Seminar
Friday, 21 June 2013
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13:15, Room V2-213
Sefi Ladkani (Bonn): Jacobian algebras from closed surfaces, derived equivalences and Brauer graph algebras
Abstract: To any ideal triangulation of a surface with marked points Labardini-Fragoso has associated a quiver with potential, thus linking the work of Fomin, Shapiro and Thurston on cluster algebras arising from marked surfaces with the theory of quivers with potentials and their mutations initiated by Derksen, Weyman and Zelevinsky.
We show that for any surface without boundary, the associated quivers with potentials are not rigid and their (completed) Jacobian algebras are finite-dimensional, symmetric and derived equivalent. This settles a question that has been open for some time and also provides an explicit construction of infinitely many families of finite-dimensional symmetric Jacobian algebras. Moreover, these Jacobian algebras are closely related to Brauer graph algebras arising naturally from triangulations of the surface.
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14:30, Room V2-213
Hideto Asashiba (Shizuoka): Lax functors of bicategories and derived equivalences with application to triangular matrix algebras
Abstract: Let k be a field. We first review a gluing process of derived equivalences of k-categories using Grothendieck constructions of colax functors from a small category I to the 2-category of k-categories. Next we discuss a generalization of this process by extending the definition of Grothendieck constructions to those of lax functors from I to the bicategory of k-categories and bimodules over them to recover triangular matrix algebras (or more generally tensor algebras of k-species).
For a regular email announcement please contact birep.
Future Talks
Friday, 19 July 2013
Wednesday, 24 July 2013
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13:15, Lecture Hall H9
Chrysostomos Psaroudakis (Ioannina): tba
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14:30, Lecture Hall H9
Ryan Kinser (Boston): Type A quiver loci and Kazhdan-Lusztig varieties
Abstract: We show how to embed a representation variety of a type A quiver into a Kazhdan-Lusztig variety (Schubert variety intersected with opposite Schubert cell). The embedding takes orbit closures to Schubert varieties intersected with the opposite cell. The talk will be example based, requiring no previous knowledge of Schubert varieties.
This has implications for the geometry of the orbit closures, such as recovering a theorem of Zwara and Bobiński that the orbit closures are normal and Cohen-Macaulay, and also leads to formulas for cohomology and K-classes of the orbit closures.
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16:00, Lecture Hall H9
Grzegorz Bobinski (Torun): tba
Friday, 08 November 2013
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Catharina Stroppel (Bonn): tba
Seminar Archive
Grzegorz Bobinski made his notes from some of the seminar talks available on his web page.
Friday, 14 June 2013
Saturday, 08 June 2013
Friday, 07 June 2013
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13:15, Room V2-213
Adam-Christiaan van Roosmalen (Berkeley): Cluster categories associated to new hereditary categories
Abstract: This is joint work with Jan Šťovíček. Given a finite quiver, one can associate a cluster category by considering orbits of the bounded derived category of finite dimensional representations. In this talk, we want to replace the original quiver by a suitable small category such that the orbit construction still makes sense, thus obtaining new examples of 2-Calabi-Yau categories with cluster tilting subcategories. We will consider some examples where one can use combinatorics to describe the cluster tilting subcategories, as is done by Holm and Jørgensen in the case of the infinite Dynkin quiver A_infinity using triangulations of the infinity-gon.
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14:30, Room V2-213
Julia Worch (Kiel): Module categories and Auslander-Reiten theory for generalized Beilinson algebras
Abstract: Inspired by the work of Carlson, Friedlander, Pevtsova and Suslin in the modular representation theory of finite group schemes, we introduce the categories of modules of constant Jordan type and modules with the equal images property for generalized Beilinson algebra. We give a homological characterization of these subcategories which enables us to apply general methods from Auslander-Reiten theory and thereby obtain information concerning the occurrence of the corresponding modules within the Auslander-Reiten quiver of the Beilinson algebra.
Friday, 31 May 2013
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13:15, Room V2-213
Julia Sauter (Leeds): From Springer theory to monoidal categories
Abstract: To every Springer Theory one gets a category of (shifts of) perverse sheaves generated by direct summands in the BBD decomposition theorem, which we call Lusztig's perverse sheaves. When one chooses "additive" families of Springer theories, it is possible to define a convolution product on the associated category of perverse sheaves. This way one gets a monoidal category, the homomorphisms are given by Steinberg algebras. Lusztig proved that when one starts with quiver-graded Springer theory, then this gives a monoidal categorification of the positive half of the quantum group associated to the quiver. We study this construction for more general Springer theories and explain the example of symplectic quiver-graded Springer theory.
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14:30, Room V2-213
Michael Cuntz (Kaiserslautern): Weyl groupoids and arrangements
Abstract: The Weyl groupoid is a symmetry structure which was originally introduced as an invariant of Nichols algebras. The classification of finite Weyl groupoids revealed further applications in geometry and combinatorics. In this talk we will see this connection for more general Cartan schemes, and discuss the recently initiated classification of affine Weyl groupoids.
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16:00, Room V2-213
Jose Antonio de la Pena (Guanajuato): On the Mahler measure of Coxeter polynomials
Abstract: Let A be a finite dimensional algebra over an algebraically closed field k. Assume A is basic connected and triangular, hence of finite global dimension. We say that A is of cyclotomic type if the characteristic polynomial p(x) of of the Coxeter transformation is a product of cyclotomic polynomials, equivalently, if the Mahler measure M(p)=1. We consider the many examples of algebras of cyclotomic type in the representation theory literature and show some common properties. We also consider algebras not of cyclotomic type with small Mahler measure of their Coxeter polynomial. In 1933, D. H. Lehmer found that the polynomial T^{10} + T^9 - T^7 - T^6 - T^5 - T^4 - T^3 + T + 1 has Mahler measure m = 1.176280..., and he asked if there exist any smaller values exceeding 1. We prove that either M(p)=1 or M(p)≥m for strongly simply connected algebras A.
Friday, 24 May 2013
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14:00, Room V2-213
Julia Sauter (Leeds): Classical and quiver-graded Springer theory
Abstract: We introduce Springer Theory as a geometric construction of (some) graded convolution algebras (Steinberg algebras) together with certain modules, called Springer fibre modules. The BBD-decomposition theorem gives a parametrization of (graded) indecomposable projectives and simple modules for the Steinberg algebras. The two main examples are classical and quiver-graded Springer theory. For the classical Springer Theory the Steinberg algebra is the group ring of the Weyl group (ass. to a reductive group) and the Springer correspondence identifies simple modules with isotypic subspaces of the Springer fibre modules. The Steinberg algebras for quiver-graded Springer theory are quiver Hecke algebras (=KLR-algebras) introduced by Khovanov-Lauda and Rouquier. My result here is an explicit calculation of Steinberg algebras in a more general setup.
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15:15, Room V2-213
Matthias Warkentin (Chemnitz): On the global structure of infinite mutation graphs
Abstract: Let Q be an acyclic quiver and K an algebraically closed field. The exchange graph of tilting modules over KQ introduced by Riedtmann and Schofield has been studied extensively by Happel and Unger. After the introduction of cluster algebras and cluster categories it has been shown that this exchange graph can be seen as a part of the exchange graph of the cluster algebra given by Q, which is governed by the combinatorics of quiver mutations. We explain how elementary considerations about quiver mutations can be used to understand the structure of the corresponding exchange graphs. In particular, our results (combined with results by Felikson, Shapiro and Tumarkin) yield an "almost complete" answer to Unger's conjecture about the number of connected components.
Friday, 26 April 2013
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13:15, Room V2-213
Phillip Linke (Bielefeld): Computational approach to the Artinian conjecture (Part I)
Abstract: What is generic representation theory? When looking at the category F=Func(mod F_q,Mod F_q) we obtain that a functor G in F generically gives rise to representations of GL(V) for all V in mod F_q. By the Yoneda-lemma we know how certain projectives in F look like. For each V in mod F_q, Hom(V,-) is projective. Such a projective is called a standard projective. It turns out that these standard projective even generate the whole category.
In the 1980s Lionel Schwartz conjectured that all the standard projectives would be noetherian. If true this would imply that every finitely generated functor in F admits a projective resolution by finitely generated projectives. There are partial results that back up this conjecture but no solution so far.
In the talk we will not reach quite as far. The aim is to give an idea why the category F is at least coherent. That means that every finitely presented functor admits a resolution by finitely generated projectives. To get to this goal we will use certain combinatorial properties of the dimension function phi(G,n)=dim_{F_q}G(F_{q^n}) for a functor G in F.
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14:30, Room V2-213
Phillip Linke (Bielefeld): Computational approach to the Artinian conjecture (Part II)
Abstract: See Part I.
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16:00, Room V2-213
Sven Meinhardt (Wuppertal): Motivic DT-invariants of (-2)-curves
Abstract: In the first part of my talk I will gently introduce (0,-2)-curves and sketch how they show up in resolutions of singular 3-folds. After that, an alternative non-commutative resolution using quivers with potential is given. Finally, I will briefly introduce Donaldson-Thomas invariants and state the answer in our situation which is the main result of a joint work with Ben Davison.
Friday, 19 April 2013
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14:30, Room V2-213
Martin Kalck (Bielefeld): Singularity categories of gentle algebras
Abstract: We give an explicit description of the triangulated category of singularities (in the sense of Buchweitz and Orlov) for all finite dimensional gentle algebras. Examples include Jacobian algebras arising from triangulations of unpunctured marked Riemann surfaces and algebras which are derived equivalent to certain singular projective curves. Moreover, we recover part of a derived invariant for gentle algebras, which was discovered by Avella-Alaminos & Geiß.
Friday, 12 April 2013
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Workshop Noncrossing Partitions
09:00, Room V2-210/216
Claus Michael Ringel (Bielefeld): The non-crossing partitions for any Dynkin type are the antichains in the corresponding root poset. On antichains in posets and in additive categories
Abstract: Dealing with simply laced Dynkin diagrams, Ingalls and Thomas (Compos. Math. 145, 2009) gave an interpretation of the set of non-crossing partitions in terms of the representation category of a Dynkin quiver: they exhibited, for example, a bijection between the non-crossing partitions and the wide subcategories or also the torsion classes. These results can be reformulated in terms of antichains in additive categories and extended to the non-simply laced cases B_n, C_n, F_4, G_2 and the corresponding hereditary abelian categories. We will show in which way the representation theory approach sheds light on the relationship between crossing and nesting; this relationship is well-known in the cases A_n, but seemed to be quite mysterious in the remaining cases.
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Workshop Noncrossing Partitions
10:15, Room V2-210/216
Friedrich Götze (Bielefeld): Free Probability and Noncrossing Partitions
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Workshop Noncrossing Partitions
11:30, Room V2-210/216
Patrick Wegener (Bielefeld): The dual braid monoid (after Bessis)
Abstract: Considering a finite Coxeter system (W,S) one can construct a monoid structure for the associated Artin group, the so called classical braid monoid. Replacing (W,S) by (W,T,c), where T is the set of all reflections in W and c a Coxeter element, we construct a new monoid structure for the associated Artin group. Essential for the construction is the lattice of noncrossing partitions and some of its properties. Like the classical monoid this monoid will be Garside. This analogy indicates that there might be a "dual" way of studying Coxeter systems.
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Workshop Noncrossing Partitions
14:00, Room V2-210/216
Philipp Lampe (Bielefeld): Combinatorial models for cluster algebras via noncrossing partitions
Abstract: A cluster algebra is a commutative ring together with a distinguished set of generators called cluster variables. We obtain the cluster variables from given initial variables by a very concise combinatorial mutation process. The cluster algebras with only finitely many cluster variables have been classified by finite type root systems. Here, cluster variables correspond to almost positive roots. In this talk, we wish to discuss which almost positive roots arise from the same cluster. We introduce several combinatorial models and bijections between clusters, Coxeter-sortable elements and noncrossing partitions.
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Workshop Noncrossing Partitions
15:15, Room V2-210/216
Henning Krause (Bielefeld): A K-theoretic study of exceptional sequences
Abstract: Given a category of representations, we consider its Grothendieck group together with the Euler form (the bilinear form defined by the alternating sum of dimensions of Ext-spaces). In this setup, one defines roots, reflections, a Weyl group, and exceptional sequences. We associate to each exceptional sequence a Coxeter element (a product of reflections in the Weyl group). Under suitable assumptions, this yields a bijection between all exceptional sequences and the noncrossing partitions (viewed as elements of the Weyl group). In my talk, I'll explain this construction and discuss some examples.
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Workshop Noncrossing Partitions
16:30, Room V2-210/216
Gennadiy Chistyakov (Bielefeld): Distributions of commutators and anti-commutators
Thursday, 11 April 2013
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Workshop Noncrossing Partitions
15:30, Room V2-210/216
Christopher Voll (Bielefeld): Noncrossing partitions and Coxeter groups
Abstract: I will explain some fundamental aspects of the lattice of noncrossing partitions of a general (finite) Coxeter group. The exposition will be almost self-contained; some familiarity with the basics of Coxeter group theory might help, but is not essential.
Friday, 25 January 2013
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13:15, Lecture Hall H6
Britta Späth (Kaiserslautern): An approach to global/local conjectures in the representation theory of finite groups
Abstract: Much of the recent work in the representation theory of finite groups is centered around the global/local conjectures, notably the conjectures from Alperin, Brauer and McKay. An underlying idea of these conjectures is that certain aspects of the representation theory of a finite group should be determined "locally", that is, by the representation theory of so-called local subgroups (e.g., the normalisers of certain p-subgroups).
In the talk I describe how these conjectures can be reduced to questions on simple groups. Furthermore I sketch in which cases these questions can be answered completely.
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14:30, Lecture Hall H6
Jan Schröer (Bonn): The representation type of Jacobian algebras
Abstract: This is joint work with Christof Geiss and Daniel Labardini-Fragoso. We determine the representation type of (almost) all Jacobian algebras P(Q,S) arising from a 2-acyclic quiver Q and a non-degenerate potential S. Such algebras were introduced by Derksen, Weyman and Zelevinsky and play a central role in relating cluster algebras with the representation theory of quivers.
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16:00, Lecture Hall H6
Jon Carlson (Athens, Georgia): Modules of constant radical type and bundles on Grassmannians
Abstract: This is joint work with Eric Friedlander and Julia Pevtsova. We introduce higher rank variations on the notion of $\pi$-points as defined by the second two authors for representations of finite group schemes. Using this we can define module of constant r-radical and r-socle type. Such modules determine bundles over the Grassmannian associated to the higher rank $\pi$-points in the case that the group scheme is infinitesimal of height one. When the group scheme is an elementary abelian p-group, there is universal function for computing the kernel bundles as modules over the structure sheaf of the Grassmannian of r-planes in n space. These ideas also extend to various sorts of subalgebra of restricted p-Lie algebras.
Friday, 18 January 2013
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13:15, Lecture Hall H6
Lennart Galinat (Köln): Orlov's Equivalence and Maximal Cohen-Macaulay Modules over the Cone of a (plane) Elliptic Curve
Abstract: In 1982 Kahn showed that the category of MCM modules over a simple elliptic surface singularity is representation tame. However his description of its indecomposable objects is far from being explicit.
In my talk I shall present a classification of all rank one matrix factorisations of a cone over a plane elliptic curve which is based on more recent techniques including Orlov's equivalence for graded MCMs.
Moreover I shall explain a (computer algebra based) way to describe all indecomposable matrix factorisations for such singularities.
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14:30, Lecture Hall H6
Claus Michael Ringel (Bielefeld): From submodule categories to preprojective algebras
Abstract: Let S(n) be the category of invariant subspaces of nilpotent operators with nilpotency index at most n. Such submodule categories have been studied already in 1936 by Birkhoff, they have attracted a lot of attention in recent years, for example in connection with some weighted projective lines (Kussin, Lenzing, Meltzer). On the other hand, we consider the preprojective algebra of type A_n; the preprojective algebras were introduced by Gelfand and Ponomarev, they are now of great interest, for example they form an important tool to study quantum groups (Lusztig) or cluster algebras (Geiss, Leclerc, Schroeer). Direct connections between the submodule category S(n) and the module category of the preprojective algebra of type A_{n-1} have been established quite a long time ago by Auslander and Reiten, and recently also by Li and Zhang, but apparently this remained unnoticed. The lecture is based on joint investigations with Zhang Pu and will provide details on this relationship. As a byproduct we see that here we deal with ideals I in triangulated categories T such that I is generated by an idempotent and T/I is abelian.
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16:00, Lecture Hall H6
Vanessa Miemietz (Norwich): The extension algebra of Weyl modules for GL_2
Abstract: I will explain how to use a homological duality of 2-functors to give an explicit construction of the Ext-algebra of Weyl modules, which in particular yields a multiplicative (up to sign) basis.
Thursday, 17 January 2013
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10:15, Room V5-227
Vanessa Miemietz (Norwich): 2-functors and homological duality
Abstract: We will explain how certain 2-functors encoding the rational representation theory of GL_2 in positive characteristic commute with homological dualities, which makes it possible to compute various extension algebras.
Friday, 21 December 2012
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13:15, Lecture Hall H6
Lutz Hille (Münster): On the irreducible components for algebras over double quivers
Abstract: Several algebras defined by a double quiver with certain relations, like the preprojective algebra, are of geometric interest. In particular, the number of irreducible components of the corresponding representation space play an important role. One of the most prominent examples is the construction of the crystal (in the sense of Kashiwara) in terms of nilpotent representations of the preprojective algebra.
In the talk we present a construction to determine the irreducible components of the space of all locally nilpotent representations of the preprojective algebra using nilpotent classes. This space contains the space of nilpotent representations, and the irreducible components form a subset of the irreducible compenents of the space of all locally nilpotent representations.
Friday, 30 November 2012
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13:15, Lecture Hall H6
Valentin Katter (Bielefeld): Reduced representations in the representation ring of rooted tree quivers
Abstract: For two representations V,W of a quiver Q we can define a pointwise tensor product. This tensor product together with the direct sum induces a ring structure on the set of isomorphism classes of representations of Q. We call this ring the representation ring of the quiver Q and denote it with R(Q). We can construct orthogonal idempotents and give a decomposition of R(Q) via the Möbius algebra on the partial ordered set of subquivers of Q. In this talk we will look at the ring structure of R(Q) for rooted tree quivers, which are quivers that have exactly one sink and whose underlying graph is a tree. Kinser discovered that for a rooted tree quiver, R(Q) modulo its nilpotent elements is a finitely generated Z-module, where the generators can be obtained by so called reduced representations. These reduced representations arise from a combinatorial construction and can be defined via the property that V is a direct summand of V².
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14:30, Lecture Hall H6
Greg Stevenson (Bielefeld): Gorenstein small categories and representations of finite projective dimension
Abstract: We will discuss certain conditions on a small category C which ensure the category of representations of C, over a Gorenstein ring, is Gorenstein. In special cases, for instance mesh categories of simply laced Dynkin quivers, we will then demonstrate that, over a regular ring, one can characterise the representations of finite projective dimension in terms of exactness conditions coming from the structure of C. Time permitting, the motivating problem of finding universal coefficient theorems for triangulated categories will also be discussed. This is ongoing joint work with Ivo Dell'Ambrogio and Jan Stovicek.
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16:00, Lecture Hall H6
Thorsten Weist (Wuppertal): On the recursive construction of indecomposable quiver representations
Abstract: Besides known techniques we investigate new techniques which can be used to construct indecomposable quiver representations recursively. These recursions come always along with a certain decomposition of some fixed root into smaller Schur roots. Often there exists a „well-behaved“ decomposition saying how to construct indecomposable representations. But one can also easily produce examples where it seems that only more complicated decompositions exist. This construction can also be used to construct indecomposable tree modules.
Friday, 23 November 2012
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13:15, Lecture Hall H6
Zhe Han (Bielefeld): The homotopy categories of injective modules of derived discrete algebras
Abstract: The derived classification of algebras with discrete derived categories (derived discrete algebras) was given by Dieter Vossieck. Concerning the unbounded derived category D(Mod A) and the homotopy category K(Inj A) for some finite dimensional algebra A, I will give a characterization of generically trivial derived categories and a classification of the indecomposable objects in K(Inj A) for radical square zero algebras A which are derived discrete. As a consequence, all the indecomposable objects are endofinite.
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14:30, Lecture Hall H6
Henning Krause (Bielefeld): Discrete derived categories and Krull-Gabriel dimension
Abstract: Discrete derived categories were introduced by Vossieck. In my talk I'll explain a conjecture, which says that a derived category is discrete iff its Krull-Gabriel dimension is bounded by one.
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16:00, Lecture Hall H6
Dieter Vossieck (Bielefeld): Representation-discrete algebras and the second Brauer-Thrall conjecture
Abstract: We want to discuss the following statement which is equivalent to the second Brauer-Thrall conjecture / theorem of Nazarova-Roiter / theorem of Bautista-Bongartz:
Over an algebraically closed field k , let k[[Q]] be the complete path-algebra of a finite quiver Q and let I be a closed ideal of k[[Q]] consisting of (possibly infinite) linear combinations of paths of length at least 2. Assume that k[[Q]]/I is minimal representation-infinite but admits only finitely many indecomposables of any given dimension. Then Q is an oriented cycle and I = 0 .
Friday, 09 November 2012
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14:00, Lecture Hall H6
Andreas Nickel (Bielefeld): Non-commutative Fitting invariants
Abstract: One can associate to each finitely presented module M over a commutative ring R an ideal Fitt(M) which is called the (zeroth) Fitting ideal of M over R and which is an important natural invariant of M. For instance, it is always contained in the annihilator of M. We generalize this notion to orders over complete commutative noetherian local domains in separable algebras.
Friday, 02 November 2012
Friday, 26 October 2012
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14:00, Lecture Hall H6
Sira Gratz (Hannover): Cluster Algebras of Infinite Rank
Abstract: The combinatorics of a cluster algebra of type Q, where Q is an orientation of the Dynkin diagram A_n, can be expressed via triangulations of the (n + 3)-gon. As has been observed by Fomin and Zelevinsky, it follows that there is a cluster algebra structure of type Q on the homogeneous coordinate ring C[Gr(2, n + 3)] of the Grassmannian of planes, which is defined as the coordinate of the affine cone of Gr(2, n + 3) via the Plücker embedding. By allowing infinite countable clusters, this idea can be extended to the infinite case, motivated by results by Holm and Jørgensen, who have analysed a category, whose cluster tilting subcategories correspond to triangulations of the ∞-gon. We study the cluster algebra structures arising from the cluster structure on this category, obtaining infinite cluster algebra structures on the homogeneous coordinate ring C[Gr(2, ±∞)], where Gr(2, ±∞) is the space of planes in the pro-finite dimensional vectorspace k[[t,t−1]]. Moreover, the results of Grabowski and Launois on the quantum algebra structure on the quantum Grassmannian C_q[Gr(2,n)] can be generalized to the infinite case, yielding infinite quantum cluster algebra structures on C_q[Gr(2,±∞)].
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15:15, Lecture Hall H6
Jorge Vitória (Stuttgart): Ring epimorphisms and universal localisations
Abstract: Ring epimorphisms are relevant to study certain subcategories of a fixed category of modules or of its derived category. One way to construct ring epimorphisms is to consider universal localisations, as defined by Cohn and Schofield. In this talk we will show that, in some cases, ring epimorphisms with a particularly nice homological property (so called homological ring epimorphisms) are precisely those given by universal localisations. Moreover, we will present a generalisation of universal localisation, introduced by Krause, and discuss necessary and sufficient conditions for its existence.
Friday, 19 October 2012
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13:15, Lecture Hall H6
Xiaojin Zhang (Nanjing): The Gorenstein projective conjecture
Abstract: In this talk, we report that the Gorenstein projective conjecture is left and right symmetric and the co-homology vanishing condition can not be reduced in general. Moreover, the Gorenstein projective conjecture is true for CM-finite algebras.
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14:30, Lecture Hall H6
Luke Wolcott (Lisbon): Not every object in the derived category of a ring is Bousfield equivalent to a module
Abstract: Given W and X in a tensor triangulated category, we say W is X-acyclic if W tensors with X to zero. Two objects X and Y are called Bousfield equivalent if they have the same acyclics. In this talk we give a (non-constructive) proof that there exist objects in the derived category of graded modules over a certain graded non-Noetherian ring that are not Bousfield equivalent to any module. This contrasts with the Noetherian case, and has consequences for subcategory classification.
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16:00, Lecture Hall H6
Giovanni Cerulli Irelli (Bonn): Desingularization of quiver Grassmannians
Abstract: Given a Dynkin quiver Q and a (finite-dimensional) Q-representation M, let us consider a quiver Grassmannian X=Gr_e(M) associated with M, i.e. the projective variety of all subrepresentations of M of dimension vector e. This projective variety is not smooth in general, and its geometry is quite complicated. Our aim is to construct an explicit desingularization of X, i.e. a proper birational morphism f:\hat{X}->X from a smooth projective variety \hat{X}. The variety \hat{X} turns out to be again a quiver Grassmannian for a representation \hat{M} of an algebra $B_Q$ derived-equivalent to the Auslander algebra of kQ.
This is a joint work with Evgeny Feigin and Markus Reineke (arXiv:1209.3960).
Friday, 12 October 2012
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14:00, Lecture Hall H6
Takuma Aihara (Bielefeld): On upper bounds of derived dimensions
Abstract: The notion of the dimension of a triangulated category has been introduced by Rouquier. It measures how many extensions are needed to build the triangulated category out of a single object, up to finite direct sum, direct summand and shift. It is still a hard problem in general to give a precise value of the dimension of a given triangulated category. In the talk, we will focus on dimensions of bounded derived categories (derived dimensions) and give several upper bounds of derived dimensions.
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15:15, Lecture Hall H6
Daniel Labardini-Fragoso (Bonn): On a family of species with potentials
Abstract: I will talk on work in progress, joint with Andrei Zelevinsky, regarding possible extensions of Derksen-Weyman-Zelevinsky's mutation theory of quivers with potentials to the setting where the matrix encoded by the quiver is not skew-symmetric but rather skew-symmetrizable.
For information on earlier talks please check the complete seminar archive.
