会议名称：2018年代数表示论学术研讨会

会议时间：2018年5月5日；

会议地点：海韵园实验楼105报告厅

报告安排：

学术报告题目与摘要：

1. 报告人：陈小伍，中国科学技术大学

题目：Equivariantization and weighted projective lines

摘要：We will recall that finite group actions and the equivariantization arise naturally from weighted projective lines. We will concentrate on the domestic cases, where the results are very classical.

2. 报告人：韩喆，河南大学

题目：Derived equivalences via HRS tilting

摘要：Given an abelian category with a torsion pair, there is a corresponding t-structure in the bounded derived category of this category. Happel, Reiten and Smalo defined a new abelian category, called HRS tilt, which is the heart of the t-structure. In this talk, I will give some criterion for these two abelian categories being derived equivalence.  Finally, I will show how to apply these criterion to get concrete derived equivalences. This is a joint work with Chen Xiaowu and Zhou Yu.

3. 报告人：章超，贵州大学

题目：On the representation type of subcategories of derived categories

摘要：In this talk, we mainly introduce some results on the representation type of subcategories of the bounded derived category. We define the representation type and some homological invariants including cohomological length, width, range for subcategories. Moreover, for a finite-dimensional algebra $A$ of finite global dimension, we establish the first Brauer-Thrall type theorem of certain contravariantly finite subcategories $\mathcal{C}$ of $D^b(A)$, that is, $\mathcal{C}$ is of finite type if and only if its cohomological range is finite.

4. 报告人：张孝金，南京信息工程大学

题目：Tilting modules over Auslander-Gorenstein Algebras

摘要：For a finite dimensional algebra A and a non-negative integer n, we characterize

when the set tiltA of additive equivalence classes of tilting modules with projective dimension at most n has a minimal (or equivalently, minimum) element. This generalize results of Happel-Unger.  Moreover, for an n-Gorenstein algebra A with n >= 1, we construct a minimal element in tiltA. As a result, we give equivalent conditions for a k-Gorenstein algebra to be Iwanaga-Gorenstein. Moreover, for an 1-Gorenstein algebra A and its factor algebra B = A/(e), we show that there is a bijection between tiltA and the set st-tiltB of isomorphism classes of basic support tau-tilting B-modules, where e is an idempotent such that eA is the additive generator of projective-injective A-modules. This is a joint work with Osamu Iyama.

5. 报告人：张海诚，南京师范大学

题目：Hall algebras of 1-cyclic perfect complexes and PBW-bases

摘要：Letbe the path algebra of a Dynkin quiver Q over a finite field, and letbe the category of 1-cyclic complexes of projective-modules. In this talk, we will give a PBW-basis and a minimal set of generators of the Hall algebra of. Using this PBW-basis, we will prove the degenerate Hall algebra ofis the universal enveloping algebra of the Lie algebra spanned by all indecomposable objects. Moreover, we will give a relation between the degenerate Hall algebra ofand that of. 

6. 报告人：耿圣飞，四川大学

题目：Modules over cluster-tilted algebras of tubular type

摘要：Let $\Gamma$ be a cluster tilted algebra of tubular type. In this talk, we will give a classification of rigid, $\tau$-rigid and Schurian $\Gamma$-modules. Then, when $\Gamma$ is  of type $(2,4,4)$,$(3,3,3)$ or $(2,3,6)$, we will show that its indecomposable $\tau$-rigid modules  are determined by their dimension vectors. This is a joint work with Changjian Fu.

7. 报告人：刘品，西南交通大学

题目： On $\tau$-tilting theory  

摘要：Mutation is an ingredient in the construction of Fomin-Zelevinsky's cluster algebras. It deals with replacing an element in the free generating set (x_1, x_2, …, x_n) of the rational function field Q(x_1, x_2, …, x_n) by another element. In module categories for finite dimensional algebras, which is called support $\tau$-tilting modules have a similar behavior. They are built up to by n parts, and there is an operation of mutation.  In this talk, we introduce some results on $\tau$-tilting theory and their links with cluster algebras.