Seminar

No talks have been announced for this week.

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Future Talks

Friday, 24 January 2025

• 13:15, Room X-E0-228
  Luca Pol (Regensburg): tba

Seminar Archive

Friday, 10 January 2025

• 13:15, Room X-E0-228
  Florian Tecklenburg (Bonn): Generalising Keller's counterexample on the telescope conjecture
  Abstract: Building on results of Bazzoni–Šťovíček, we give an explicit construction of an infinite family of commutative rings which generalise the first counterexample on the generalised telescope conjecture of Bernhard Keller in 1994. In particular, the telescope conjecture for their derived categories does not hold. Generalising the construction of these rings further, we give a complete classification of the frame of smashing ideals for the derived category of a finite dimensional valuation domain. As a consequence, we deduce that the Krull dimension of the Balmer spectrum and the smashing spectrum can differ arbitrarily for rigidly-compactly generated tensor-triangulated categories.
  The talk is based on joint work with Scott Balchin, see https://arxiv.org/abs/2407.11791.

Friday, 13 December 2024

• 13:15, Room X-E0-228
  Claudius Heyer (Paderborn): A 6-functor formalism for smooth mod p representations
  Abstract: The formalism of six operations was introduced by Grothendieck to show that many phenomena in the étale cohomology of schemes can be formally deduced from a small set of axioms. Since then these six operations have been constructed in many of other contexts like D-modules, motives and rigid-analytic geometry. But only recently has there been a formal definition of a 6-functor formalism, mainly due to Liu–Zheng and then further simplified by Mann in his PhD thesis. Also in Fargue–Scholze's geometrization of the local Langlands correspondence the six operations are a guiding theme.
  In this talk I will report on joint work with Lucas Mann where we construct a full 6-functor formalism in the setting of smooth representations of p-adic Lie groups with mod p coefficients. As an application we use the formalism to construct a canonical anti-involution on derived Hecke algebras generalizing earlier work by Schneider–Sorensen.
  

Friday, 06 December 2024

• 13:15, Room X-E0-228
  Mahrud Sayrafi (Leipzig): Splitting of Vector Bundles on Toric Varieties
  Abstract: In 1964, Horrocks proved that a vector bundle on a projective space splits as a sum of line bundles if and only if it has no intermediate cohomology. Generalizations of this criterion, under additional hypotheses, have been proven for other toric varieties, for instance by Eisenbud-Erman-Schreyer for products of projective spaces, by Schreyer for Segre-Veronese varieties, and Ottaviani for Grassmannians and quadrics. This talk is about a splitting criterion for arbitrary smooth projective toric varieties, as well as an algorithm for finding indecomposable summands of sheaves and modules in the more general setting of Mori dream spaces.
• 14:30, Room X-E0-228
  Markus Schmidmeier (Boca Raton): Wild categories: screwy or adaptable?
  Abstract: For n a natural number, the invariant subspace category S(n) consists of all systems (V,T,U) where V is a finite dimensional vector space, T a nilpotent linear operator acting on V with nilpotency index at most n, and U a T-invariant subspace of V. For increasing n, the S(n) form a chain of categories with increasing complexity; in particular, S(n) has wild representation type for n>6.
  A dimension vector is called Brauer-Thrall if each positive multiple can be realized by a parametrized family of pairwise nonisomorphic indecomposable objects. We discuss the question in the title with regards to regions of BTh-vectors for S(n).
  This is a report about joint work with Claus Michael Ringel, see arxiv.org/abs/2405.18592.

Friday, 29 November 2024

• 13:15, X-E0-228
  Markus Kirschmer (Bielefeld): Chow groups of one-dimensional noetherian domains
  Abstract: We discuss various connections between ideal classes, divisors, Picard and Chow groups of one-dimensional noetherian domains. As a result of these, we give a method to compute Chow groups of orders in global fields and show that there are infinitely many number fields which contain orders with trivial Chow groups. This is joint work with J. Klüners.

Friday, 22 November 2024

• 13:15, Room X-E0-228
  Jan Schröer (Bonn): Projective presentations of maximal rank
  Abstract: First, I will discuss the connection between projective presentations of maximal rank and generically tau-regular components of module varieties. Then I will present some classification results for generically tau-regular components. This is joint work with Grzegorz Bobinski.

Friday, 15 November 2024

• Colloquium in Honour of Lutz Hille

Friday, 25 October 2024

• 13:15, Room X-E0-228
  Peter Schneider (Münster): What is smooth representation theory about?
  Abstract: This talk will be a survey talk first on how number theory leads to the introduction of smooth representation theory of p-adic groups in characteristic zero. Then I will report on the recent development of the characteristic p coefficient case, which is radically different and where little is known yet.

Friday, 18 October 2024

• 13:15, Room X-E0-228
  David Nkansah (Aarhus): Rank Functions in the Framework of Higher Homological Algebra
  Abstract: Chuang and Lazarev introduced the concept of rank functions on triangulated categories as a generalisation of classical work by Cohn and Schofield on Sylvester rank functions. In this talk, we propose a generalisation of this notion to the broader framework of higher homological algebra.

Friday, 11 October 2024

• 13:15, Room X-E0-228
  Alexandre Minets (Bonn): Hecke symmetries of sheaves on surfaces
  Abstract: For a smooth algebraic surface S, I will explain how to construct an action of a quantum toroidal-type algebra on the cohomology of moduli of coherent sheaves on S. I will recall how this unifies several known results in geometric representation theory, and sketch the role of this action in our proof of P=W conjecture of de Cataldo-Hausel-Migliorini.
  

Friday, 12 July 2024

• 13:15, Room V2-200
  Eduardo Vital (Bielefeld): Matroids and Euler characteristics of quiver Grassmannians
  Abstract: We introduce morphisms of matroids with coefficients, which leads to a categorical framework for Baker-Bowler theory. Inspired by the idea that matroids are linear subspaces of F1-vector spaces, we construct quiver Grassmannians of matroids for quiver representations over F1. It turns out that in "nice" cases, the cardinality of F1-rational points (in a suitable sense) of a matroid quiver Grassmannian and the Euler characteristic of its associated complex variety are the same. This is a joint work with Manoel Jarra and Oliver Lorscheid.
  

Friday, 05 July 2024

• 13:15, Room V2-200
  Shiquan Ruan (Xiamen): A geometric model for weighted projective lines of domestic type
  Abstract: In this talk we will give a geometric model for the category of coherent sheaves over the weighted projective lines of domestic type (p,q) and (2,2,n) in terms of an infinite marked strip. We establish a bijection between indecomposable sheaves over the weighted projective lines and certain homotopy classes of oriented curves, and prove that the dimension of extension groups between indecomposable sheaves equals the positive intersection number between the corresponding curves.
  As applications, we provide combinatorial interpretations for the titling graph of tilting bundles, the Picard group action, vector bundle duality, projective cover and injective hull of extension bundles, etc. This is joint work with Jianmin Chen and Hongxia Zhang and Jinfeng Zhang.

Friday, 28 June 2024

• 13:15, Room V2-200
  Edith Hübner (Münster): Animated lambda-rings and Frobenius lifts
  Abstract: We recall Grothendieck’s notion of a lambda-ring and then introduce an infinity-categorical extension of ordinary lambda-rings: animated lambda-rings. As our main result, we prove a characterization of animated lambda-rings in terms of animated rings equipped with a family of coherently compatible Frobenius lifts. In particular, this provides a new perspective on classical lambda-rings which inherently depends on the notion of higher homotopy. We build on Bhatt and Lurie’s results on animated delta-rings in the context of absolute prismatic cohomology and review the necessary infinity-categorical prerequisites during the talk.
• 14:30, Room V2-200
  Severin Barmeier (Köln): Derived equivalences of associative algebras via Fukaya categories
  Abstract: By work of Haiden-Katzarkov-Kontsevich and Lekili-Polishchuk there is a correspondence between derived categories of gentle algebras and partially wrapped Fukaya categories of surfaces with boundary. This correspondence allows one to study derived categories of gentle algebras by their geometric surface models. For example, one may classify indecomposable objects of the derived category in terms of curves on the surface. I will present a generalization of this correspondence to surfaces with orbifold singularities. Their Fukaya categories admit a description by A-infinity algebras whose higher structures can be given explicitly. Using the orbifold surface it is possible to characterize when the Fukaya category is equivalent to the derived category of an associative algebra. This gives a geometric framework for studying derived equivalences between certain classes of associative algebras including skew-gentle algebras and algebras of type D. This is based on joint work with Sibylle Schroll and Zhengfang Wang.
  

Friday, 21 June 2024

• 13:15, Room V2-200
  Victor Torres-Castillo (Ankara): Quantum nonlocal games and the d-torsion commutative space
  Abstract: Nonlocal games have played a prominent role in quantum information theory by demonstrating the power of entanglement. In particular, the 'magic' examples due to Mermin and Peres belong to the class of linear system games. The Mermin-Peres games have no classical solutions, but they admit operator solutions.
  In this talk, we translate the problem of finding operator solutions into a problem of extensions for partial groups (in the sense of Broto-Gonzalez). In particular, we define the d-torsion commutative nerve for groups, whose homotopy structure is crucial to identify a practical criterion (in terms of higher limits) to test a conjecture due to Chung-Okay-Sikora regarding linear system games over Z_d, with d odd.
  This is joint work in progress with Ho Yiu Chung and Cihan Okay.

Friday, 31 May 2024

• 13:15, Room V2-200
  Kevin Schlegel (Stuttgart): Exact structures and purity
  Abstract: We relate the theory of purity of a locally finitely presented category with products to the study of exact structures on the full subcategory of finitely presented objects. Moreover, we focus on the case of a module category over an Artin algebra.

Friday, 24 May 2024

• 13:15, Room V2-200
  Stefan Dawydiak (Bonn): Central extensions in Lusztig's asymptotic Hecke algebra, lower modifications, and tempered representations
  Abstract: Lusztig's asymptotic Hecke algebra J is a based ring whose structure reflects the one- and two-sided cells of an affine (or finite) Weyl group. In the late 80s, Lusztig conjectured that it could be realized as the equivariant K-theory of the square of a finite set, and Bezrukavnikov and Ostrik proved a weak version of this statement in the early 2000s. In joint work with Bezrukavnikov and Dobrovolska, we gave an unexpected counterexample showing that the weak version is in fact optimal. We will explain this, and also give a conceptual explanation for this counterexample via the relationship between J and representations of p-adic groups given by Braverman and Kazhdan.

Friday, 03 May 2024

• 13:15, Room V2-200
  Anish Chedalavada (Baltimore): A derived refinement of a classical theorem in tt-geometry
  Abstract: In this talk, we explain how to equip the Balmer spectrum of a rigidly-compactly generated symmetric monoidal stable infinity-category with a natural structure sheaf, generalizing gluing techniques of Balmer-Favi in a systematic fashion. Following tensor-triangular philosophy in porting over statements from algebraic geometry, we provide a universal property for this equipment (in the style of an affine scheme). As an application, we explain how to recover the computation of the thick tensor ideals of the perfect complexes on a qcqs scheme, in addition to partially generalizing the statement to nice classes of spectral stacks. In another direction, we explain how one might utilise these techniques to import methods from spectral algebraic geometry into a wider variety of contexts.
  

Friday, 26 April 2024

• 13:15, Room V2-200
  Sven-Ake Wegner (Hamburg): The two derived categories of the LB-spaces
  Abstract: Let LB be the category of LB-spaces, which has as objects precisely those Hausdorff locally convex spaces that can be written as a countable inductive limit of Banach spaces, and as morphisms the continuous linear maps between them. In the talk we will firstly review LBs categorical properties and explain its place in the general hierarchy of non-abelian categories. After that we will show that there are (at least) two natural, but not naturally equivalent, ways to define a derived category of LB.
  

For information on earlier talks please check the complete seminar archive.