Exact Results in Quantum Theory & Gravity
sala 1.40, ul. Pasteura 5
2023-02-24 (14:15) 
Robert Conte (Centre Borelli, École normale supérieure Paris-Saclay)
Bonnet surfaces and the natural Lax pair of the sixth Painlevé equation
The moving frame of the surfaces built by Bonnet in 1867 is extrapolated to a new, second-order, isomonodromic matrix Lax pair of the sixth Painlevé equation, whose elements depend rationally on the dependent variable and quadratically on the monodromy exponents $\theta_j$. Next, by converting back this Lax pair to a moving frame, we obtain an extrapolation of Bonnet surfaces to analytic surfaces with two more degrees of freedom.