Vol. 9, No. 6, 2015

Download this article
Download this article For screen
For printing
Recent Issues

Volume 13
Issue 8, 1765–1981
Issue 7, 1509–1763
Issue 6, 1243–1507
Issue 5, 995–1242
Issue 4, 749–993
Issue 3, 531–747
Issue 2, 251–530
Issue 1, 1–249

Volume 12, 10 issues

Volume 11, 10 issues

Volume 10, 10 issues

Volume 9, 10 issues

Volume 8, 10 issues

Volume 7, 10 issues

Volume 6, 8 issues

Volume 5, 8 issues

Volume 4, 8 issues

Volume 3, 8 issues

Volume 2, 8 issues

Volume 1, 4 issues

The Journal
About the Journal
Editorial Board
Subscriptions
Editors' Interests
Submission Guidelines
Submission Form
Editorial Login
Ethics Statement
ISSN: 1944-7833 (e-only)
ISSN: 1937-0652 (print)
Author Index
To Appear
 
Other MSP Journals
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