Project Description

Prof. Carlos Simpson, CNRS, Université Côte d’Azur, Nice, will give a series of lectures on Hodge theory and local systems in the period March 3-5, 2020.

Other lecturers will be Prof. Alexander Efimov (Steklov Mathematical Institute of Russian Academy of Sciences), Prof. Ludmil Katzarkov, Prof. Viсtor Przyjalkowski (Steklov Mathematical Institute of Russian Academy of Sciences).

They will cover the following topics:

 

  • Kähler manifolds, Laplacians and the Kähler identities
  • the Hodge decomposition on cohomology
  • smooth morphisms or families of varieties
  • monodromy, the Gauss-Manin connection, motivic local systems
  • variation of Hodge structures
  • Zucker’s theorem: cohomology with coefficients in a VHS
  • Norm estimates, nilpotent and SL2-orbit theorems
  • character varieties, harmonic bundles and Higgs bundles
  • C*-action and deformation to a VHS, spectral curves and the Hitchin fibration
  • Dolbeault cohomology with VHS coefficients, Higgs bundle coefficients
  • rigid local systems and motivicity conjecture

 

The lectures will take place in the building of the Institute of Mathematics and Informatics, Bulgarian Academy of Sciences.

Programme:

March 3, 2020
9:00 am – 10:00 am               C. Simpson
10:30 am – 11:30 am             C. Simpson
Lunch
2:30 pm – 3:30 pm                 V. Prizhalkovskii
4:00 pm                                  Office Hours

March 4, 2020
9:00 am – 10:00 am               C. Simpson
10:30 am – 11:30 am             C. Simpson
Lunch

2:30 pm – 3:30 pm                 L. Katzarkov
4:00 pm                                  A. Efimov
Dinner

March 5, 2020
9:00 am – 10:00 am               C. Simpson
10:30 am – 11:30 am             C. Simpson
Lunch
2:30 pm – 3:30 pm                 Office Hours