Seminar
Friday, 18 October 2019
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14:15, Room V2-200
Alexander Slávik (Prague): On flat generators and Matlis duality for quasicoherent sheaves
Abstract: We show that for a quasicompact quasiseparated scheme X, the following assertions are equivalent: (1) the category QCoh(X) of all quasicoherent sheaves on X has a flat generator; (2) for every injective object E of QCoh(X), the internal hom functor into E is exact; (3) the scheme X is semiseparated. Joint work with Jan Šťovíček.
For a regular email announcement please contact birep.
Future Talks
Friday, 25 October 2019
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14:15, Room V2-200
Fei Xie (Bielefeld): The derived category of a singular quintic del Pezzo surface
Abstract: I will give a semiorthogonal decomposition for the bounded derived category of coherent sheaves on a quintic del Pezzo surface with mild singularity (rational Gorenstein) over algebraically closed fields. The decomposition has three components. Two components are equivalent to derived categories of the base field. The remaining component is equivalent to the derived category of products of truncated polynomials with total length 5. The decomposition is obtained by studying the semiorthogonal decomposition of the minimal resolution of the surface. I will also briefly mention how to obtain a similar decomposition using Homological Projective Duality and how to obtain a decomposition over non-algebraically closed fields.
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15:30, Room V2-200
Paul Wedrich (Bonn): Quivers for SL(2) tilting modules
Abstract: I will explain how diagrammatic algebra can be used to give an explicit generators-and-relations presentation of all morphisms between indecomposable tilting modules for SL(2) over an algebraically closed field of positive characteristic. The result takes the form of a path algebra of an infinite, fractal-like quiver with relations, which can be considered as the (semi-infinite) Ringel dual of SL(2). Joint work with Daniel Tubbenhauer.
Friday, 15 November 2019
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Bielefeld-Paderborn Seminar
Room V2-200
William Crawley-Boevey (Bielefeld): Clanish algebras revisited
Friday, 22 November 2019
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Gustavo Jasso (Bonn): tba
Seminar Archive
Thursday, 26 September 2019
Wednesday, 25 September 2019
Tuesday, 24 September 2019
Monday, 16 September 2019
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14:15, Room V5-227 (60 minutes)
Marc Stephan (Bonn/Augsburg): Interactions between elementary abelian p-group actions in topology and algebra
Abstract: I will provide a selective overview about rank conjectures for actions of elementary abelian p-groups. They estimate the size of the total dimension in homology over a field of characteristic p for free actions on finite CW complexes or finite chain complexes. Recently, Iyengar and Walker found algebraic examples with smaller homology than predicted, while joint work with Henrik Rüping shows that these counterexamples can not be realized topologically.
To establish bounds for the total dimension in homology, it is still interesting to consider the algebraic version and connect it to problems in commutative algebra. I will explain such a connection from joint work with Jeremiah Heller, and how it is related to constructions of vector bundles on projective space from modules of constant Jordan type due to Benson and Pevtsova.
Monday, 09 September 2019
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BiBo Seminar in Bielefeld
11:15, Room U2-200 (60 minutes)
Biao Ma (Bielefeld): Combinatorics of faithfully balanced modules
Abstract: In this talk, I will give a combinatorial characterization of faithfully balanced modules for the path algebra of the quiver An with linear orientation. By using this characterization one can deduce that the number of basic faithfully balanced modules is the nth 2-factorial number. Among them are n! modules with exactly n indecomposable summands which form a lattice (with respect to some appropriate partial order) – this extends the lattice of tilting modules. This is joint work with William Crawley-Boevey, Baptiste Rognerud and Julia Sauter.
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Bielefeld-Bochum-Seminar
13:30, Room U2-200 (60 minutes)
Alexander Pütz (Bochum): Degenerate Affine Flag Varieties and Quiver Grassmannians
Abstract: We study degenerate flag varieties where certain projections replace the identity maps in the inclusion relations for the chains of the spaces in the geometric interpretation of the flag variety. Quiver Grassmannians are projective varieties parametrising subrepresentations of a quiver representation.
We show that certain quiver Grassmannians for the equioriented cycle provide finite dimensional approximations of the degenerate affine flag variety of type GL_n. These quiver Grassmannians admit a finite cellular decomposition parametrised by affine Dellac configurations. Their irreducible components are normal, Cohen-Macaulay, have rational singularities and are parametrised by grand Motzkin paths. The Poincaré polynomials of the approximations admit a description based on the affine Dellac configurations. This research links the theory of quiver Grassmannians with the representation theory of affine Kac-Moody groups.
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Bielefeld-Bochum-Seminar
15:00, Room U2-200 (30 minutes)
Julia Sauter (Bielefeld): Relative geometry of representations - II
Abstract: We have a closer look at F-hereditary structures. Every algebra of representation dimension at most three admits an F-hereditary structure. All relative representation spaces are smooth if and only if the relative structure is F-hereditary. Furthermore, for relative quiver Grassmannians we can show that they are smooth if we have an F-hereditary structure and an F-rigid module.
Friday, 05 July 2019
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14:15, Room T2-208
Estanislao Herscovich (Grenoble): The cohomology of the Fomin-Kirillov algebra on 3 generators
Abstract: The aim of the talk is to present an elementary computation of the algebra structure of the Yoneda algebra of the Fomin-Kirillov algebra on 3 generators, based on a bootstrap technique built over the (non-acyclic) Koszul complex.
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15:30, Room T2-208
Grzegorz Bobiński (Torun): A characterization of representation infinite quiver settings
Abstract: We characterize pairs (Q,d) consisting of a quiver Q and a dimension vector d, such that over a given algebraically closed field k there are infinitely many representations of Q of dimension vector d. We also present an application of this result to the study of algebras with finitely many orbits with respect to the action of (the double product) of the group of units.
Friday, 07 June 2019
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14:15, Room T2-208
Philipp Lampe (Canterbury): The growth of real seeds and a determinant from group representation theory
Abstract: This talk provides a taster of an ingredient that we added to a proof in a joint work with Anna Felikson. In particular, we will look at a determinant assembled from the characters of a finite group. First, we give an overview of its long and colourful history going back to Catalan, Dedekind, Burnside and Frobenius. Second, we explain how the determinant helped to estimate growth rates of real seeds in cluster theory.
Friday, 24 May 2019
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14:15, Room T2-208
Janina Carmen Letz (Salt Lake City): Local to global principles for generation time over Noether algebras
Abstract: In the derived category of modules over a Noether algebra a complex G is said to generate a complex X if the latter can be obtained from the former by taking finitely many summands and cones. The number of cones needed in this process is the generation time of X. I will present some local to global type results for computing this invariant, and also discuss some applications.
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15:30, Room T2-208
Zhengfang Wang (Bonn): Tate-Hochschild cohomology and B-infinity algebra
Abstract: Tate-Hochschild cohomology was implicitly defined in Buchweitz’ unpublished manuscript in 1986, using his stable derived category. Analogous to Hochschild cohomology, it is interesting to ask whether there is a Gerstenhaber algebra structure on Tate-Hochschild cohomology.
In this talk, we will give an affirmative answer to the above question. For this, we first construct a natural complex to compute Tate-Hochschild cohomology. Then we show that there is a so-called B-infinity algebra structure on this complex by giving an explicit action of the little 2-discs operad on it. In particular, passing to cohomology, we get a Gerstenhaber algebra structure. If time permits, we will also talk about Keller’s very recent result and conjecture.
Friday, 17 May 2019
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Bielefeld-Münster Representation Theory Seminar
13:15, Room T2-208
Biao Ma (Bielefeld): Faithfully balanced modules and applications in relative homological algebra
Abstract: For a finite-dimensional algebra we revisit faithfully balanced modules and introduce the relative version of them. As applications, we establish the relative version of Brenner-Butler's tilting theorem and (higher) Auslander correspondence. Examples will be given to explain the main results. This is joint work with Julia Sauter.
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Bielefeld-Münster Representation Theory Seminar
14:30, Room T2-208
Haydee Lindo (Williamstown, MA): Endomorphism invariant modules and ring classifications
Abstract: I will speak on modules which are invariant under endomorphisms of their envelopes. This will include connections to the general theory of trace modules with some preliminary applications to ring classifications and conjectures involving modules with no self-extensions.
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Bielefeld-Münster Representation Theory Seminar
16:00, Room T2-208
Lutz Hille (Münster): Tilting Modules for the Auslander Algebra with a View to Derived Categories
Abstract: We consider the Auslander algebra of the truncated polynomial ring and classify exceptional modules and spherical modules. Using a recent result of Geuenich, we can describe all tilting modules as universal extensions of full exceptional sequences. Then we use spherical twists to construct also tilting complexes in the derived category, which have a very explicit description.
It is still open in general whether this is already the full classification, so we discuss the known results and the open problems.
This is joint work with David Ploog.
Saturday, 04 May 2019
Friday, 03 May 2019
Thursday, 02 May 2019
Friday, 12 April 2019
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13:30, Room T2-208
Markus Linckelmann (London): On Picard groups of finite group algebras
Abstract: The Picard group of self Morita equivalences of a finite-dimensional algebra over an algebraically closed field k is an algebraic group. By contrast, the Picard group of a finite group algebra over a p-adic ring with finite residue field is a finite group. The structure of the automorphism group of a finite group algebra over a p-local domain with an algebraically closed residue field is largely unknown; it seems to be unknown in general whether this group is finite. A recent result by F. Eisele shows that this group is also an algebraic group over the residue field. In joint work with R. Boltje and R. Kessar, we identify a `large' subgroup of the Picard group of a block algebra in terms of the fusion systems of the blocks and the Dade groups of its defect groups. This is partly motivated by the - to date open - question whether Morita equivalent block algebras have isomorphic defect groups and fusion systems. Another motivation comes from recent work of Eaton, Eisele, and Livesey, where the above results on Picard groups play a role in the proof of special cases of Donovan's finiteness conjecture.
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14:45, Room T2-208
Dave Benson (Aberdeen): Some exotic symmetric tensor categories in characteristic two
Abstract: This talk is about joint work with Pavel Etingof. A theorem of Deligne says that in characteristic zero, any symmetric tensor category "of moderate growth" admits a tensor functor to vector spaces or to super (i.e., Z/2-graded) vector spaces. In prime characteristic, this is not true, but one may ask whether there is a good list of "incompressible" symmetric tensor categories to which they they do all map. We construct an infinite ascending chain of finite symmetric tensor categories in characteristic two, all of which are incompressible. The constructions are based on the theory of tilting modules over the finite groups SL(2,2^n). Similar examples should exist in other prime characteristics, but the details have not yet been worked out.
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16:00, Room T2-208
Jon Carlson (Athens, Georgia): Lots of categories for the Green correspondence
Abstract: This is joint work with Lizhong Wang and Jiping Zhang.
The object is to establish a Green correspondence for categories of complexes of modules as well as their homotopy categories and derived categories. There is a categorical expression of the Green correspondence that is similar to a construction of Benson and Wheeler. At a key point in the constuction, we must assume that one of the categories has idempotent completion. This condition holds provided the category has countable direct summands. But under that assumption there are many categories that satisfy the hypothesis.
For information on earlier talks please check the complete seminar archive.
