| Wednesday 24 April 2024 | |
| Events for day: Wednesday 07 March 2018 |
| 11:00 - 12:00 Lecture Tilting Theory over Commutative Rings School MATHEMATICS Tilting theory has a long history originating in the representation theory of finite-dimensional algebra [Hap] and algebraic geometry [Bei]. Later, infinitely generated tilting modules were introduced as a formal generalization of tilting objects representing derived equivalences. It turned out recently that in the context of commutative rings, there is a very geometric classification of tilting modules up to additive equivalence in terms of support and using very well-known homological theories [APST], [HS]. If time allows, I will touch recent results which elaborate the relevance of the geometric point of view further - the Zarisk ... 13:00 - 14:00 Lecture Tilting Theory over Commutative Rings School MATHEMATICS Tilting theory has a long history originating in the representation theory of finite-dimensional algebra [Hap] and algebraic geometry [Bei]. Later, infinitely generated tilting modules were introduced as a formal generalization of tilting objects representing derived equivalences. It turned out recently that in the context of commutative rings, there is a very geometric classification of tilting modules up to additive equivalence in terms of support and using very well-known homological theories [APST], [HS]. If time allows, I will touch recent results which elaborate the relevance of the geometric point of view further - the Zarisk ... 9:30 - 10:30 Lecture G-groups School MATHEMATICS Let G be a group. A G-group is a pair (H,f), where H is a group and f:G --> Aut(H) is a group homomorphism. The category G-Grp of all G-groups shows a behaviour that is a very pleasant combination of the behaviour of groups and that of left modules over a ring. We will describe several properties of this category G-Grp. In particular, the existence, discovered by Remak, of the central automorphism in the statement of the classical Krull-Schmidt Theorem for finite groups has a natural explanation interpreting this result in the category G-Grp. ... |