Topics in Complex analysis and geometry [ LMAT2260 ]

LMAT1222 Analyse complexe and LMAT2110 Eléments de 
géométrie différentielle.

In complex analysis, Toeplitz determinants, orthogonal 
polynomials, Riemann-Hilbert problems, the nonlinear steepest descent 
method, asymptotic behavior and the Ising model will be studied. In 
complex geometry, the principal theorems in the theory of compact 
Riemann surfaces, the Riemann-Roch theorem, Abel's theorem and Jacobi's 
inversion problem, and their applications to the Toda lattice will be 
studied.

The course will in alternance treat subjects in complex analysis 
and complex geometry, in relation to applications in the theory of 
integrable systems, orthogonal polynomials and random matrices. The goal 
of the course is to give an introduction to a modern topic related to 
complex analysis or geometry, and to initiate them to research in this 
domain.

oral exam or oral and written presentation of a project 
made during the semester.

Course : 3 h./week.