| Wednesday (S3) | Thursday (S8) | Friday (S8) | Saturday (S8) | |
|---|---|---|---|---|
| 09:30–10:30 | Osamu Iyama | Bernard Leclerc | Karin Erdmann | Andrzej Skowroński |
| 10:30–11:00 | Coffee break | Coffee break | Coffee break | Coffee break |
| 11:00–12:00 | Lidia Angeleri Hügel | Pierre-Guy Plamondon | Ralf Schiffler | Gordana Todorov |
| 12:10–13:10 | Jan Stovicek | Claire Amiot | Kiyoshi Igusa | Peter Jørgensen |
| 13:10–14:30 | Lunch break | Lunch break | Lunch break | Lunch break |
| 14:30–15:30 | Robert Marsh | Gustavo Jasso | Dag Madsen | Dan Zacharia |
| 15:30–16:00 | Coffee break | Coffee break | Coffee break | Coffee break |
| 16:00–17:00 | Henning Krause | Jan Schröer | Helmut Lenzing | Ragnar Buchweitz |
| 19:00– | Conference dinner | |||
All talks on Wednesday will be held in the auditorium S3 (click for map), and in S8 the remaining days. S3 is located on the ground floor between Sentralbygg 1 and 2 (the two tallest buildings) on campus Gløshaugen. The auditoriums have proper blackboards and video projectors.
The coffee breaks will take place in Smia (appears as Vegas on the map), on the first floor.
The participants will have to buy their own lunch. There are several cafeterias on campus, and the closest is Hangaren. There is also a kiosk close by, where you can get food to go.
This is joint work with Pierre-Guy Plamondon.
In this talk, I will give a parametrization of all indecomposable objects in the cluster category associated with a surface with punctures in term of curves on the surface, generalizing the results due to Brüstle-Zhang and Qiu-Zhou. This description uses strongly the construction of a new surface without punctures together with a triangle functor between the corresponding two cluster categories (cf P-G Plamondon's talk).
We investigate ring epimorphisms of commutative noetherian rings, comparing different constructions and discussing parametrisations of ring epimorphisms by subsets of the Zariski spectrum. This is joint work with Jorge Vitória, Frederik Marks, Jan Stovicek and Ryo Takahashi.
Whenever a triangulated category admits a tilting object T, it identifies with the derived category of E = End(T). How does one get back from that derived category to the original one?
We describe an algorithm for the case that E is an artinian algebra of finite global dimension. As an example, we use this to identify all matrix factorizations of yd – xd for d ≥ 2, thus, answering a question raised several years ago by physicists.
(Joint work with Petter Bergh.)
We apply results of Bergh and Jorgensen on categorical matrix factorisations to a class of finite-dimensional quantum complete intersections.
This is joint work with PJ Apruzzese. In 2003 Reineke conjectured that for every Dynkin quiver there is a central charge Z which makes all modules stable and he proved it for An with straight orientation. In 2015, Yu Qiu found, for at least one orientation of each Dynkin quiver a central charge making all modules stable.
PJ and I solved the analogous statement for all cyclic quivers, i.e., those of affine type A and Dn cluster-tilted. We found the maximum length of maximal green sequences in all of these cases, found all possible sets of stable modules of MGSs of this maximal length and show that each of them is given by a linear MGS (a central charge). As a special case (deleting a vertex) we prove Reineke's original conjecture for type An with any orientation.
For a finite dimensional algebra A, there are canonical bijections between several important objects in representation theory of A, due to Koenig–Yang, Ingalls–Thomas, Adachi–Iyama–Reiten, Marks–Stovicek, Asai, and many other people.
For simplicity, I will discuss the case when A is tau-tilting finite. Then there are canonical bijections between torsion classes, support tau-tilting modules, semibricks, and wide subcategories. The set tors A of torsion classes form a lattice, and its Hasse quiver has a natural labelling of arrows by bricks of A. I will explain how it is useful to understand representation theory of A. This is a joint work with L. Demonet, N. Reading, I. Reiten and H. Thomas.
I will survey known results and constructions in higher Auslander–Reiten theory whose common feature is that they all can be regarded as having (higher dimensional) "type A" origins.
We develop a general framework for c-vectors of 2-Calabi–Yau categories with respect to arbitrary cluster tilting subcategories, based on Dehy and Keller's treatment of g-vectors. This approach deals with cluster tilting subcategories which are in general unreachable from each other, and does not rely on (finite or infinite) sequences of mutations.
We prove a duality theorem for c-vectors which generalises the combinatorial duality of Nakanishi and Zelevinsky to the framework of unreachable subcategories. We propose a general program for decomposing sets of c-vectors and identifying each piece with a root system.
From work of Auslander and Reiten we know that the stable category of maximal Cohen-Macaulay modules over a Gorenstein algebra admits a Serre functor. The talk is devoted to an analogue of Grothendieck's local duality in that context, which is induced by Auslander-Reiten duality and employs the action of Hochschild cohomolgy on the category of maximal Cohen-Macaulay modules. This action has played an important role in the support theory a la Snashall and Solberg, and we need to assume their finite generation condition. A crucial ingredient is base change - a technique which seems somewhat neglected in representation theory of finite dimensional algebras. This is based on joint work with Benson, Iyengar, and Pevtsova.
This is a joint work with C. Geiss and J. Schröer. We extend the Caldero–Chapoton formula for cluster algebras of finite type to the skew-symmetrizable case. This is done by replacing representation categories of Dynkin quivers by categories of locally free modules over the Iwanaga–Gorenstein algebras H(C,D,Ω) introduced in our previous work.
I will discuss two of Idun's papers from the 1980s, describe their influence in further development and finally mention how the results fit into the current mathematical landscape. The talk will further contain a discussion of examples and applications.
Uematsu and Yamagata proved that a Nakayama algebra is quasi-hereditary if and only if there is a simple module of projective dimension two. In an earlier paper I proved that a Nakayama algebra is of finite global dimension if and only if there is a simple module of even projective dimension. In this talk I will discuss the above and the following new result. Let A be a Nakayama algebra with n non-isomorphic simple modules, one of the simple modules having even projective dimension 2m. Then the global dimension of A is bounded by n+m–1.
This is joint work with Rene Marczinzik.
Joint work with Idun Reiten. We classify the indecomposable rigid and Schurian modules over a cluster-tilted algebra of tame representation type in terms of where they appear in the Auslander-Reiten quiver. This has an application to the corresponding cluster algebra: although not every denominator vector is the dimension vector of an indecomposable module over the cluster-tilted algebra, it is the sum of the dimension vectors of at most three rigid indecomposable modules.
This is joint work with Claire Amiot.
To any triangulation of a surface with punctures, one can associate a quiver with potential. If all punctures are adjacent to self-folded triangles, then there is a natural group action on this quiver with potential. In this talk, we use this group action to study the cluster category of the triangulation. Specifically, we build a new surface, without punctures, whose quiver with potential yields the skew-group algebra of the original one. (cf. C.Amiot's talk).
This talk is on a combinatorial realization of continued fractions in terms of perfect matchings of the so-called snake graphs, which are planar graphs that have first appeared in expansion formulas for the cluster variables in cluster algebras from triangulated marked surfaces. I will also explain applications to cluster algebras, as well as to elementary number theory. This is a joint work with Ilke Canakci.
We study finite-dimensional algebras A such that for each d all connected components of the affine variety of d-dimensional A-modules are irreducible. This is joint work with Grzegorz Bobiński (Toruń).
A finite dimensional K-algebra A over a field K is called a selfinjective algebra of infinite tilted type if A is isomorphic to an orbit algebra B̂/G of the repetitive category B̂ of a tilted algebra B not of Dynkin type, with respect to an infinite cyclic group G of automorphisms of B̂. Two selfinjective algebras A and Λ are called socle equivalent if the quotient algebras A/soc(A) and Λ/soc(Λ) are isomorphic. We will discuss characterizations and invariants of selfinjective algebras socle equivalent to selfinjective algebras of infinite tilted type. In particular, we will show that the representation dimension of these algebras is equal to three, and provide an explicit construction of the Auslander generator of their module category. Moreover, we will show that all selfinjective algebras A whose Auslander–Reiten quiver contains a τA-right regular slice belong to this class of algebras.
I will discuss two different classes of ring epimorphisms. One might either wish the ring epimorphism to be homologically well behaved, which leads to the notion of a flat ring epimorphism. These have been studied in commutative algebra and algebraic geometry, as well as in the context of localizing triangulated categories. The second class is that of silting ring epimorphisms, which is a generalization of localization, i.e. adding multiplicative inverses formally.
The main result is that for commutative noetherian rings these two classes coincide. I will also discuss finiteness conditions, i.e. when silting ring epimorphisms reduce to the more classical notion of a universal localization (due to Schofield).
This is a part of a joint project with Lidia Angeleri, Frederik Marks and Jorge Vitoria.
(Joint with Van Nguyen, Idun Reiten and Shijie Zhu.)
We study tilting modules which are both generated and cogenerated by projective-injective modules. We show that the existence of such a tilting module is equivalent to the algebra having dominant dimension at least 2. We also show that existence of such a tilting module which is also cotilting is equivalent to algebra being 1-Auslander–Gorenstein.
Auslander algebras satisfy all of the above.
My talk is on joint work with Otto Kerner. Let R be the exterior algebra in n+1 indeterminates. I will talk about the thick subcategories of the stable category of finitely generated graded R-modules. As a special case, I will present a representation theoretical classification of the thick subcategories generated by the graded modules of complexity one.
Last updated: 08.05.2017, 14:20.