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Deformation Theory Seminar

Monday, October 18, 2021 - 2:00pm

Alfredo Najera

UNAM- Oaxaca


University of Pennsylvania


same zoom link as recently

 The purpose of this talk is to explain a fruitful  
interaction between ideas/constructions coming form the theory of  
cluster algebras, representation theory of associative algebras and  
deformation theory.
The representation theory of associative algebras is a well developed  
branch of mathematics that has been very active for nearly 50 years.  
The theory of cluster algebras is much younger, it was initiated by  
Fomin and Zelevinsky in 2001.  Various important developments in these  
theories have emerged in the last 15 years thanks to the deep relation  
that exists in between them. After an introduction to this circle of  
ideas I will recall the construction of a simplicial complex $  
\Delta(A)$ -- the \tau-tilting complex-- associated to a finite  
dimensional associative algebra $A$. Then I will report on one aspect  
of work-in-progress with Nathan Ilten and Hipólito Treffinger. We show  
that if $ \Delta(A)$ is a cluster complex of finite type then the  
associated cluster algebra with universal coefficients is equal to a  
canonically identified subfamily of the semiuniversal family for the  
Stanley-Reisner ring of $ \Delta(A)$. Time permitting I will elaborate  
on some aspects of the "non-cluster" case (namely,  when $\Delta(A)$  
is not a cluster complex).