新春代数表示论会议

主讲人:特邀报告人
时间: 星期五,星期六 9:00-16:50,2021 - 1 - 15 ~ 16
地点:腾讯会议

摘要

组织者:邓邦明,邱宇,肖杰,徐帆,张贺春,周宇,朱彬

报告人简介

1月15日

Tencent Meeting ID: 720 820 583

Password: 011516

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09:00-09:50常文 (陕西师大)
Title: A geometric realization of silting theory for gentle algebras
10:00-10:50陈小伍 (中科大)
Title: Folding via EI categories of Cartan type
11:00-11:50曹培根 (巴黎大学)
Title: The valuation pairing on an upper cluster algerba
14:00-14:50阮诗佺 (厦大)
Title: Group action on weighted projective lines
15:00-15:50方明  (中科院)
题目:Some results on representations of Schur algebras
16:00-16:50付昌建 (川大)
题目:A conjectural remark on c-vectors


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1月16日

Tencent Meeting ID: 536 966 540

Password: 011516

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09:00-09:50樊赵兵 (哈工程)
Title: Quantum Borcherds-Bozec algebras
10:00-10:50肖维 (深圳大学)
Title: JANTZEN COEFFICIENTS AND CATEGORY O^p
11:00-11:50覃帆 (上海交大)
Title: Bases for surface type cluster algebras


**********************Date: Jan 15th************************************* 

Speaker: Prof. Wen Chang 常文(Shaanxi Normal University) 

Title: A geometric realization of silting theory for gentle algebras

Abstract: A gentle algebra gives rise to a dissection of an oriented marked surface with boundary into polygons and the bounded derived category of the gentle algebra has a geometric interpretation in terms of this surface. I will talk about silting theory in the bounded derived category of a gentle algebra in terms of its underlying surface. In particular, I will give a geometric realization of silting mutations, silting reductions and braid group actions on exceptional sequences. This is based on joint work with Sibylle Schroll.

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Speaker: Prof. Xiaowu Chen 陈小伍(USTC) 

Title: Folding via EI categories of Cartan type

Abstract: The folding of root lattices is fundamental in Lie theory when getting from the simply-laced cases to the non-simply-laced cases. Following Gabriel and Geiss-Leclerc-Schroer, the root lattices are categorified by module categories. We obtain a categorification of the folding projection. The main tools are skew group categories and finite EI categories of Cartan type. This is joint with Ren Wang at USTC.

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Speaker: Prof. Peigen Cao 曹培根(Université de Paris) 

Title: The valuation pairing on an upper cluster algerba

Abstract: It is known that many (upper) cluster algebras are not unique factorization domains. In order to study the local factorization properties of upper cluster algebras, we introduce the valuation pairing on any upper cluster algebra U. To each pair (A,M) consisting of a cluster variable A and an element M in U, it associates the largest integer s (maybe infinity) such that M/A^s still belongs to U. Using the valuation pairing we prove that any full rank upper cluster algebra has the following locally unique factorization property: For each seed t of U, any non-zero element M can be uniquely factorized as M=N L, where N is a cluster monomial in t and L is an element in U not divisible by any cluster variable in t. We give many applications to d-vectors, F-polynomials, factoriality of upper cluster algebras and combinatorics of cluster Poisson variables. This is a joint work with Bernhard Keller and Fan Qin.

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Speaker: Prof. Shiquan Ruan 阮诗佺(Xiamen University) 

Title: Group action on weighted projective lines

Abstract: Weighted projective lines are introduced by Geigle and Lenzing, which provide a geometric approach to canonical algebras in the sense of Ringel. It is well known that weighted projective lines are related to smooth projective curves via equivariantization.

In this talk, we will see how to use the viewpoint of group actions to relate weighted projective lines with compact Riemann surfaces or weighted projective curves. If time allowed, some application on tilting theory will be formulated.

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Speaker: Prof. Ming Fang 方明(CAS) 

Title: Some results on representations of Schur algebras

Abstract: Schur-Weyl duality between the (classical) Schur algebra S(n,r) and the group algebra of the symmetric group kS_r has been extensively studied mainly in the stable case n\geq r. In this talk, we extend certain results to the unstable case n

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Speaker: Prof. Changjian Fu 付昌建(Sichuan University) 

Title:  A conjectural remark on c-vectors

Abstract: Several classes of integer vectors have played important roles in the theory of cluster algebras. In this talk, I will focus on the c-vectors, which were introduced by Fomin and Zelevinsky to parametrize coefficients. 

Surprisingly, according to the work of Gross-Hacking-Keel-Knotsevich, the c-vectors can be used to parametrize clusters. I will report a conjectural observation on c-vectors basing on the sign-coherence of c-vectors. 

Acyclic skew-symmetric cluster algebras  and the Markov cluster algebra provide evidences for this conjectural observation. This is based on joint work with S. Geng and P. Liu. 


****************************Date: Jan 16th*******************************

Speaker: Prof. Zhaobing Fan 樊赵兵(Harbin Engineering University) 

Title: Quantum Borcherds-Bozec algebras

Abstract: In this talk, I will introduce quantum Borcherds-Bozec algebras and their recent developments, including classical limit , representations and geometric realization etc.

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Speaker: Prof. Wei Xiao 肖维(Shenzhen University) 

Title: JANTZEN COEFFICIENTS AND CATEGORY O^p

Abstract: In this talk, we discuss the Jantzen coefficients of generalized Verma modules. They come from the Jantzens simplicity criteria for generalized Verma modules and have a deep relation with the structure of O^p . We develop a reduction process to compute those coefficients. In particular, we give those coefficients for classical Lie algebras.

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Speaker: Prof.Fan Qin 覃帆(Shanghai Jiao Tong University) 

Title: Bases for surface type cluster algebras

Abstract: We review bases for cluster algebras arising from surfaces, which are realized as homotopy classes of curves. We explain a recent progress which identifies the bracelets with the theta basis elements.

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