Bi-annual Algebraic and Tropical Meetings of
Brown and YaLE

Fall 2014 @ Yale
November 20, 2014

The BATMOBYLE is a vehicle for bringing together the algebraic and tropical geometry groups of Brown and Yale for a biannual day of talks alternating between the two universities.

Jerzy Weyman

Jerzy Weyman

(University of Connecticut)

Semi-invariants of quivers, cluster algebras, and
the hive model

The saturation theorem for Littlewood-Richardson coefficients was a fashionable subject about a decade ago. There are two completely different proofs of the theorem: the original one by Knutson-Tao based on their hive model, and a proof based on quiver representations given by Harm Derksen and myself. So far there was no link between these two proofs.

Recently Jiarui Fei discovered a remarkable cluster algebra structure on the ring SI(Tn,n,n, β(n)) of semi-invariants of a triple flag quiver, whose weight spaces have dimensions that are Littlewood-Richardson coefficients. In proving his result he uses both the hive model and the quiver representations. It turns out that the link between the two approaches is the quiver with potential underlying the cluster algebra structure. The combinatorics of g-vectors for this quiver with potential turns out to be identical to the hive model.

In my talk I will explain the notions involved and basic ideas behind Jiarui Fei's proof.

11:00 - 12:00 Tropical Talk: Artin fans in tropical geometry
Martin Ulirsch (Brown University)
Watson Center
Lecture Room A60
12:00 - 02:00 Lunch Hockey Rink
Food trucks
02:00 - 03:00 Afternoon Talk: Local cohomology modules
Emily Witt (University of Utah)
Watson Center
Lecture Room A60
03:00 - 04:00 Tea Dunham Labs
Math Lounge
04:00 - 05:00 Plenary Talk: Semi-invariants of quivers
Jerzy Weyman (University of Connecticut)
Dunham Labs
Room 220

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Yale Organizers:
Asher Auel (Yale), Angie Cueto (Columbia), José González (Yale), Nathan Kaplan (Yale), and Sam Payne (Yale).

Brown Organizers:
Dan Abramovich (Brown), Melody Chan (Harvard), and Nathan Pflueger (Brown).