26 July (Sunday), Room I-307

11:00-12:00 Hiroyuki Minamoto (Kyoto University)

Ampleness of two-sided tilting complexes and Fano algebras

In this talk we introduce a notion of ampleness for two-sided tilting

complexes over finite dimensional algebras of finite global dimension,

and show its basic properties, which justify the name "ampleness".

We define Fano algebras by the anti-ampleness of shifted Serre functor.

Fano algebras have remarkable properties. Some classes of algebras

studied before are Fano. There is good supply of new Fano algebras.

We can construct Fano algebras from AS-regular algebras (without

finiteness of Gelfand-Kirillov dimension). As an application, we prove

that AS-regular algebras are graded coherent.

13:30--14:30 David Ploog (Berlin)

Comparing categorical lifts of certain root lattices

Abstract: This is a report about work in progress (with Chris Brav). We

present a setting in which full exceptional collections and spherical

collections can be compared. This allows to relate two different ways in

which the ADE root lattices (coming from ADE singularities) can be lifted

to triangulated categories: via graded matrix factorisations (following

Kajiura, Saito, Takahashi, Ueda) or via sheaves on the resolution.

15:00--16:00 Atsushi Takahashi (Osaka University)

TBA

16:30--17:30 Bernhard Keller (Paris 7)

Derived equivalences of deformed Calabi-Yau completions

Abstract: We recall the construction of deformed Calabi-Yau completions and the

Ginzburg algebra. We use this framework to give a conceptual proof of the derived

invariance theorem for Ginzburg algebras, which was first obtained in joint work

with Dong Yang.

27 July (Monday)

10:00--11:00, Room I-307, Martin Herschend (Nagoya University)

The Clebsch-Gordan problem for string algebras

String algebras are a class of tame algebras whose indecomposable finite

dimensional modules are classified by strings and bands. They originate from

the classification of Harish-Chandra modules over the Lorentz group by

Gelfand and Ponomarev. By definition, any string algebra is defined as the

path algebra of a quiver subject to certain monomial relations. Hence its

module category is equipped with a tensor product defined point-wise and

arrow-wise in terms of the underlying quiver. This leads to the following

problem: given two indecomposable modules over a string algebra, decompose

their tensor product into a direct sum of indecomposables. In my talk I will

present the solution to this problem for all string algebras. Moreover, I

will describe the corresponding representation rings.

11:30--12:30, Room I-307, Yoshiyuki Kimura (Kyoto University)

Affine quivers and the crystal $B(\infty)$

This talk is based on a joint work with Hiraku Nakajima.

We study a relationship between the two geometric construction of the

crystal $B(\infty)$. One is the Lusztig's canonical base which is described

as simple perverse sheaves and another is the Lagrangian construction by

using Lusztig's quiver varieties due to M.Kashiwara and Y.Saito.

More precisely, we give an estimate of characteristic variety of canonical

base in general affine quiver cases (these simple perverse sheaves were

descrived by G.Lusztig (Y.Li and Z.Lin) in terms of Dlab-Ringel's theory

of affine quivers). In particular, we introduce a partial order on

$B(\infty)$ which is motivated by the order on (affine) PBW base defined by

Beck-Chari-Pressley and Beck-Nakajima.

13:30--14:30, Room I-307, Tomoki Nakanishi (Nagoya University)

T-systems, Y-systems, and cluster algebras

The T-systems and Y-systems are systems of relations originated from

the study of integrable quantum systems in 90's and relevant to the

representation theory of the quantum groups. Initiated by

Fomin-Zelevinsky and Keller, the periodicity phenomena of the systems

recently attract attention from the point of views of cluster algebras

and cluster categories. In this talk I will given an introductory

review of what the T- and Y-systems are and how they are related to

cluster algebras.

15:00--16:00, Room I-552, Matthew Clarke (University of Cambridge)

Bismash products and group algebras

We will begin by introducing Hopf algebras together with the easiest

examples, group algebras and their duals, before giving a

rough overview of the classification attempt for finite-dimensional

complex semisimple Hopf algebras. We will then go on to describe more

interesting constructions, bicrossed and bismash products,

which can be defined using any finite group with a given factorisation into

trivially intersecting subgroups, and explain a way of studying

bismash products using character theory. We will examine a particular

family of bismash products arising from factorisations of the projective

general linear group over a finite field together with their

comultiplication twistings, which have been shown to be examples of so-called

non-trivial Hopf algebras. We also consider what happens if the factorised

group we started is a) a semidirect product, b) a Frobenius group.

16:30--17:30, Room I-552, Nanhua Xi (Chinese Academy of Sciences)

A new proof for classification of irreducible modules of a Hecke algebra of type $ A_{n-1}$

The classification of irreducible modules of a Hecke algebra of

type $A\_{n-1}$ was obtained by Dipper and James in 1986. In this talk

I will give a new proof for the classification. Essentially the idea

is due to Dipper and James, Murphy, but we use Kazhdan-Lusztig

theory and an affine Hecke algebra of type $\tilde A_{n-1}$ to prove

this result by a direct calculation.