Geometry, Combinatorics, and Integrable Systems  

  Spring 2019

Time: Thursdays 3-4pm
Location: 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)  
q-analogues of representation-theoretic 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 
 
( )  



Abstracts


(Baker): In tropical geometry, linear spaces are in 1-1 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, q-analogues of continuous processes from mathematical physics (log-gas systems, eigenvalues of random matrices, etc). It is conjectured that the probability measures in question are related to the representation theory of quantum groups.


(Wormleighton):


(Singh):


(Karp):


(Liu):


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Past Seminars

Autumn 2018

Spring 2018

Autumn 2017

Spring 2017