Курс лекций "Studies on the Painleve equations"

На следующей неделе Hidetaka Sakai (Хидэтака Сакаи, Токийский Университет, Япония) прочтёт курс лекций по теме: «Studies on the Painleve equations (Исследования уравнений Пенлеве)» .

Лекции пройдут на факультете математики в ауд. 207 с 28.09 по 02.10 в 18:30.

Studies on the Painleve equations
1. Biquadratic Hamiltonian and elliptic functions
2. Classification of the Painleve equations
3. From Surface theory to differential equations
4. Affine Weyl group symmetry
5. Moduli of surfaces

Аннотация курса:
The Painleve equations were presented in the beginning of the
20th century, as differential equations that define special functions
having a place next to the elliptic functions and the hypergeometric functions.
Those equations, which were inspired by the purely mathematical idea,
have been studied intensively in the relation with physics, since
correlation functions of Ising model were expressed by a Painleve transcendent.

It is also interesting that properties of equations are understood from
theory of rational surfaces. Each equations are connected to a certain
generalization of rational elliptic surfaces, and we can tell the symmetries
of equations, the existence of particular solutions, and so on, from
this aspect.

We will see that kind of algebraic geometry related to the Painleve
equations in this series of talks.