University of Connecticut

Cluster Algebras Seminar

 

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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
Speaker:
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 (Universite 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.

Title: A geometric realization of representations of posets of width 2 as diagonals of polygons
Speaker: Robinson Julian Serna Vanegas (Universidad Nacional de Colombia)
Time: Friday, October 26, 2018 at 3:00 pm
Place: MONT 313

Title: Unistructurality of cluster algebras
Speaker: Ralf Schiffler
Time: Friday, November 2, 2018 at 3:00 pm
Place: MONT 313Abstract: The unistructurality conjecture says the set of cluster variables in a cluster algebra determines the clusters. I will report on a proof of this conjecture by Cao and Li.

Title: Green Conjecture for general canonical curves
Speaker: Jerzy Weyman
Time: Friday, November 9, 2018 at 3:00 pm
Place: MONT 313Abstract: Green conjecture predicts the shape of free resolution of the coordinate ring of curve of genus g embedded by canonical divisor.In the case of general curve of genus g the conjecture was proved by Claire Voisin in two breakthrough papers about fifteen years ago. I will discuss a new proof of this result, based on joint work with Marian Aprodu, Gabi Farkas, Stefan Papadima and Claudiu Raicu.

Title: no seminar
Speaker:
Time: Friday, November 23, 2018 at 3:00 pm
Place: MONT 313

Title: Joint spectra and representation theory
Speaker: Alex Tchernev (SUNY Albany)
Time: Friday, November 30, 2018 at 3:00 pm
Place: MONT 313Abstract: We will discuss the notion of joint spectrum from operator theory, and how it can be applied to representation theory. We will pose some general open problems that go back to founding work of Frobenius, and present solutions for special classes of Coxeter groups. We will conclude with more related open problems.


Organizer Ralf Schiffler