Algebra Seminar

In 1990, V. Drinfeld introduced the Grothendieck-Teichmueller group $GT$. This group receives a homomorphism from the absolute Galois group $G_Q$ of rational numbers, and this homomorphism is injective due to Belyi's theorem. In his 1990 ICM talk, Y. Ihara posed a very hard question about the surjectivity of this homomorphism from $G_Q$ to $GT$. In my talk, I will introduce the groupoid of $GT$-shadows and show how this groupoid is related to the group $GT$. I will formulate a version of Ihara's question for $GT$-shadows and describe a family of objects of the groupoid for which this question has a positive answer. My talk is loosely based on the joint paper with I. Bortnovskyi, B. Holikov and V. Pashkovskyi.

Yelena Mandelshtam, IAS Princeton

The Kadomtsev-Petviashvili (KP) equation is a partial differential equation whose study yields fascinating connections between integrable systems, algebraic geometry, and combinatorics. In this talk I will describe some of the various approaches to connecting KP solutions to algebraic objects such as algebraic curves (due to Krichever) and the positive Grassmannian (due to Sato and later Kodama-Williams). I will then discuss recent and ongoing work to build bridges between these approaches.