The Bielefeld Algebraic and Arithmetic Geometry Seminar SS2025

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, Eike Lau, Michael Spiess, Charles Vial, and Thomas Zink.

Talks

Wednesday 16 April, 2025
14:15	V2 210/216	Igor Burban (U Paderborn) Algebraic geometry of the torus model of the fractional quantum Hall effect [Abstract] The experimental discovery of the quantum Hall effect is widely considered to be a one of the major events in the condensed matter physics in the second half of the twentieth century. Both experimental and theoretical aspects of this phenomenon still continue to attract an enormous attention. In 1985 Haldane and Rezyai introduced a quantum-mechanical model to explain the quantum Hall effect. This model is specified by a choice of a complex torus $E$ and a natural number $m$ describing the strength of the extreior magnetic field. I am going to explain a construction of a hermitian holomorphic vector bundle bundle of rank $m$ on $E$, whose fibres can be identified with the space of wave functions of Haldane and Rezayi. A rigorous construction of this bundle involves the technique of Fourier-Mukai transforms. I shall also prove that this bundle is stable and its canonical Bott-Chern connection is projectively flat.This talk is based on a joint work with Semyon Klevtsov
15:45	V2 210/216	Vladimir Lazić (U Saarbrücken) Analytic approach to the Abundance conjecture [Abstract] The Abundance conjecture predicts that on a minimal projective klt pair (X,D), the adjoint divisor K_X+D is semiample. In this talk, I will explain how currents play a role in recent progress towards a proof of the Abundance conjecture for minimal klt pairs with non-vanishing Euler-Poincaré characteristic. This is mostly joint work with Thomas Peternell.
Wednesday 30 April, 2025
14:15	V2 210/216	Martin Ulirsch (U Paderborn) How to tropicalize algebraic groups (and why we should care) [Abstract] Tropical geometry studies a piecewise linear combinatorial shadow of classical algebraic geometry. In this talk I will explain what little we currently know about the tropical geometry of algebraic groups. Different avenues of progress towards an answer to this question lead to new insights both within and beyond tropical geometry, in particular in the context of vector bundles and the geometry of buildings. This talk will touch upon joint work with Luca Battistella, Desmond Coles, Andreas Gross, Inder Kaur, Kevin Kühn, Arne Kuhrs, Annette Werner, Alejandro Vargas, and Dmitry Zakharov.
15:45	V2 210/216	TBA TBA [Abstract] TBA
Wednesday 7 May, 2025
16:15	V2 210/216	Sören Sprehe (Bielefeld) Antisymmetry in the theory of rigid meromorphic cocycles (thesis defense)
Wednesday 14 May, 2025
14:15	V2 210/216	Catrin Mair (TU Darmstadt) The Role of Condensed Mathematics in Homotopy Theory [Abstract] The ∞-category Cond(Ani) of condensed anima combines the homotopy-theoretic direction of anima with the topological space direction of condensed sets. For example, we can recover the shape of a sufficiently nice topological space from the corresponding condensed anima. My talk will focus on a joint refinement of the etale homotopy type and the pro-etale fundamental group of a scheme, realised as an object in Cond(Ani). This is closely related to work of Barwick, Glasman and Haine on exodromy. I will give an overview of results from my dissertation and an ongoing project jointly with Haine, Holzschuh, Lara and Wolf.
15:45	V2 210/216	Remy van Dobben de Bruyn (Utrecht) Constructible sheaves on toric varieties [Abstract] Given a reasonable topological space or algebraic variety, its covering spaces are classified by the fundamental group, via the monodromy correspondence. Recently, this was upgraded to an exodromy correspondence, classifying constructible sheaves as representations of a 'stratified fundamental category'. I will show how to prove this for toric varieties over an arbitrary field, including an explicit determination of the fundamental category. Over the complex numbers, this is a simplification of a result of Braden and Lunts from 2006.
Wednesday 28 May, 2025
14:00	V2 210/216	TBA TBA [Abstract] TBA
16:30	V2 210/216	TBA TBA [Abstract] TBA
Wednesday 11 June, 2025
14:15	V2 210/216	Robin de Jong (Leiden University) On Néron’s canonical local height functions for abelian varieties [Abstract] We discuss Néron's canonical local heights on abelian varieties over non-archimedean valued fields from the point of view of Berkovich analytic spaces. We present a refinement of Néron's classical result relating his local heights with intersection multiplicities on the Néron model. Our result yields an extension to higher dimensions of Tate's explicit formulas for the canonical local heights on elliptic curves. This is based on joint work with Farbod Shokrieh.
15:45	V2 210/216	Carlos Caralps (University Duisburg-Essen) CM points and periods on products of non-Archimedean upper half-planes [Abstract] CM points over Shimura curves can be related to periods of a rigid analytic space using the theory of p-adic uniformization. In this talk, we will introduce the key points of this relationship and study a setting where the inverse process can be made explicit. More specifically, following the work of Bertolini, Darmon, and Green, we will show that some periods defined by integrals over products of non-Archimedean upper half-planes are related to CM points of Shimura curves.
Wednesday 25 June, 2025
14:15	V2 210/216	Alessio Bottini (Bonn University) Moduli of sheaves on hyper-Kähler manifolds [Abstract] Hyper-Kähler manifolds are higher dimensional analogues of K3 surfaces. While the general theory is well-developed, few examples are known, with all the known examples being, up to deformation, related to moduli spaces of semistable sheaves on symplectic surfaces. In the 90’s it was observed that moduli spaces of sheaves on higher dimensional hyper-Kähler manifolds are good candidates to be hyper-Kähler themselves. However, due to its high technical difficulty, this approach was ignored until recently. In this talk, I will outline the recent developments of the theory of sheaves on higher dimensional hyper-Kähler manifolds, focusing on a specific construction of O'Grady's 10-dimensional example as a moduli space of sheaves on a hyper-Kähler fourfold.
15:45	V2 210/216	Zachary Gardner (Boston College) Moduli of prismatic (𝒢,μ)-apertures [Abstract] We study the derived moduli stack BT_n^𝒢,μ of (level-n truncated) prismatic (𝒢,μ)-apertures, where 𝒢 is a smooth affine group scheme over ℤ_p and μ is a 1-bounded cocharacter of 𝒢 defined over an unramified extension of ℤ_p. Inspired by ideas of Drinfeld and Lau, we show that BT_n^𝒢,μ serves as a powerful group-theoretic generalization of the moduli stack of (n-truncated) p-divisible groups, endowed with analogous smoothness, finiteness, and representability properties as well as natural analogues of Dieudonne theory and Grothendieck-Messing theory. This opens the door to an intrinsically group-theoretic study of Rapoport-Zink spaces and potentially suggests new applications of derived algebraic geometry to the study of F-zips (among other objects). This is joint work with Keerthi Madapusi.
Wednesday 9 July, 2025
14:15	V2 210/216	Charlotte Dombrowsky (Leiden University) Central Values of L-Functions of Twisted Modular Forms [Abstract] Computing the central value of the L-function of a twisted modular form is a hard problem in general. In this talk, we present a result by Males, Mono, Rolen, and Wagner, who provide a criterion for predicting whether the product of two such central values is zero. Their approach relies on locally harmonic mass forms. While their result is proven for square-free levels, we extend their work to modular forms with general composite levels. We will discuss the key ideas behind the proof and present some examples.
15:45	V2 210/216	TBA TBA [Abstract] TBA

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The Bielefeld Algebraic and Arithmetic Geometry Seminar SS2025

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16 April, 2025

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30 April, 2025

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7 May, 2025

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14 May, 2025

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28 May, 2025

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11 June, 2025

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