Σεμινάριο Άλγεβρας, Θεωρίας Αριθμών και Μαθηματικής Λογικής
Πέμπτη 18 Οκτωβρίου, 2018, 12:15-13:00, Αίθουσα Μ2, 3ος Όροφος Κτιρίου Σ.Θ.Ε.
Ομιλητής: Steffen Oppermann, Norwegian University of Science and Technology (NTNU)
Τίτλος: Auslander-Reiten quivers and higher dimensional analogs
Περίληψη: In my talk I will first discuss some classical concepts in representation theory of finite dimensional algebras. In particular we will look at Auslander Reiten quivers, and what information these quivers contain.
I will then focus on a more recent twist: the generalization of Auslander Reiten theory to a “higher dimensional” version, and discuss some aspects that generalize nicely (as well as possibly some that don’t).
Πέμπτη 18 Οκτωβρίου 2018, 13:15-14:00, Αίθουσα Μ2, 3ος Όροφος Κτιρίου Σ.Θ.Ε.
Ομιλητής: Torkil Stai, Norwegian University of Science and Technology (NTNU)
Τίτλος: Triangulated categories and orbit categories
Περίληψη: The concept of a triangulated category comes up everywhere, in particular in mathematics! Our primary objective is to provide some very basic intuition for this notion, with an emphasis on connections and similarities with the more familiar abelian categories. For instance, taking subcategories and quotients of triangulated categories is straightforward.
A much more mysterious construction is that of an orbit category of a triangulated category with respect to an automorphism; there is no a priori reason why this gadget should be triangulated. The secondary aim of this talk is to explain how algebraists have coped with this nightmare over the last decade. Time permitting, I will report on ongoing work with Steffen Oppermann on the topic.