Akane Nakamura（Josai University) 

Recovering linear from nonlinear 
17：0018：30, 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 4dimensional Painlevétype 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.

