From exceptional to τ-exceptional sequences in module categories - Aslak Bakke Buan (NTNU Trondheim)

This is a recorded version of the following talk from our "New Directions in Group Theory and Triangulated Categories" series. To receive updates about this series, or to suggest speakers (including yourself), please email me at [email protected].

More details about this seminar series are here -
https://sites.google.com/view/ndgttc/...
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96th Meeting of "New Directions in Group Theory and Triangulated Categories"

Date: May 30, 2024; Thursday

Time: 4 pm UK

Speaker: Aslak Bakke Buan (NTNU Trondheim)

Title: From exceptional to τ-exceptional sequences in module categories

Abstract: This is based on joint work with Eric Hanson and Bethany Marsh.

Exceptional sequences and their mutations were first considered in triangulated categories by the Moscow school of algebraic geometers. In the early nineties, Crawley-Boevey and Ringel studied exceptional sequences for module categories of hereditary algebras. We first recall their definitions and their main results, and then proceed to discuss a natural generalization to all (not necessarily hereditary) finite dimensional algebras. This is the theory of τ-exceptional sequences, which was developed in joint work with Marsh, motivated by τ-tilting theory, by Adachi-Iyama-Reiten, by Jasso's reduction techniques for such modules and corresponding torsion pairs, and by the introduction of signed exceptional sequences by Igusa-Todorov.

The interplay between theories for τ-rigid modules, torsion pairs, and wide subcategories is central to our discussions.
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