Event
Ann du Crest de Villeneuve, Université d'Angers, France
Tuesday, May 1, 2018 15:30to16:30
Room 4336, Pav. André-Aisenstadt, 2920, ch. de la Tour, CA
Polynomial tau functions of the Drinfeld--Sokolov hierarchies.
In 1985, Drinfeld and Sokolov showed how to associate to any semi-simple Lie algebra an infinite sequence of Hamiltonian PDE's now called the Drinfeld--Sokolov hierarchies. They generalize the Korteweg--de Vries (KdV) equation and have found applications in mathematical physics and enumerative geometry. It is possible to express the components of a given solution as the logarithmic derivatives of one single function called the tau function. This property called the tau symmetry is essential in many situations and relies on the Hamiltonian structure itself. I aim to present a way to compute polynomial tau functions (the simplest ones) of any Drinfeld--Sokolov hierarchy using the theory of Toeplitz determinants and what to do with these polynomials.