In this talk I will first review some aspects of Painlevé equations and their connection to four dimensional gauge theory; then I will generalise this construction to q-difference Painlevé equations and topological string theory. I will show that their tau-functions are Fredholm determinant of operators associated to quantum mirror curves on a corresponding geometry. As a consequence, the zeroes of these tau-functions compute the exact spectrum of the associated quantum integrable systems. I will focus on the particular example of q-Painlevé III_3 which is related to topological string on local P1xP1 and to relativistic Toda system.
Building: | Randall Laboratory |
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Event Type: | Workshop / Seminar |
Tags: | Free, Graduate Students, Lecture, Physics, Science, Talk, Undergraduate Students |
Source: | Happening @ Michigan from HET Brown Bag Series, Department of Physics |