Ring Theory and Representation Theory Seminar

Cluster Algebra Seminar

Ring Theory and Representation Theory Seminar

Cluster Algebra Seminar

Research Seminar in Representation Theory coorganized by Martin Herschend

26 November (Tuesday), Room 317 in Science Bldg. A

13:00--14:30 Idun Reiten (NTNU)

Coxeter groups, preprojective algebras and path algebras 2

Abstract: For a finite acyclic quiver $Q$ we consider the associated Coxeter group $W_Q$, path algebra $kQ$ (for an algebraically closed field $k$) and preprojective algebra $\Pi_Q$. We discuss a one-one correspondence between the elements in $W_Q$ and the cofinite quotient closed subcategories of the category of finite dimensional $kQ$-modules, from work with Oppermann and Thomas. We include background matetial from papers with Iyama, Buan-Iyama-Scott and Amiot-Iyama-Todorov.

15:00--16:30 Timothy Logvinenko (Cardiff)

Spherical DG-functors

Abstract: Seidel-Thomas twists are certain autoequivalences of the derived category D(X) of an algebraic variety X. Roughly, they are the mirror symmetry analogues of Dehn twists along Lagrangian spheres on a symplectic manifold. In this talk I will explain the definition of a Seidel-Thomas twist, illustrate it with a number of geometrical examples, and then report on my recent joint work with Rina Anno (UPitt) which generalises the notion from the twist along an object of D(X) to the twist along a functor into D(X). Geometrically, this corresponds to working, instead of a single object, with a fibration over a non-trivial base.

25 November (Monday), Room 207 in Science Bldg. A

13:00--14:30 Idun Reiten (NTNU)

Coxeter groups, preprojective algebras and path algebras 1

Abstract: For a finite acyclic quiver $Q$ we consider the associated Coxeter group $W_Q$, path algebra $kQ$ (for an algebraically closed field $k$) and preprojective algebra $\Pi_Q$. We discuss a one-one correspondence between the elements in $W_Q$ and the cofinite quotient closed subcategories of the category of finite dimensional $kQ$-modules, from work with Oppermann and Thomas. We include background matetial from papers with Iyama, Buan-Iyama-Scott and Amiot-Iyama-Todorov.

7 November (Thursday), Room 317 in Science Bldg. A

13:00--14:30 Joseph Karmazyn (Edinburgh)

Deformed Reconstruction Algebras

Abstract: The preprojective algebras arise as non-commutative resolutions of Kleinian singularities. They have a very interesting class of deformations, the deformed preprojective algebras, which were introduced and studied by Crawley-Boevey and Holland. The reconstruction algebras were introduced by Wemyss as non-commutative resolutions of general surface quotient singularities. These algebras provide a generalisation of the preprojective algebras. It is then a natural question to ask whether there is a similar class of deformations for these algebras, generalising the deformed preprojective algebras. I will recall the case of the deformed preprojective algebras, and then discuss some of my results towards finding such a class of deformations for the reconstruction algebras.

8 October (Thursday), Room 317 in Science Bldg. A

13:00--14:30 Michael Wemyss (Edinburgh)

From noncommutative deformations of curves to self-injective algebras

Abstract: In the first half of my talk, I will explain background about noncommutative deformations of modules and coherent sheaves. I will try to motivate why we want to study this, and why commutative deformations are in general different. In the second half of my talk, I will explain how noncommutative deformations arise in the study of flopping curves in 3-folds, and how tilting allows us to calculate this very easily. I will briefly link this to birational geometry, but I will mainly focus on the algebraic aspects. In particular, it is possible to use birational geometry to construct many examples of new self-injective finite dimensional algebras, and I will try to explain how understanding aspects of the representation theory of these algebras allows us to construct objects in geometry.

15:00--16:30 Ryo Kanda (Nagoya)

Specialization orders on atom spectra of Grothendieck categories

Abstract: The atom spectrum of a Grothendieck category is a generalization of the prime spectrum of a commutative ring. The inclusion relation between prime ideals of a commutative ring is generalized as the specialization order on the atom spectrum with respect to some topology on it. We show that every partially ordered set is realized as the atom spectrum of some Grothendieck category. In order to do that, we introduce some method to construct Grothendieck categories from colored quivers.

19 September (Thursday), Room 317 in Science Bldg. A

13:00--14:30 Mitsuyasu Hashimoto (Nagoya)

Equivariant class groups and almost principal fiber bundles

Abstract: We define the equivariant class group of a locally Krull scheme with an action of a flat group scheme, study its basic properties, and apply it to prove the finite generation of the class group of an invariant subring. We also define almost principal fiber bundles, and prove that the equivariant class groups behaves well with respect to this "quotient." We will see how almost principal fiber bundles are ubiquitous in invariant theory.

15:00--16:30 Yusuke Nakajima (Nagoya)

Dual $F$-signature of Cohen-Macaulay modules over rational double points

The dual $F$-signature is a numerical invariant defined via Frobenius morphisms in positive characteristic. It is known that the dual $F$-signature characterizes some singularities. However, the value of dual $F$-signature is not well known. In this talk, we determine the dual $F$-signature of Cohen-Macaulay modules over two-dimensional rational double points.

9 August (Friday), Room 317 in Science Bldg. A

13:00-- Martin Herschend (Nagoya)

Tilting objects for Geigle-Lenzing projective spaces

15:00-- Darpoe Erik (Nagoya)

n-representation finite self-injective algebras

7 August (Wednesday)

量子群の圏化とKLR代数

6 August (Tuesday)

量子群の圏化とKLR代数

5 August (Monday), Room 317 in Science Bldg. A

13:00--14:30 Aaron Chan (Aberdeen)

Simple-minded and mutation theories of representation-finite self-injective algebras

Abstract: In a joint work with Steffen Koenig and Yuming Liu, we classify all simple-minded systems, a notion defined by my coauthors in their previous paper, of representation-finite self-injective algebras. For such algebras, we also exploit some interesting connections between these systems with other "simple-minded" and "projective-minded" objects, as well as their mutation theories. If time allows, I will also motivate the study for the connection between simple-minded systems and tau-tilting modules.

1 August (Thursday), Room 332 in Science Bldg. A

13:00-- Yu Liu (Nagoya)

13:00-- Laurent Demonet (Nagoya)

30 July (Tuesday), Room 317 in Science Bldg. A

13:00-- Yuya Mizuno (Nagoya)

23 July (Tuesday), Room 317 in Science Bldg. A

13:00-- Pierre-Guy Plamondon (Orsay)

19 July (Friday), Room 317 in Science Bldg. A

13:00-- Luo Xueyu (Nagoya)

14:45-- Yann Palu (Amiens)

16 July (Tuesday), Room 317 in Science Bldg. A

13:00-- Yann Palu (Amiens)

14:45-- Pierre-Guy Plamondon (Orsay)

10 July (Wednesday), Room 317 in Science Bldg. A

14:45-- Gustavo Jasso (Nagoya)

9 July (Tuesday), Room 317 in Science Bldg. A

13:00-- Hailong Dao (University of Kansas)

Cohen-Macaulay cones and asymptotic behavior of system of ideals

Abstract: In this joint project with Kazuhiko Kurano, we study cones of maximal Cohen-Macaulay modules inside finite dimensional quotients of the Grothendieck group of a Cohen-Macaulay local ring R. I will describe what is known about these cones, and how their shapes are related to subtle questions about asymptotic behavior of graded families of ideals. Applications will be discussed, for example we can show that certain rings have only finitley many maximal Cohen-Macaulay modules of rank one.

11 June (Tuesday), Room 552 in Mathematics Bldg.

13:00--14:00 Tomoki Nakanishi (Nagoya)

28 May (Tuesday), Room 317 in Science Bldg. A

13:00--14:30 Osamu Iyama (Nagoya)

Geigle-Lenzing spaces and canonical algebras in dimension d

Weighted projective lines were introduced by Geigle and Lenzing. One key property is that they have tilting bundles, whose endomorphism rings are canonical algebras. They have been important objects in representation theory and studied intensively. In this talk we will introduce the notion of Geigle-Lenzing d-spaces, generalizing the concept of weighted projective lines. In this case we obtain a nice tilting bundle, whose endomorphism ring we call a d-canonical algebra. We will then focus on some properties of Geigle-Lenzing d-spaces and their Cohen-Macaulay representation theory. This is based on joint works with Martin Herschend, Boris Lerner, Hiroyuki Minamoto and Steffen Oppermann.

15:00--16:30 Dong Yang (Nagoya)

The interplay between 2- and 3-Calabi--Yau triangulated categories

Abstract: 2-CY triangulated categories with cluster-tilting objects are the main objects of study in cluster-tilting theory, while 3-CY triangulated categories with simple-minded collections play an important role in algebraic geometry and mathematical physics. In this talk, I will report on the recent progress on the study of these categories, including constructions and interplays.

27 May (Monday), Room 455 in Science Bldg. I

09:30--10:30 Yu Liu (Nagoya)

Hearts of twin cotorsion pairs on exact categories

In the papers of Nakaoka, he introduced the notion of hearts of (twin) cotorsion pair on triangulated categories and showed that they have structures of (semi-) abelian categories. We study a twin cotorsion pair $(\s,\T),(\U,\V)$ on an exact category $\B$ with enough projectives and injectives and introduce a notion of the heart. First we show that its heart is preabelian. Moreover we show the heart of a single cotorsion pair is abelian. These results are analog of Nakaoka's results in triangulated categories. We also consider special cases where the heart has nicer structure.

11:00--12:00 Gustavo Jasso (Nagoya)

Reduction of $\tau$-tilting modules and torsion pairs

Abstract: Adachi, Iyama and Reiten recently introduced a generalization of tilting theory for finite dimensional algebras which they called $\tau$-tilting theory. Roughly speaking, this generalization is obtained by replacing $\Ext^1$-rigid modules by modules which have no non-zero morphisms to its Auslander-Reiten translate. An important feature of $\tau$-tilting theory is that it provides a completion of tilting theory from the point of view of mutations. In the first part of this talk we will explain the basics of $\tau$-tilting theory and compare it to usual tilting theory and compute some easy examples. After, given a finite dimensional algebra $A$, we will study all basic support $\tau$-tilting $A$-modules which have a given basic $\tau$-rigid $A$-module as a direct summand. We will sketch the construction of a bijection between such $A$-modules and all support $\tau$-tilting modules over an algebra $C$ strongly related to $U$.

25 April (Thursday) Room A-358

13:00--14:00 Hirotaka Koga (Tsukuba)

Derived equivalences and Gorenstein dimension

Abstract: For derived equivalent left and right coherent rings we show that the triangulated categories of complexes of finite Gorenstein dimension are equivalent.

24 April (Wednesday) Room A-317

18:00--19:00 Kota Yamaura (Kagoshima)

Construction of a natural t-structure on the stable category of graded modules over a positively graded self-injective algebra

Abstract: Dieter Happel had studied relationships between the derived category of a given algebra and the stable category of modules over the trivial extension. First he realized the module category of the original algebra as a heart of a t-structure on the stable category. Secondly he showed that the derived category can be embedded in the stable category. In my talk, I give some generalization of these works of D. Happel.

11 March (Monday) Room A-317

13:00--14:30 Kotaro Kawatani (Nagoya)

14:45--16:15 Kotaro Kawatani (Nagoya)

20 February (Wednesday) Room A-317

13:00--14:30 Martin Kalck (Bielefeld)

13 February (Wednesday) Room A-317

13:00--14:30 Torkil Utvik Stai (NTNU)

4 February (Monday) Room A-317

13:00--14:30 Masahide Konishi (Nagoya)

30 January (Wednesday) Room A-317

13:00--14:30 Ryoichi Kase (Osaka)

23 January (Wednesday) Room A-317

13:00--14:30 Dong Yang (Nagoya)

22 January (Tuesday) Room A-207,

13:30-- Yasuyoshi Yonezawa

1変数多項式環の圏化, part 3

15 January (Tuesday) Room I-555,

13:30-- Yasuyoshi Yonezawa

1変数多項式環の圏化, part 2

9 January (Wednesday) Room A-317

13:00--14:30 Kenneth Chan (Washington)

4 January (Friday) Room I-309

15:00--16:30 Kenneth Chan (Washington)

Noncommutative ruled surfaces

Abstract: The noncommutative minimal model program (MMP) uses the techniques of Mori theory to classify noncommutative surfaces, which we assume to be finite over their centres. The main result is a very pleasing analogy with the commutative theory, a noncommutative surface is either birational to a unique minimal model, or a noncommutative ruled surface. In this talk, I will explain how to associate a Brauer pair to a noncommutative surface, and how to run the MMP for these Brauer pairs. Although this is similar in spirit to the log MMP, there are some differences. Noncommutative ruled surfaces arise naturally in this context, and we will conclude with some structural results about them obtained by moduli theory.

19 December (Wednesday) Room A-317

14:00--15:30 Boris Lerner

18 December (Tuesday) Room A-435

13:30-- Yasuyoshi Yonezawa

1変数多項式環の圏化, part 1

Abstract: arXiv:1101.0293 "Categorification of the polynomial ring"を数回のセミナーで紹介します。初回は論文でなされていることの説明です。

12 December (Wednesday) Room A-317

10:30--12:00 Hyohe Miyachi

7 December (Friday) Room A-442

14:45--16:15 Yoshiyuki Kimura (Osaka city)

Quiver varieties and quantum cluster algebras

Abstract: Cluster algebras were introduced by Fomin and Zelevinsky with an aim to provide concrete and combinatorial formalism for the study of Lusztig's dual canonical basis and total positivity. Inspired by a previous work of Nakajima, we consider a class of (equivariant) perverse sheaves on acyclic graded quiver varieties and study the Fourier-Sato-Deligne transform from representation theoretic point of view. In particular, we identify the corresponding quantum Grothendieck ring and the acyclic quantum cluster algebra and show that the set of quantum cluster monomials is contained in the "dual canonical basis". This talk is based on a joint work with Fan Qin(Paris 7/MSRI).

6 December (Thursday) Room I-552

10:30--12:00 Takuma Aihara (Bielefeld)

Some examples of silting quivers

Abstract: The notion of silting mutation was introduced in the joint work with Iyama. In this talk, we will give some examples of silting quivers and observe their shapes. In particular, we will show that the silting quiver of a Brauer tree algebra does not depend on the multiplicity of the Brauer tree.

21 November (Wednesday) Room I-409

13:00--14:30 Kota Yamaura

7 November (Wednesday) Room 1-452

13:00--14:30 Hiroyuki Minamoto (Nagoya)

Derived bi-duality via homotopy limit

Abstract: (This talk is based on a recent preprint available at arXiv math 1210.5582.) We show that a derived bi-duality dg-module is quasi-isomorphic to the homotopy limit of a certain tautological functor. This is a simple observation, which seems to be true in wider context. From the view point of derived Gabriel topology, this is a derived version of results of J. Lambek about localization and completion of ordinary rings. However the important point is that we can obtain a simple formula for the bi-duality modules only when we come to the derived world from the abelian world. We give applications. 1. we give a generalization and an intuitive proof of Efimov-Dwyer-Greenlees-Iyenger Theorem which asserts that the completion of commutative ring satisfying some conditions is obtained as a derived bi-commutator. (We can also prove Koszul duality for dg-algebras with Adams grading satisfying mild conditions. (A part of joint work with A. Takahashi.)) 2. We prove that every smashing localization of dg-category is obtained as a derived bi-commutator of some pure injective module. This is a derived version of the classical results in localization theory of ordinary rings. These applications shows that our formula together with the viewpoint that a derived bi-commutator is a completion in some sense, provide us a fundamental understanding of a derived bi-duality module. Since bi-duality is ubiquity in Mathematics, we can expect that our main result will have a lot of applications.

24 July (Tuesday) Room I-409

13:00--14:30 Colin Ingalls (New Brunswick)

Rationality of Brauer-Severi Varities of Sklyanin Algebras

Abstract: Iskovskih's conjecture states that a conic bundle over a surface is rational if and only if the surface has a pencil of rational curves which meet the discriminant in 3 or fewer points, (with one exceptional case). We generalize Iskovskih's proof that such conic bundles are rational, to the case of projective space bundles of higher dimension. The proof involves maximal orders and toric geometry. As a corollary we show that the Brauer-Severi variety of a Sklyanin algebra is rational.

9 July (Monday) Room A-328

13:00--14:30 Hiroyuki Minamoto (Nagoya)

Derived Gabriel topology, localization and completion of dg-algebras.

Abstract: Gabriel topology is a special class of linear topology on rings, which plays an important role in the theory of localization of (not necessary commutative) rings. Several evidences have suggested that there should be a corresponding notion for dg-algebras. In this talk I will introduce a notion of Gabriel topology on dg-algebras, derived Gabriel topology, and show its basic properties.

15:00--16:30 Izuru Mori (Shizuoka)

Points of a quantum projective space

Abstract: The notion of point of a noncommutative projective scheme has been an issue since the beginning of noncommutative algebraic geometry. Due to the recent work by Herschend, Iyama and Oppermann, points of a quantum projective space may be useful to study regular modules over an n-representation infinite algebra if they are suitably defined. In this survey talk, I will define a notion of point and provide an idea of this notion using various examples.

6--7 July

Shizuoka Seminar on Algebra

2 July (Monday) Room A-328

15:00--16:30 Erik Darpö

25 June (Monday) Room A-328

15:00--16:30 Laurent Demonet

1--3 May

Conference on resolution of singularities and the McKay correspondence

23 April (Monday) Room A-328

15:00--16:30 Hiruyuki Minamoto

2 April (Monday) Room A-328

15:00--16:30 Takahide Adachi

12--16 March

Representation Theory of Chevalley Groups and Related Topics

6 March (Tuesday) Room I-409

15:00--16:30 Hiroki Abe (Tsukuba)

Tilting modules arising from two-term tilting complexes

Abstract: At first, we give the summary of torsion theories induced by two-term tilting complexes, which is introduced by Hoshino, Kato and Miyachi. After that, we develop the torsion theories and show that every two-term tilting complex over an Artin algebra has a tilting module over a certain factor algebra as a homology group. Also, we determine the endomorphism algebra of such a homology group.

2--5 March

第17回代数学若手研究会, 第4回代数学若手会セミナー

1 March (Thursday) Room I-307

13:00--14:30 Ryo Takahashi (Shinshu)

Resolving subcategories of modules of finite projective dimension

Abstract: A lot of classification theorems of subcategories of a given category have been obtained so far in several areas of mathematics. In this talk, we concentrate on studying classification of resolving subcategories of modules of finite projective dimension over a commutative noetherian ring. This talk is based on joint work with Hailong Dao.

21 February (Tuesday) Room I-309

16:30--18:00 Ivan Marin (Paris)

Group theoretic properties of complex braid groups : homology and center

20 February (Monday) Room A-328

13:00--14:30 Research Seminar in Representation Theory

15:00--16:00 Kota Yamaura (Nagoya)

Realizing stable categories as derived categories I

16:30--17:30 Kota Yamaura (Nagoya)

Realizing stable categories as derived categories II

10 February (Friday) Room I-309

17:00--18:30 Zhaoyong Huang (Nanjing)

Proper resolutions and Gorenstein categories

Abstract: Let $\mathscr{A}$ be an abelian category and $\mathscr{C}$ an additive full subcategory of $\mathscr{A}$. We provide a method to construct a proper $\mathscr{C}$-resolution (resp. coproper $\mathscr{C}$-coresolution) of one term in a short exact sequence in $\mathscr{A}$ from that of the other two terms. By using these constructions, we answer affirmatively an open question on the stability of the Gorenstein category $\mathcal{G}(\mathscr{C})$ posed by Sather-Wagstaff, Sharif and White; and also prove that $\mathcal{G}(\mathscr{C})$ is closed under direct summands. In addition, we obtain some criteria for computing the $\mathscr{C}$-dimension and the $\mathcal{G}(\mathscr{C)}$-dimension of an object in $\mathscr{A}$.

27 January (Friday) Room I-309

15:00--16:30 Ryo Kanda (Nagoya)

Classifying Serre subcategories via atom spectrum

Abstract: In this talk, we introduce the atom spectrum of an abelian category as a topological space consisting of all the equivalence classes of monoform objects. In terms of the atom spectrum, we give a classification of Serre subcategories of an arbitrary noetherian abelian category.

17:00--18:30 Takahiko Furuya (Tokyo University of Science)

Hochschild cohomology of cluster-tilted algebras of Dynkin types $A_{n}$ and $D_{n}$

Abstract: In this talk, we show that all cluster-tilted algebras of Dynkin type $A_{n}$ are $(D,A)$-stacked monomial algebras (with $D=2$ and $A=1$), and then study their Hochschild cohomology rings modulo nilpotence. We also describe the ring structures of the Hochschild cohomology rings modulo nilpotence for several cluster-tilted algebras of Dynkin type $D_{n}$. This talk is based on joint work with Takao Hayami.

20--23 December, Osaka University

Quantum cluster algebras and related topics

15 December (Thursday) Room A-440,

16:30--18:00 Joseph Grant (Nagoya)

Higher preprojective algebras and Koszul duality

12 December (Monday) Room I-109,

15:00--16:30 Sarah Scherotzke (Bonn)

Linear recurrence relations for Cluster variables

Abstract: Using the additive categorification of the cluster algebra, we show that sequences of cluster variables satisfy linear recurrence relations if and only if the quiver is Dynkine or affine.

17:00--18:30 Erik Darpö (Nagoya)

On the representation rings of the dihedral 2-groups

9 December (Friday) Room I-309,

16:30--18:00 Sarah Scherotzke (Bonn)

The Integral Cluster Category

Abstract: In my talk, we will consider the question when orbit categories of triangulated categories are again triangulated. I will present some examples where this fails. In joint work with Bernhard Keller, we proved that the Cluster category defined over certain commutative rings are triangulated, we classify the Cluster-tilting objects and show that they are linked by mutation.

2--4 December, Shizuoka University

Shizuoka Seminar on Algebra

25 November (Friday) Room I-309,

16:30--18:00 Gustavo Jasso (Nagoya)

The growth of a cluster algebra of tubular type

22 October (Saturday) Room I-309,

11:00--12:00 Keiichiro Iima (Nara)

Torsionfreeness with respect to a semidualizing module

13:00--14:00 Michio Yoshiwaki (Osaka city)

Dimensions and covering techniques

14:20--15:20 Osamu Iyama (Nagoya)

Algebras with large dimension of derived categories

Abstract: We introduce a class of algebras with global dimension $n$ called $n$-representation tame algebras. We show that they have derived dimension $n$ and representation dimension at least $n+2$.

15:40--16:40 Tokuji Araya (Tokuyama)

Approximation of Auslander-Bridger type

17:00--18:00 Ryo Takahashi (Shinshu, Nebraska)

Dimensions of resolving subcategories

Abstract: Let R be a commutative Noetherian ring, and let mod R be the category of finitely generated R-modules. In this talk, we define the dimension of a resolving subcategory of mod R. Our main results are concerning its finiteness, which are also related to the celebrated theorem of Auslander-Huneke-Leuschke-Wiegand and a recent result of Oppermann-Stovicek. This talk is based on joint work with Hailong Dao.

14 October (Friday) Room I-309,

15:00--16:30 Steffen Oppermann (NTNU)

Cohomological symmetry in triangulated categories

20 September (Tuesday) Room I-309,

13:00--14:30 Dong Yang

Silting objects, simple-minded objects and (co-)t-structures

22--25 August

Summer school on commutative ring theory (note1, note2, note3, note4, note5 by Luo and Konishi)

19 August (Friday) Room I-309,

13:00--14:30 Zhaoyong Huang (Nanjing)

Invariant properties of representations under excellent extensions

12 August (Friday) Room I-309,

13:00--14:30 Zhaoyong Huang (Nanjing)

The construction of proper resolutions I

15:00--16:30 Zhaoyong Huang (Nanjing)

The construction of proper resolutions II

3 August (Wednesday) Room I-453,

13:00--14:30 Takuma Aihara (Chiba)

Dimensions of derived categories

22 July (Friday) Room I-309,

13:00--14:30 Benjamin Elias (Columbia)

Algebraic approaches to the Kazhdan-Lusztig conjecture

21 July (Thursday) Room I-309,

13:00--14:30 Benjamin Elias (Columbia)

Categorifications of the Hecke Algebra, and an Introduction to Soergel Bimodules

15:00--16:30 Benjamin Elias (Columbia)

Pretty Pictures for Soergel Bimodules

13 July (Wednesday) Room I-453,

13:00--14:30 Kota Yamaura (Nagoya)

Tilting theory for stable module categories over self-injective algebras

17 June (Friday) Room I-309,

13:00--14:30 Michio Yoshiwaki (Osaka city)

On derived dimension and stable dimension of finite-dimensional algebra

15:00--16:00 Osamu Iyama (Nagoya)

Representation dimension of n-representation infinite algebras

16 June (Thursday)

13:15--14:45, A-444, Osamu Iyama (Nagoya)

Tilting theory and Cohen-Macaulay modules

15:00--, I-452, Tomoki Nakanishi (Nagoya)

Classical and quantum dilogarithm identities

15 June (Wednesday) Room I-453,

10:30--12:00 Yoshiyuki Kimura (Kyoto)

Cluster structure on unipotent subgroup and its q-analogue (informal talk)

1 June (Wednesday) Room I-453,

13:00--14:30 Hyohe Miyachi (Nagoya)

How I used derived equivalences? (informal talk)

27--28 May, Shizuoka University

Shizuoka Seminar on Algebra

25 May (Wednesday) Room I-453,

13:00--14:30 Yuya Mizuno (Nagoya)

Gabriel's Theorem for cluster tilting

21--22 May, Nara National College of Technology

Yamato-Koriyama Seminar on Algebra

11 May (Wednesday) Room I-453,

16:30--18:00 Tomoki Nakanishi (Nagoya)

Introduction to Y-systems

Abstract: This is a rather informal and elementary introduction of what are called the Y-systems, which appear in several contexts of mathematics and mathematical physics. In particular, I try to explain its origin in the thermodynamic Bethe ansatz method for integrable models in 90's.

18 April (Monday) Room A-328,

16:30--18:00 Michael Wemyss (Edinburgh)

Derived equivalences and mutations of some geometric algebras in higher dimensions.

Abstract: I will explain some techniques to obtain derived equivalences between spaces with singularities, and I will explain how Q-factorial singularities fit into this picture. I will then discuss how this picture generalizes into higher dimensions, and give an analogue of the Bridgeland-King-Reid criterion in the algebraic setting. This criterion is on the base singularity, and so can easily be checked. Most of this work is joint with Iyama.

14--16 March

Workshop on non-commutative geometry and the McKay correspondence

11 March (Friday) Room I-307,

15:00-- Takuma Aihara (Chiba)

Silting objects and covariantly finite subcategories

17:00--18:30

Discussion with Claire Amiot (Strasbourg) on Cluster categories and derived equivalence

4 March (Friday) Room I-307,

16:30--18:00

Discussion with Claire Amiot (Strasbourg) on Cluster categories of quivers with potential

18 February (Friday) Room I-307,

14:45--16:15 Hiroyuki Minamoto (Kyoto)

Introduction to Fano algebra and it's construction

11 February (Friday) Room I-455,

10:30--11:30 Pierre-Guy Plamondon (Paris)

Generalized cluster categories I

13:00--14:00 Pierre-Guy Plamondon (Paris)

Generalized cluster categories II

8 February (Tuesday) Room I-455,

10:30--11:30 Pierre-Guy Plamondon (Paris)

Introduction to cluster algebras and categorification

9 December (Thursday) Room A-328,

13:00--14:30 Kentaro Nagao (Nagoya)

Donaldson-Thomas theory for triangulated surfaces

Abstract: In this talk, I will talk on a quiver (with a potential) associated to a triangulated surface. Compositions of cluster transformations give an action of the mapping class group on the torus associated to the quiver. Donaldson-Thomas theory for the quiver with the potential gives an intertwiner of the action.

14:45--16:15 Martin Herschend (Uppsala)

Construction of 2-representation-finite algebras

Abstract: This talk concerns joint work with Osamu Iyama (see arXiv: 0908.3510, 1006.1917). Let n be a positive integer. A finite dimensional algebra A is called n-representation finite if it has global dimension at most n and and there exists an n-cluster tilting A-module M. This concept is a natural analogue of representation finiteness from the view point of higher Auslander-Reiten theory. In particular 1-representation-finite algebras are precisely hereditary and representation-finite, which by Gabriel's Theorem are given by Dynkin quivers. In my talk I will treat the next natural case, i.e., 2-representation-finite algebras. I will focus on constructing 2-representation-finite algebras from pairs of Dynkin diagrams using various methods including tensor products, tilting and mutation.

preprojective algebraと量子群に関する勉強会

場所：名古屋大学多元数理科学研究科 A-358

（17日(水）午後のみ部屋は I-452 です）

期間：11月15日（月）から18日（木）

講演者：

伊山 修（名古屋大学）

木村 嘉之（京都大学）

斉藤 義久（東京大学）

プログラム： 月 火 水 木

10:30-11:45 伊山 斉藤 斉藤 木村

13:00-14:15 伊山 斉藤 斉藤 木村

14:45-16:00 斉藤 伊山 伊山 木村

16:30-17:45 斉藤 伊山 伊山 木村

概要：

(1) preprojective algebraの表現論・傾理論

(2) preprojective algebraの量子群への応用

に関する勉強会で、３人の講演者による、予備知識をなるべく 仮定しない入門的な連続講義が行われます。

(1)では、preprojective algebraの定義と基本性質からはじめて、 最近のBuan-Iyama-Reiten-Scott, Geiss-Leclerc-Schroerらによる、 preprojective algebra上の傾加群の構成と、それを用いた 2-Calabi-Yau三角圏とそのクラスター傾対象の構成が解説されます。

(2)では予備知識を仮定せず、量子群の定義と基本事項からはじめて、 preprojective algebraの表現論と量子群の関係に関する、Lusztig, Kashiwara-Saito, Geiss-Leclerc-Schroerらによる研究が、丁寧に 解説されます。

勉強会の目標は、preprojective algebraを応用する事により、 ある種の量子群と、近年活発に研究されているクラスター代数の関係を 明らかにする事です。(Geiss-Leclerc-Schroer, Kimura)

4 November (Thursday) Room A-328,

16:30--18:00 Joseph Grant (Nagoya)

Periodic algebras and derived equivalences

Abstract: I will present a way to construct self-equivalences of derived categories for symmetric algebras, generalising some work of Rouquier-Zimmermann in the representation theory of finite groups. This construction is also related to the geometric twists of Seidel-Thomas and Huybrechts-Thomas.

28 October (Thursday) Room A-328,

13:00--14:30 Laurent Demonet (Nagoya)

Categorification of some skew-symmetric and skew-symmetrizable cluster algebras by categories of representations of preprojective algebras II

Abstract: After recalling the definition of cluster algebras, we will show an explicit example of a categorification of a cluster algebra. We will explain how this type of categorification can be generalized. At the end, we will explain how to generalize this type of result to skew-symmetrizable cluster algebras.

21 October (Thursday) Room A-328,

14:45--16:15 Laurent Demonet (Nagoya)

Categorification of some skew-symmetric and skew-symmetrizable cluster algebras by categories of representations of preprojective algebras

Abstract: After recalling the definition of cluster algebras, we will show an explicit example of a categorification of a cluster algebra. We will explain how this type of categorification can be generalized. At the end, we will explain how to generalize this type of result to skew-symmetrizable cluster algebras.

18--22 October Room I-552,

Hiraku Nakajima (Kyoto)

量子アファイン環の有限次元表現とクラスター代数

Abstract: 量子アファイン環の有限次元表現については、箙多様体の理論により、 既約表現の指標公式が知られているが、テンソル積の構造は複雑である。 最近、特別な表現については、クラスター代数との関係が見つかり、 新たな知見が得られつつある。この現象を紹介することが目的である。 証明で、箙多様体の理論を用いる部分については、省略する予定である。

1 August (Sunday) Room I-552,

10:00--11:30 Steffen Oppermann (Trondheim)

Cluster equivalence and graded derived equivalence

13:00--14:30 Martin Herschend (Nagoya)

Selfinjective quivers with potential and 2-representation-finite algebras

15:00--16:30 Jeanne Scott (Chennai)

Surfaces, dimers, and Laurent expansions

Abstract: I will discuss a geometric instance of mutation (as defined by Fomin and Zelevinsky) for a bipartite graph embedded in surface and describe quantities connected to the graph's dimer partition function which are conserved under mutation. As application I will compute Laurent expansions anticipated in theory of cluster algebras for "twisted" Pl\"ucker coordinates of a Grassmannian.

17:00--18:30 Hugh Thomas (New Brunswick)

Higher Auslander algebras, cyclic polytopes, and analogues of tropical cluster algebras

31 July (Saturday) Room I-552,

10:00--11:30 Jeanne Scott (Chennai)

The Grassmannian's cluster algebra structure

Abstract: In this this talk I will explain how to endow the homogeneous coordinate ring of the Grassmannian with a cluster algebra structure. This will entail a discussion about a special class of planar diagrams which are used to construct cluster consisting entirely of Pl\"ucker coordinates. If time permits I will touch on the twist automorphism and its categorification by Geiss-Leclerc-Schr\"oer.

13:00--14:30 Hugh Thomas (New Brunswick)

Faithfulness of finite-type braid group actions on derived categories of preprojective algebras

15:00--16:30 Osamu Iyama (Nagoya)

Calabi-Yau algebras, higher preprojective algebras and cluster categories

Abstract: There is a strong relationship between Calabi-Yau algebras and n-representation-infinite algebras (Minamoto's Fano algebras) via the notion of higher preprojective algebras. As an application we realize the stable categories of certain Gorenstein quotient singularities as Amiot's cluster categories.

17:00--18:30 Erik Darpö (Oxford)

Left simple algebras

Abstract: Nowadays, several important classes of non-associative algebras, including Lie, Jordan, alternative, Malcev and quadratic algebras have been studied and reasonably understood. In spite of this, almost no theory exists for general, non-associative algebras. I shall present an approach leading to the description of all unital left simple algebras over an arbitrary field. An algebra is left simple if it is non-zero and has precisely two left ideals. If time so allows, I will also try to convince the audience that similar methods may be employed to study all simple algebras over a field.

20 April (Tuesday), Room I-552,

13:30--14:30 Ryo Takahashi (Shinshu University)

Classifying thick subcategories of derived categories

14:45--16:15 Tokuji Araya (Nara University of Education)

Strong test modules for projectivity and regular local rings

3--5 March

第15回代数学若手研究会

20 February, Room I-409,

10:30--11:30 Kentaro Wada (Nagoya University)

Cellular algebras and representation type

13:00--14:00 Kentaro Wada (Nagoya University)

The representation type of Ariki-Koike algebras and cyclotomic q-Schur algebras

14:30--15:30 Mitsuo Hoshino (Tsukuba University)

Derived equivalences of artin algebras I

16:00--17:00 Mitsuo Hoshino (Tsukuba University)

Derived equivalences of artin algebras II

19 February, Room I-409,

13:00--14:00 Michio Yoshiwaki (Osaka City University)

On selfinjective algebras of stable dimension zero (abstract)

14:30--15:30 Tomoki Nakanishi (Nagoya University)

Dilogarithm identities in conformal field theory and cluster algebras I

16:00--17:00 Tomoki Nakanishi (Nagoya University)

Dilogarithm identities in conformal field theory and cluster algebras II

19 December, Room I-309,

10:30--11:30 Yoshiyuki Kimura (Kyoto University)

Introduction to quiver varieties

13:00--14:00 Hiroyuki Nakaoka (Tokyo University)

Some homological constructions on a triangulated category II

14:30--15:30 Changchang Xi (Beijing Normal University)

Derived equivalences of Auslander-Yoneda algebras II

18 December, Room I-452,

14:00--15:00 Hiroyuki Nakaoka (Tokyo University)

Some homological constructions on a triangulated category I

15:15--16:15 Changchang Xi (Beijing Normal University)

Derived equivalences of Auslander-Yoneda algebras I

24--27 November, Osaka

Symposium on Commutative Ring Theory

23 November, Osaka Prefecture University

10:15--11:45, Igor Burban (Universität Bonn)

Cohen-Macaulay modules over minimally elliptic singularities and vector bundles on genus one curves

13:00--14:30, Yuji Yoshino (Okayama University)

Introduction to representation theory of Cohen-Macaulay modules

22 November, Osaka Prefecture University

13:00--14:30, Igor Burban (Universität Bonn)

Cohen-Macaulay modules over curve singularities and matrix problems

14:50--16:20, Osamu Iyama (Nagoya University)

Cluster tilting for hypersurface singularities

16:40--18:10, Kazushi Ueda (Osaka University)

Cohen-Macaulay modules over Gorenstein affine toric 3-folds and dimer models

19 November, Room I-307,

13:00--14:00, Steffen Oppermann (NTNU)

Dimension of triangulated categories via Koszul objects

14:20--15:20, Martin Herschend (Uppsala University)

Planar algebras and 2-representation-finite algebras I

15:40--16:40, Osamu Iyama (Nagoya University)

Planar algebras and 2-representation-finite algebras II

17:00--18:00, Steffen Oppermann (NTNU)

Tilting for d-representation finite algebras of type A

6--7 November, Shizuoka University

Shizuoka Seminar on Algebra

26--27 July

Post-workshop Seminar on "Algebraic Triangulated Categories and Related Topics"

22--24 July, Kyoto University

Algebraic Triangulated Categories and Related Topics

24--26 June, Osaka Prefecture University

Summer Seminar on Ring Theory

19--20 June, Shizuoka University

Shizuoka Seminar on Algebra

6 June (Saturday), Room A-454,

10:30-- Hiroyuki Minamoto (Kyoto University)

AS-regular algebras are coherent

13:00-- Tokuji Araya (Nara University of Education)

Perpendicular categories and configurations

14:30-- Takuma Aihara (Chiba University)

Silting mutation quivers for a self-injective algebra

16:00-- Osamu Iyama (Nagoya University)

Stable categories of (n+1)-preprojective algebras

5 June (Friday), Room A-454,

13:00-- Kota Yamaura (Nagoya University)

The classification of tilting modules over Harada algebras

14:45--

Free discussion

16:30-- Michael Wemyss (Nagoya University)

From triangulated categories to Reconstruction Algebras

9 May (Saturday)

10:30--12:00, Room I-307, Ryo Takahashi (Shinshu University)

Thick subcategories of stable categories of Cohen-Macaulay modules

13:30--15:00, Room I-307, Hiroyuki Minamoto (Kyoto University)

Ampleness of two-sided tilting complexes

15:30--17:00, Room I-307, Osamu Iyama (Nagoya University)

$n$-representation-finite algebras and fractionally Calabi-Yau algebras

8 May (Friday)

13:00--14:30, Room A-452,

Free discussion

14:45--16:15, Room I-203, Kiriko Kato (Osaka Prefecture University)

Introduction to DG algebras

16:30--18:00, Room A-454,

Free discussion

14 March (Saturday)

13:00--14:00 Takuma Aihara (Chiba University)

Mutation and Okuyama's method

14:30--16:00 Hiroki Abe (Tsukuba University)

Derived equivalences for triangular matrix rings

24 Feb. (Tuesday)

10:00--11:30, Room A-438, Osamu Iyama (Nagoya University)

$n$-repesentation-finite algebras of type A

13:00--14:30, Room A-438, Takuma Aihara (Chiba University)

Dimension of triangulated categories

15:00--16:30, Room A-438, Martin Herschend (Uppsala University)

Solution to the Clebsch-Gordan problem for string algebras

17:00--18:30, Room A-438, Michael Wemyss (Nagoya University)

Reconstruction algebras of type D

23 Feb. (Monday)

13:00--14:30, Room A-438, Yuhi Sekiya (Nagoya University)

G-Hilbert schemes and Groebner bases

Abstract: G-Hilbert schemes are introduced by Ito-Nakamura

to explain McKay correspondence.

So firstly, I will talk about Ito-Nakamura type McKay correspondence.

And next, for any abelian subgroup of GL(n,C),

I will construct G-Hilb by using Grobner bases via Nakamura's G-graphs.

15:00--16:30, Room A-438, Tokuji Araya (Nara University of Education)

Exceptional sequences of path algebras of type D

13 Feb. (Friday)

13:00--15:00, Room I-307, Kota Yamaura (Nagoya University)

Structure of AR-quiver of representation-finite self-injective algebras II

5 Feb. (Thursday)

13:00--14:00, Room I-455, Mitsuo Hoshino (Tsukuba University)

Families of derived equivalent algebras

4 Feb. (Wednesday)

10:30--12:00, Room A-438, Yukari Ito (Nagoya University)

Special McKay correspondence II

14:00--16:00, Room A-438, Osamu Iyama (Nagoya University)

Auslander-Reiten theory for Cohen-Macaulay modules

28 Jan. (Wednesday)

10:30--12:00, Room A-438, Yukari Ito (Nagoya University)

Special McKay correspondence

13:00--15:00, Room A-438, Kota Yamaura (Nagoya University)

Structure of AR-quiver of representation-finite self-injective algebras

16--17 Dec. Osaka Prefecture University

Osaka seminar on Algebra

5--6 Dec. Shizuoka University

Shizuoka Seminar on Algebra

26 Nov. (Wednesday)

10:30--12:00, Room A-438, Michael Wemyss (Bristol University)

GL(2) McKay correspondence

13:30--15:00, Room I-309, Alvaro Nolla de Celis (Warwick)

Dihedral groups and G-Hilb

20--21 Nov. RIMS

Representation theory of finite groups and algebras, and related topics

19 Nov. (Wednesday), Room A-438,

13:00--15:00 Kentaro Nagao (Kyoto University)

Mutations and noncommutative Donaldson-Thomas invariants

15 Nov. (Saturday), Room A-440,

10:30--12:00 Martin Herschend (Uppsala University)

On the Clebsch-Gordan problem for quiver representations III (note1, note2, note3)

14:00--15:30 Osamu Iyama (Nagoya University)

Cluster tilting in 2-Calabi-Yau categories

14 Nov. (Friday), Room A-440,

14:30--16:00 Oeyvind Solberg (Norwegian University of Technology and Science)

Introduction to support varieties II (note1, note2)

16:30--18:00 Kiriko Kato (Osaka Prefecture University)

On Auslander and Bass Categories (note)

12 Nov. (Wednesday), Room A-438,

13:00--15:00 Osamu Iyama (Nagoya University)

Special CM modules

17 Oct. (Friday), Room 552 in Bldg. Sci. 1,

13:00--14:30 Martin Herschend (Uppsala University)

On the Clebsch-Gordan problem for quiver representations II (note1, note2, note3)

15 Oct. (Wednesday), Room A-438,

13:00--15:00 Michael Wemyss (Bristol University)

Quiver representation and the moduli space III

6 Oct. (Monday), Room A-438,

16:30--18:00 Michael Wemyss (Bristol University)

Quiver representation and the moduli space II

4. Oct. (Saturday), Room 552 in Bldg. Sci. 1,

10:30--12:00 Osamu Iyama (Nagoya University)

Finiteness of representation dimension

14:00--15:30 Tokuji Araya (Nara University of Education)

Exceptional sequences of type A_n quivers

3 Oct. (Friday), Room 552 in Bldg. Sci. 1,

13:00--14:30 Oeyvind Solberg (Norwegian University of Technology and Science)

Introduction to support varieties (note1, note2)

15:00--16:30 Martin Herschend (Uppsala University)

On the Clebsch-Gordan problem for quiver representations (note1, note2, note3)

Abstract: On the category of representations of a given quiver we define a tensor

product point-wise and arrow-wise. This tensor product commutes with

direct sums so it is meaningful to pose the Clbesch-Gordan problem:

for any pair of indecomposable representations, decompose their tensor

product into a direct sum of indecomposables.

My lecture will be the first in a series concerned with this problem

and its solutions. I will introduce the problem and give an overview of

the known results. If time allows I will present the solution for the

loop quiver together with a proof.

1 Oct. (Wednesday), Room A-438,

13:00--15:00 Michael Wemyss (Bristol University)

Quiver representation and the moduli space I

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