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Geometric and homological methods in representation theory

5-7 January 2022, online

Geometric and homological methods have long been two key approaches in representation theory. Geometric models have been developed in a wide variety of settings and underpin links between representation theory, cluster theory, combinatorics and symplectic geometry. Homological algebra provides powerful techniques to obtain invariants for mathematical objects. The utility of these methods has been recognised well beyond their birthplace in algebraic topology, occurring in representation theory, algebraic and symplectic geometry, Lie theory and mathematical physics, e.g. homological mirror symmetry, among many other subjects.

The purpose of this workshop is to bring together researchers focusing on geometric and homological methods applied in representation theory and related areas, with particular focus on recent advances in geometric models and cluster-tilting theory in both positive and negative Calabi-Yau settings.


All times are in GMT.

Wednesday 5th January

  • 10:00-11:00: Osamu Iyama (Tokyo), "Singularity categories and cluster tilting" (Iyama - slides)
  • 11:00-11:30: Anya Nordskova (Hasselt), "Derived Picard groups of representation-finite symmetric algebras" (Nordskova - slides)
  • 11:30-12:00: Break
  • 12:00-13:00: Joe Grant (University of East Anglia), "On periodic trivial extension algebras"
  • 14:45-15:45: Peter Jørgensen (Aarhus), "The index with respect to a rigid subcategory of a triangulated category"
  • 15:45-16:00: Break
  • 16:00-16:30: Jeremy Brightbill (UC Santa Barbara), "The N-stable Category" (Brightbill - slides)

Thursday 6th January

  • 10:00-11:00: Aaron Chan (Nagoya), "Categorification of curves and quasi-triangulations on unpunctured non-orientable marked surfaces" (Chan - slides)
  • 11:00-11:30: Haibo Jin (Cologne), "Cutting surfaces and recollements of gentle algebras" (Jin - slides)
  • 11:30-12:00: Break
  • 12:00-13:00: Alexandra Zvonareva (Stuttgart), "t-structures and thick subcategories of discrete cluster categories" (Zvonareva - slides)
  • 14:45-15:45: Ana Garcia Elsener (Glasgow), "Extensions in Jacobian algebras via punctured skein relations" (Garcia-Elsener - slides)
  • 15:45-16:00: Break
  • 16:00-17:00: Alex Dugas (University of the Pacific), "Semisimple-homology resolutions of modules" (Dugas - slides)

Friday 7th January

  • 10:00-11:00: Karin Baur (Leeds/Graz), "Cluster structures for Grassmannians" (Baur - slides)
  • 11:00-11:30: Francesca Fedele (Verona), "Generalised cluster categories from n-Calabi-Yau triples" (Fedele - slides)
  • 11:30-12:00: Break
  • 12:00-13:00: Yadira Valdivieso-Díaz (UDLAP, Mexico), "Caldero-Chapoton functions for orbifolds and snake graphs"
  • 14:30-15:00: Dixy Msapato (Leeds), "The Karoubi envelope of an extriangulated category" (Msapato - slides)
  • 15:00-15:15: Break
  • 15:15-16:15: Steffen König (Stuttgart), "Almost self-injective algebras"


List of abstracts Accordion



The meeting will be held online and details sent to registered participants closer to the meeting.

The organisers are Raquel Coelho Simões, Jan Grabowski and David Pauksztello.

We are grateful to the European Union’s Horizon 2020 research and innovation programme for funding under grant agreement No. 838706.