Akane Nakamura(Josai University)
Recovering linear from nonlinear
17:00--18:30, February 14 (Thu), 2019
Room B301, Faculty of Science
Abstract:
One of the important aspects of the integrable systems is that these nonlinear systems possess linear problems. However, it is not easy to find a linear problem (Lax equation) just by looking at the nonlinear equations. In this talk, we will explain a way to recover a linear problem from the nonlinear autonomous 4-dimensional Painlevé-type systems (the Hitchin systems). Our way is to compare generic degenerations of the families of curves arising from the nonlinear problem (i.e., the boundary divisors adjoined in the compactification of the Liouville tori) and curves appearing in the linear side (the spectral curves). We have proved that the Jacobian of generic curve of these systems has unique principal polarization, so that we can recover curves. This talk is based on joint work with Eric Rains.