Kazuki Hiroe

Title: Invariants of differential equations and algebraic curves

Abstract: From algebraic differential equations on  Riemann surfaces,
we can define algebraic curves which we will call spectral curves.
I will explain that  structures of singularities of these algebraic curves have
a close connection with those of irregular singularities of differential equations.
In particular, I will make comparisons between
(1) Milnor number & Komatsu-Malgrange irregularity,
(2) blow up & Fourier transform,
(3) knot structure & Stokes phenomenon,
(4) cohomology of curves & de Rham cohomology of differential equations,
and so on.