##### Department of Mathematics,

University of California San Diego

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### Symplectic Geometry Seminar

## Jeffrey M. Rabin

#### UCSD

## Supercurves and Duality (Part 2)

##### Abstract:

Supercurves are the simplest class of complex supermanifolds, â€œone-dimensionalâ€ in some sense and thus analogs of Riemann surfaces. I will describe a remarkable duality between pairs of supercurves that generalizes Serre duality for Riemann surfaces. Self-dual supercurves are precisely the â€œsuper Riemann surfacesâ€ introduced by physicists in connection with string theory. Iâ€™ll suggest connections between this duality and the classical duality between points and hyperplanes in projective space. No prior knowledge of supergeometry is required. (This is a continuation of the talk I gave earlier this quarter, and will begin with a review of that talk.)

Organizer: Alvaro Pelayo

### June 3, 2016

### 4:00 PM

### AP&M 6402

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