Broken lines and theta functions

event Monday, February 17, 2020
access_time 5:30 PM
room PHSC 1105
info Pizza will be served after the talk.

Abstract: Cluster algebras were introduced in 2001 to axiomatize and generalize certain nice bases for important algebras. While they succeeded spectacularly in generalizing the "algebra" part, numerous attempts to generalize the "basis" part only succeeded in limited generality...that is, until 2014, when Gross-Hacking-Keel-Kontsevich introduced the "theta basis". These theta functions are constructed by counting certain piecewise linear objects called "broken lines". While this construction is fairly straightforward to state, computing theta functions remains a daunting problem outside the smallest examples. Time permitting, I will discuss the string-theoretic origins of this counting problem, and some tantalyzing open problems in the subject.


For more information on this event, please contact Paul Regier.