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) TBA [Abstract] TBA
15:45	V2 210/216	Carlos Caralps (University Duisburg-Essen) TBA [Abstract] TBA
Wednesday 25 June, 2025
14:15	V2 210/216	Alessio Bottini (Bonn University) TBA [Abstract] TBA
15:45	V2 210/216	Zachary Gardner (Boston College) TBA [Abstract] TBA
Wednesday 9 July, 2025
14:15	V2 210/216	Charlotte Dombrowsky (Leiden University) TBA [Abstract] TBA
15:45	V2 210/216	TBA TBA [Abstract] TBA

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The Bielefeld Algebraic and Arithmetic Geometry Seminar SS2025

Talks

Wednesday

16 April, 2025

Wednesday

30 April, 2025

Wednesday

7 May, 2025

Wednesday

14 May, 2025

Wednesday

28 May, 2025

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11 June, 2025

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25 June, 2025

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9 July, 2025