##### Department of Mathematics,

University of California San Diego

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### Algebraic Geometry Seminar

## Mitch Rothstein

#### UGA

## Ruled surfaces over hyperelliptic curves, the free associative algebra in two variables, and the Schwarzian Korteweg-DeVries equation.

##### Abstract:

If R is the free associative algebra in two variables, say over the complex numbers, then the ring of two by two matrices over R is also a quotient of R by a differential ideal I. Playing off the two descriptions of R/I leads naturally to the Schwarzian Korteweg-DeVries equation, in which a function of x evolves in time driven by the Schwarzian derivative. I will present this abstract setup and then explain how ruled surfaces (appropriately chosen) over hyperelliptic curves provide solutions of the equation. I will also describe several commuting flows.

Host: Elham Izadi

### October 28, 2016

### 2:00 PM

### AP&M 5829

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