linear series - one for each degenerating family. We describe all limit collections of linear series for stable curves that are general within a given dual graph stratum, in the sense that the markings given by the nodes on each irreducible component of the stable curve are in general position. We also construct a projective variety which parametrizes these collections. This had previously been achieved only in very special cases: for curves of compact type by Eisenbud and Harris in the 1980s, for two-component curves by Esteves and Medeiros in the 2000s, and in a few other isolated situations. The breakthrough was made possible by combining work by Bainbridge, Chen, Gendron, Grushevsky and Möller from 2016 on the residue conditions limits of differentials must satisfy, with recent work by ourselves on the tropicalization of general linear series. We will review the history - specially the latter work - and explain our analysis and construction. Time allowing, we will also discuss related projects on the subject. Joint work with Omid Amini and Eduardo Garcez.
Wednesday 17 December, 2025
14:15	M4-108	Johannes Linn (MPIM Bonn) Bounds for Kloosterman Sums for $\mathrm{GL}_n$ [Abstract] Classical Kloosterman sums defined by $S(m,n;c):=\sum_{x\in (\mathbb{Z}/c\mathbb{Z})^*}e\Big(\frac{mx+n\overline{x}}{c}\Big)$ for $m,n\in\mathbb{Z}$ and $c\in\mathbb{Z}^+$ have become ubiquitous in Number Theory appearing for example in Fourier coefficients of classical Poincaré series and therefore in the geometric side of relative trace formulae of Petersson-Kuznetsov type. Working with relative trace formulae over $\mathrm{GL}_n$ requires understanding of more general Kloosterman sums. In this talk, I will present a method to parametrize and bound the generalized Kloosterman sums for $\mathrm{GL}_n$ obtaining a power saving compared to the trivial bound and gaining insight into their structure.
15:45	TBA	Sil Linskens (U Regensburg) A 2-categorical approach to building six functor formalisms [Abstract] The idea of six functors formalisms originates in Grothendieck's work on duality for étale cohomology of schemes. Much more recently, a simple and powerful definition of this structure was given using the theory of higher categories. This has greatly improved our ability to work with such structures. However it does not simplify our task of constructing six functor formalisms, and in fact apriori it makes it much harder. Nevertheless, work of Liu-Zheng formalised the most important construction principle, which goes back to the original work of Artin, Grothendieck and Verdier on the six functor formalism on étale cohomology. I will explain a new approach to this construction principle which is joint work with Bastiaan Cnossen and Tobias Lenz. To do this we recast the problem as that of computing a certain universal (infinity,2)-category, which we then do by combining methods from parametrised and (infinity,2)-category theory.
Wednesday 14 January, 2026
14:15	H15	Mads Christensen (MPIM Bonn) Linking numbers and non-holomorphic Siegel modular forms [Abstract] A compelling selling point for the theory of classical modular forms is the frequent connections between their Fourier coefficients and other areas of mathematics. I will give some examples of this, starting with classical theta functions and ending with new results that relate certain non-holomorphic Siegel modular forms of genus 2 to arithmetic hyperbolic 3-manifolds.
15:45	H15	Edgar Assing (Bonn U) On a Katok-Sarnak type formula for hyperbolic 3 space [Abstract] The classical Katok-Sarnak formula relates averages of Maaß forms over Heegner points to certain Fourier coefficients of half integral weight modular forms. This formula is of great structural interest and has applications to equidistribution problems. A generalization to hyperbolic 3 space was, for example, given in the work of Matthes and Mizuno, which is the topic of this talk. We plan to give an accessible introduction to the topic and to sketch a new(ish) proof.
Wednesday 28 January, 2026
14:15	H15	Matteo Longo (Padova) The anticyclotomic Iwasawa main conjectures for elliptic curves [Abstract] I will report on a joint work with Massimo Bertolini and Rodolfo Venerucci in which we prove, under mild technical assumptions, the anticyclotomic Iwasawa main conjectures for rational elliptic curves. I will try to explain the different formulations in the definite and indefinite cases, and the differences occurring when the prime number p is ordinary or supersingular for the elliptic curve, and when it is split or inert in the imaginary quadratic field.
15:45	TBA	Han-Ung Kufner (Regensburg) Critical values of Hecke L-functions [Abstract] A conjecture of Deligne from 1977 relates the critical values of a motivic L-function with certain periods of the motive. The goal of this talk is to explain Deligne's conjecture and to discuss a proof in the case of Hecke L-functions. This generalizes a result of Blasius for Hecke characters of CM-fields. For the proof we use the recently constructed Eisenstein-Kronecker classes of Kings-Sprang and combine them with ideas from Blasius' proof.
Friday 6 February, 2026
14:00	TBA	Maria Abad Aldonza (Université Paris-Sackay) TBA [Abstract] TBA

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The Bielefeld Algebraic and Arithmetic Geometry Seminar WS2025/2

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Wednesday

22 October, 2025

Wednesday

5 November, 2025

Wednesday

19 November, 2025

Wednesday

3 December, 2025

Wednesday

17 December, 2025

Wednesday

14 January, 2026

Wednesday

28 January, 2026

Friday

6 February, 2026