Seminar
| Parent Program: | |
|---|---|
| Location: | SLMath: Eisenbud Auditorium, Online/Virtual |
Noncommutative surfaces and difference equations
Many important special functions either satisfy nice differential or difference equations (hypergeometric functions) or
describe nice flows in families of such equations (Painlevé, Garnier, etc.). This leads to a pair of natural problems: (1) How can one classify equations with given singularities? (E.g., when is the equation unique?) (2) What are the natural isomorphisms between the resulting moduli spaces? It turns out that there is a natural (near) identification between these problems and certain natural geometric problems in noncommutative algebraic geometry. (E.g., rigid equations
correspond precisely to $-2$-curves!) I'll explain this connection to special functions, and sketch how (with that motivation and insight from the most general case) that led to new results on the geometry side, most notably noncommutative analogues of the standard isomorphisms in birational geometry and derived equivalences of deformed elliptic surfaces. [N.b., I will be giving some more detailed talks this March in the noncommutative projective schemes seminar]