Geometry, Combinatorics, and Integrable SystemsSpring 2019Time: Thursdays 34pmLocation: MA 317 

January 17
Thurs, 3pm CH 240  Matt Baker
(Georgia Tech) 
Hyperfields, Ordered Blueprints, and Moduli Spaces of Matroids 
January 24
Thurs, 3pm  TBA
( ) 

February 7
Thurs, 3pm  Cesar Cuenca
(MIT) 
qanalogues of representationtheoretic measures 
February 14
Thurs, 3pm 
( ) 

February 21
Thurs, 3pm 
( ) 

February 28
Thurs, 3pm  Ben Wormleighton
(Berkeley) 
TBA 
March 7
Thurs, 3pm  Rahul Singh
(Northeastern) 

March 21
Thurs, 3pm 
( ) 

March 28
Thurs, 3pm  Steven Karp
(Michigan) 

April 4
Thurs, 3pm  Fu Liu
(UC Davis) 

April 11
Thurs, 3pm 
( ) 

April 18
Thurs, 3pm 
( ) 
(Baker): In tropical geometry, linear spaces are in 11 correspondence with "valuated matroids". I will discuss a unified theory which views linear subspaces, ordinary matroids, and valuated matroids as special cases of "matroids over hyperfields". I will then discuss the geometric construction of a "universal Grassmannian" which, via base change, yields (fine) moduli spaces for matroids over hyperfields. The universal Grassmannian is constructed using Oliver Lorscheid's theory of ordered blueprints, which is also useful for understanding the relationship between Berkovich spaces, skeletons, and tropicalizations. This is joint work with Nathan Bowler and Oliver Lorscheid.
(Cuenca): I will survey results from my joint work with Grigori Olshanski, about a remarkable family of probability measures, arising from the theory of orthogonal polynomials. The measures lead to discrete, qanalogues of continuous processes from mathematical physics (loggas systems, eigenvalues of random matrices, etc). It is conjectured that the probability measures in question are related to the representation theory of quantum groups.