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Title: Cluster automorphisms and quasi automorphisms
Speaker: Wen Chang (University of Connecticut and Shaanxi Normal )
Time: Friday, September 14, 2018 at 4:00 pm
Place: MONT 313Abstract: In this talk, I will report some results on the relation between the cluster automorphisms and the quasi automorphisms of a cluster algebra A. We proof that under some mild condition, satisfied for example by every skew-symmetric cluster algebra, the quasi-autmorphism group of A is isomorphic to a subgroup of the cluster automorphism group of A', and the two groups are isomorphic if A has principal or universal coefficients; here A' is the cluster algebra with trivial coefficients obtained from A by setting all frozen variables equal to the integer 1. We also compute the quasi-automorphism group of all finite type and all skew-symmetric affine type cluster algebras, and show in which types it is isomorphic to the cluster automorphism group of A'. This is joint work with Ralf Schiffler.
Title: The structure of free resolutions of length three and simple Lie algebras
Speaker: Jerzy Weyman
Time: Friday, September 21, 2018 at 3:00 pm
Place: MONT 313Abstract: I will discuss the construction of generic rings for finite free resolutions of length three. I will describe how the construction impacts the structure of perfect ideals of codimension three.
Title: no seminar
Time: Friday, September 28, 2018 at 3:00 pm
Place: MONT 313
Title: Cluster algebas and snake modules
Speaker: Bing Duan (Lanzhou University & University of Connecticut)
Time: Friday, October 5, 2018 at 3:00 pm
Place: MONT 313Abstract: In this talk, I will briefly recall quantum affine algebras and their representations. Motivated by Hernandez-Leclerc conjecture, we study a class of special modules--snake modules introduced by Mukhin-Young. We show that primes snake modules are some cluster variables in the cluster algebras constructed by Hernandez-Leclerc. Moreover, we obtained a series of exchange relations in the process of mutations. They form a system of equations which we called S-systems, which is a natural generalization of T-systems. This is joint with Jian-Rong Li, Yan-Feng Luo.
Title: On quantum cluster algebra from unpunctured surfaces: arbitrary coefficients and quantization.
Speaker: Min Huang (UniversitÃ© de Sherbrooke)
Time: Friday, October 19, 2018 at 3:00 pm
Place: MONT 313Abstract: In this talk, I will introduce a quantum Laurent expansion formula for quantum cluster algebras from unpunctured surfaces.
Organizer Ralf Schiffler