Vol. 9, No. 6, 2015

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Noncommutative geometry and Painlevé equations

Andrei Okounkov and Eric Rains

Vol. 9 (2015), No. 6, 1363–1400
Abstract

We construct the elliptic Painlevé equation and its higher dimensional analogs as the action of line bundles on 1-dimensional sheaves on noncommutative surfaces.

Keywords
noncommutative geometry, Painlevé equations
Mathematical Subject Classification 2010
Primary: 14A22
Milestones
Received: 15 May 2014
Revised: 2 April 2015
Accepted: 17 May 2015
Published: 7 September 2015
Authors
Andrei Okounkov
Columbia University
Department of Mathematics
2990 Broadway
New York, NY 10027
United States
Eric Rains
California Institute of Technology
Division of Physics, Mathematics and Astronomy
1200 East California Boulevard
Pasadena, CA 91125
United States