## Cluster Algebras Seminar

# Horizontal and vertical mutation fans

## Kiyoshi Igusa (Brandeis University)

### Friday, February 9, 2018
3:00 pm

MONT 313

Semi-invariant pictures, (also called mutation fans or scattering diagrams), are diagrams dual to the Hasse diagram of finitely generated torsion classes for any hereditary algebra. We use it to visualize maximal green sequences.

This talk is about arrays of diagrams which can be used to visualize m-cluster mutations. A talk with the same title was given at the Chern Institute at Nankai Univerisity last July.

This updated version will have more pictures, less combinatorics and more representation theory. I will show several arrays of pictures labeled with m-clusters and t-structures and concentrate on explaining the definitions and constructions. Details can be found on my webpage:

http://people.brandeis.edu/~igusa/Papers/Lectures.htm