Bi-annual Algebraic and Tropical
Meetings of
Brown and YaLE
(BATMOBYLE)
Fall 2014 @ Yale
November 20, 2014
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 (University of Connecticut) BATMOBYLE POSTER |
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 |
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).