1

Title：模型范畴与Frobenius范畴

Speaker：Pu Zhang, Shanghai Jiaotong University 

Date：8:30am-9:10am 2021-5-15（Saturday）.

2

Title：On connected components of skew group algebras

Abstract：Let $A$ be a basic connected finite dimensional associative algebra over an algebraically closed field $k$ and $G$ be a cyclic group. By Reiten -Riedtmann, there is the quiver $Q_G$ with relations $ ho_G$ such that the skew group algebras $A[G]$ is Marita equivalent to the quotient algebra of path algebra $kQ_G$ modulo by ideal $( ho_G)$. Generally, the quiver $Q_G$ is not connected any more. Motivated by Guo's work, we show a method to determine the number of connect components of $Q_G$. Meanwhile, we introduction of weight for underlying quiver of $A$ such that $A$ is $G$-graded and determine the connect components of smash product $A$#$G$. This is joint work with JM Chen and Q Dong.

Speaker：Yanan Lin, Xiamen University 

Date：9:15am-9:55am 2021-5-15（Saturday）.

3

Title：Homological Dimensions Relative to Preresolving Subcategories II

Abstract：Let $mathscr{A}$ be an abelian category having enough projective and injective objects, and let $mathscr{T}$ be an additive subcategory of $mathscr{A}$ closed under direct summands. A known assertion is that in a short exact sequence in $mathscr{A}$, the $mathscr{T}$-projective (respectively, $mathscr{T}$-injective) dimensions of any two terms can sometimes induce an upper bound of that of the third term by using the same comparison expressions. We show that if $mathscr{T}$ contains all projective (respectively, injective) objects of $mathscr{A}$, then the above assertion holds true if and only if $mathscr{T}$ is resolving (respectively, coresolving). As applications, we get that a left and right Noetherian ring $R$ is $n$-Gorenstein if and only if the Gorenstein projective (respectively, injective, flat) dimension of any left $R$-module is at most $n$. In addition, in several cases, for a subcategory $mathscr{C}$ of $mathscr{T}$, we show that the finitistic $mathscr{C}$-projective and $mathscr{T}$-projective dimensions of $mathscr{A}$ are identical.

Speaker：Zhaoyong Huang, Nanjing University 

Date：10:20am-11:00am 2021-5-15（Saturday）.

4

Title：Sheaves over categories with atomic topology and discrete representations of topological groups

Abstract：It is well known that the category of discrete G-sets of a topological group G is equivalent to the category of sheaves of sets over a certain orbit category equipped with atomic topology. This result establishes an important relation between representation theory of topological groups, representation theory of categories, and topos theory. In this talk, I will characterize sheaves of modules over arbitrary categories equipped with atomic topology, sheafification functor, and sheaf cohomology in terms of notions in representation theory of categories, and obtain equivalences between sheaf categories and Serre quotients of representation categories. Furthermore, via applying the Nakayama functor, we classify simple discrete representations of a few important topological groups such as infinite symmetric groups, infinite general linear groups over a finite field, the automorphism group of the poset of rational numbers.This work is joint with Zhenxing Di (Northwest Normal University), Li Liang (Lanzhou Jiaotong University), and Fei, Xu (Shantou University).

Speaker：Liping Li, Hunan Normal University 

Date：11:05am-11:45am 2021-5-15（Saturday）.

5

Title：Recollements associated to cotorsion pairs over upper triangular matrix rings

Abstract：Let $A$, $B$ be two rings and $T=left(egin{smallmatrix}  A & M \  0 & B \end{smallmatrix} ight)$ with $M$ an $A$-$B$-bimodule. Suppose that we are given two complete hereditary cotorsion pairs $(mathcal{A}_{A},mathcal{B}_{A})$ and $(mathcal{C}_{B},mathcal{D}_{B})$ in $A$-Mod and $B$-Mod respectively. We define two cotorsion pairs $(Phi(mathcal{A}_{A},mathcal{C}_{B}), mathrm{Rep}(mathcal{B}_{A},mathcal{D}_{B}))$ and $(mathrm{Rep}(mathcal{A}_{A},mathcal{C}_{B}),Psi(mathcal{B}_{A},mathcal{D}_{B}))$ in $T$-Mod and show that both of these cotorsion pairs are complete and hereditary.

If we are given two cofibrantly generated model structures $mathcal{M}_{A}$ and $mathcal{M}_{B}$ on $A$-Mod and $B$-Mod respectively, then using the result above, we investigate when there exists a cofibrantly generated model structure $mathcal{M}_{T}$ on $T$-Mod and a recollement of $mathrm{Ho}(mathcal{M}_{T})$ relative to $mathrm{Ho}(mathcal{M}_{A})$ and $mathrm{Ho}(mathcal{M}_{B})$. Finally, some applications are given in Gorenstein homological algebra. This talk is a report on joint work with R.M. Zhu and Y.Y. Peng.

Speaker：Nanqing Ding, Nanjing University 

Date：14:30pm-15:10pm 2021-5-15（Saturday）.

Tencent Meeting ID： 410 899 152

6

Title：关于Pr"{u}fer环的小finitistic维数

Speaker：Fanggui Wang, Sichuan Normal University 

Date：15:15pm-15:55pm 2021-5-15（Saturday）.

7

Title：Syzygy properties under recollements of derived categories

Abstract：We study when some syzygy properties are stable under recollements of derived categories.

Speaker：Jiaqun Wei, Nanjing University 

Date：16:15pm-16:55pm 2021-5-15（Saturday）.

8

Title：Homological properties of some noncommutative products of Algebras

Abstract：Algebras are supposed to describe ``spaces" as functions. As tensor products of algebras corresponding to the usual products for ``spaces", some noncommutative constructions of algebras are viewed as the functions of the imaginary noncommutative products of ``spaces".  We try to study the regularity or Gorenstein property of some noncommutative constructions of algebras. In the talk I will start from basic definitions and some general ideas, then I will introduce some related results obtained recently.

Speaker：Quanshui Wu, Fudan University 

Date：17:00pm-17:40pm 2021-5-15（Saturday）.

Tencent Meeting ID： 410 899 152

Organizer：School of Mathematical Science

Students and teachers are welcome.