Department Colloquium: Shell games with 2x2 matrices

Abstract: At the beginning of the 20th century, Paul Painlevé claimed that the generic solutions to his eponymous differential equations "could not be written in terms of classical functions." While his argument was imprecise, later work by Umemura and others made it rigorous, crucially relying on classifications of algebraic solutions to the Painlevé equations. This classification was completed only in 2014, by difficult computer calculations of Lisovyy and Tykhyy. I'll explain the history of this question, how it boils down to explicit linear algebra with 2x2 matrices, and recent work with Lam and Landesman extending the classification under mild hypotheses to a much more general situation.

Hosts: Wanlin Li, Matt Kerr

Reception time and location: 3:30- 3:55 pm in Room 200 (the Lounge)