20/07/2016, 12:30 — 13:10 — Anfiteatro Ea1, Torre Norte (Electricidade)
Yoshitsugu Takei, Kyoto University

Exact WKB Analysis for Continuous and Discrete Painlevé Equations

Generalizing the exact WKB analysis for one-dimensional Schrödinger equations established by Voros, Pham, Delabere and others, Aoki, Kawai and I developed the exact WKB analysis for continuous Painlevé equations and clarified, in particular, their Stokes geometry and connection formula. Later Iwaki discussed the wall-crossing formula for Painlevé equations as well. In this talk, after reviewing these previous works, I would like to talk about my recent research jointly done in part with N. Joshi (Sydney) on the exact WKB analysis for discrete Painlevé equations that are obtained from continuous Painlevé equations through the Bäcklund transformation. In the analysis of such discrete Painlevé equations both connection formula and wall-crossing formula for continuous Painlevé equations play the same role and appear as different kinds of connection formula.

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R-takei.pdf