Seminar

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 a regular email announcement please contact birep.

Future Talks

Friday, 03 May 2024

13:15, Room V2-200
Anish Chedalavada (Baltimore): tba

Seminar Archive

Friday, 02 February 2024

13:15, Room T2-233
Panagiotis Kostas (Thessaloniki): Injective generation for tensor rings
Abstract: In 2019 Rickard introduced a condition for rings, called injective generation and proved that if injectives generate for a finite dimensional algebra, then this algebra has finite finitistic dimension. After discussing some graded aspects of injective generation, we will prove that given a ring R and a "sufficiently nice" R-bimodule M, then injectives generate for R if and only if injectives generate for the tensor ring of R by M. This is based on joint work with Chrysostomos Psaroudakis.

Friday, 15 December 2023

13:15, Room T2-233
Lara Bossinger (Oaxaca): Brick compactifications of braid varieties using superpotentials
Abstract: Braid varieties have gained interest recently with the recovery of their cluster structures. A natural compactification of braid varieties to brick varieties was given a few years ago by Escobar. I will explain how the brick compactification of braid varieties can be obtained in the context of Gross-Hacking-Keel-Kontsevich superpotentials for cluster varieties. This is joint work in progress based on an AIMS working group formed by José Simental, Daping Weng, Iva Halacheva, Allen Knutson, Pavel Galashin et al.
14:30, Room T2-233
David Ploog (Stavanger): The heart fan of a triangulated category
Abstract: I will discuss a general construction attaching (a) a convex cone to an abelian category, (b) a fan to a bounded heart in a triangulated category and (c) a multifan to a triangulated category. These constructions generalise the g-fan of a finite-dimensional algebra. If the bounded heart is length then our fan is always complete; in particular, it provides a natural completion of the g-fan. These constructions are motivated by, and lead to a convex-geometric description of, the stability space of a triangulated category.
(Joint work with Nathan Broomhead, David Pauksztello, Jon Woolf.)

Friday, 24 November 2023

13:15, Room T2-233
Chris Parker (Bielefeld): Bounded t-structures, finitistic dimensions, and singularity categories of triangulated categories
Abstract: We will talk about recent joint work on a triangulated categorical generalisation of Neeman's theorem on the existence of bounded t-structures on the derived category of perfect complexes, which solved a bold conjecture by Antieau, Gepner, and Heller. In particular, under mild conditions, we show how the existence of a bounded t-structure on a triangulated category implies that its singularity category vanishes. To achieve this, we show that certain t-structures can be lifted from a triangulated category to its completion, as well as introduce the notion of finitistic dimension for triangulated categories. This work is joint with Rudradip Biswas, Kabeer Manali Rahul, Hongxing Chen, and Junhua Zheng.
14:30, Room T2-233
Kyungmin Rho (Paderborn): Homological mirror symmetry correspondence on an affine model
Abstract: The affine normal crossing surface singularity xyz=0 (B-model) is a mirror dual of the three-punctured Riemann sphere (A-model). On the B-model, we consider the stable category of maximal Cohen-Macaulay (a.k.a. Gorenstein projective) modules, whose indecomposable isomorphism classes have been completely classified by Burban-Drozd's representation-theoretic method. We find their corresponding curves in the Fukaya category of the A-model and show their one-to-one correspondence with immersed geodesics. We also explain some interchanges of algebraic operations and geometric symmetries and discuss how to globalize this local aspect for more general mirror pairs. This is based on joint works with Cheol-Hyun Cho, Wonbo Jeong, and Kyoungmo Kim.

Friday, 10 November 2023

13:15, Room T2-233
Umesh V. Dubey (Prayagraj): Tensor t-structures on the derived category of a Noetherian scheme
Abstract: The notion of truncation structure (t-str) was introduced in the famous paper of Beilinson, Bernstein, and Deligne (Gabber). It has found applications in various areas.
We will discuss the notion of tensor-compatible t-str (or tensor t-str) on the derived category of schemes (w.r.t. some fixed t-str). The notion of tensor t-structure is motivated by the classification of thick tensor ideal subcategories of derived categories of schemes. Thomason used tensor to extend the known classification theorem of Hopkins-Neeman from affine case to more general schemes.
We will describe our classification of compactly generated tensor t-structures on the derived category of Noetherian schemes in terms of Thomason filtrations. It extends the known classification results on the derived category of Noetherian ring. As an application, we can prove the tensor telescope conjecture for t-structures in the sense of Hrebek.
This is based on the joint work with Gopinath Sahoo.

Friday, 27 October 2023

13:15, Room T2-233
Calvin Pfeifer (Odense): On τ-tilting tameness of affine GLS algebras
Abstract: Geiß-Leclerc-Schröer (GLS) associated to every valued quiver Γ a finite-dimensional algebra H defined in terms of quivers with relations. Their algebras H are 1-Iwanaga-Gorenstein and arise as degenerations of hereditary algebras. These degenerations are representation tame whenever the valued quiver Γ is affine. In contrast, corresponding GLS algebras are often representation wild. This raises the question in which sense affine GLS are still „tame“. In this talk, we present a generic classification of locally-free representations of affine GLS algebras. We deduce that affine GLS algebras are „tame“ from the perspective of τ-tilting theory.
An integral part of our generic classification is the construction of a 1-parameter family of representations stable with respect to the defect. In particular, we verify τ-tilting versions of the second Brauer-Thrall conjecture introduced by Mousavand, for the class of GLS algebras.
14:30, Room T2-233
Kaveh Mousavand (Okinawa): Distribution of bricks -- algebraic and geometric viewpoints
Abstract: In a series of joint work with Charles Paquette, we have studied the behaviour of bricks from different perspectives. More specifically, for a (basic) finite dimensional associative algebra A over an algebraically closed field, we are mainly concerned with the behaviour of those A-modules whose endomorphism algebras are division rings. Every such module is called a brick. Our work is primarily motivated by a conjecture that I posed in 2019, which concerns the distribution of finite dimensional bricks: An algebra A admits infinitely many isomorphism classes of bricks if and only if A admits an infinite family of bricks of the same length. In this talk, I present some of our new results on this (still open) conjecture, as well as the connections to the infinite dimensional bricks and generic modules. Then, I will discuss some interesting applications of our results in the study of stability conditions and tau-tilting theory.

Friday, 13 October 2023

13:15, Room T2-233
Juan Omar Gomez (Bielefeld): Enhanced stable categories for infinite groups and applications
Abstract: Informally, the stable module category for an infinite group over a field of positive characteristic is obtained from the category of modules over the group ring by discarding modules of finite projective dimension. In this talk we will introduce an enhancement of the stable module category for infinite groups, and we will present two applications of this approach: first, we provide a formula to classify invertible modules in the stable module category for an infinite group with a finite dimensional cocompact model for the classifying space for proper actions; and second, we construct a family of infinite degree separable commutative algebras giving a negative answer to an open question by P. Balmer.

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