Sumários
Polynomial matrices and spectral curve
27 Maio 2020, 10:30 • Davide Masoero
1. Proposition 5.1 of Hitchin's book:
The equivalence between:
A)the space of conjugacy of polynomial matrices with a given smooth spectral curve X
B)J^{g-1}/Theta, where J^{g-1} is the Jacobian of degree g-1, and Theta, the theta divisor (the image of S^{g-1}X into J^{g-1})
2. The case X of genus 1
Vector bundles on a Riemann surface
20 Maio 2020, 10:30 • Davide Masoero
The Riemann-Roch theorem for vector bundles
The Birkhoff-Grothendieck theorem
Direct image of a line bundle
Line bundles and sheaves
13 Maio 2020, 10:30 • Davide Masoero
Definition of line bundle
The line bundle associated to a divisor
The bijection among equivalence classes of line bundles and equivalence classes of divisors
Real and smooth algebro-geometric solutions of KP
6 Maio 2020, 10:30 • Davide Masoero
Anti-holomorphic involutions
M-curves and Harnack inequality
Necessary and sufficient conditions for real and smooth solutions of KP
Lecture 10
29 Abril 2020, 10:30 • Davide Masoero
Baker-Akhiezer functions
Agebro-geometric solutions of KP and KdV
Genus 1, travelling wave solutions of KdV, Weiertrass P function