Bi-annual Algebraic and Tropical Meetings of
Brown and YaLE

Fall 2015 @ Yale
December 10, 2015

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.

June Huh

June Huh

Hodge theory for combinatorial geometries

A conjecture of Read predicts that the coefficients of the chromatic polynomial of any graph form a log-concave sequence. A related conjecture of Welsh predicts that the number of linearly independent subsets of varying sizes form a log-concave sequence for any configuration of vectors in a vector space. All known proofs use Hodge theory for projective algebraic varieties, and the more general conjecture of Heron, Rota, and Welsh for possibly ‘nonrealizable’ matroids is still open. In this talk, I will argue that two main results of Hodge theory, the Hard Lefschetz theorem and the Hodge-Riemann relations, continue to hold in a realm that goes beyond that of Kahler geometry. This cohomology theory gives strong restrictions on numerical invariants of tropical varieties, and in particular those conjectured by Heron, Rota, and Welsh.

Joint work with Karim Adiprasito and Eric Katz.

Printable BATMOBYLE Poster

11:00 - 12:00 Morning Talk: GIT semistability of Hilbert points of Milnor algebras
Maksym Fedorchuk (Boston College)
Room WLH 116
12:00 - 02:00 Lunch Hockey Rink
02:00 - 03:00 Afternoon Talk: Characteristic Polynomials of Hyperplane Arrangements
Tif Shen (Yale)
Room WTS A60
03:00 - 04:00 Tea Common room DL
04:00 - 05:00 Plenary Talk: Hodge theory for combinatorial geometries
June Huh (IAS)
Room WTS A60

Local area maps:   PNG   PDF   WEB
Parking: meters on Hillhouse Ave ($1.50/hour, 2 hour max) or lot listed on map ($2/hour, free after 4 pm)

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

Yale Organizers:
Asher Auel (Yale), Angie Cueto (Ohio State), José González (Yale), and Sam Payne (Yale).

Previous BATMOBYLEs: Fall 2014, Spring 2015