Hypergeometric Functions (Fall 2015)

Teachers: F.Beukers (UU), G.Heckman (RU)

The classical hypergeometric function was introduced by Euler in the eighteenth century, and was well developed in the nineteenth century, notably by Riemann, Schwarz and Klein. Hypergeometric functions appear in many areas of mathematics and its applications. Very often in mathematical physics in the 19th century, but also algebraic geometry in the 20th century. In this course we start with a brief introduction of linear differential equations in the complex plane and then focus on the hypergeometric differential equation and its solutions.

We start with the following classical subjects:

Then we continue with more recent work: We end with a discussion why this admittedly old subject of hypergeometric functions still attracts mathematicians of recent times

We will use course notes. In principle we follow the notes by Gert Heckman.
As a backup you may use the notes by Frits Beukers. However, they should still be checked for inaccuracies, etc, hence the disclaimer on the first page of the notes.

Classes take place on Mondays 13:30 - 16:30 in room BBG165 (Buys Ballot Gebouw), the first two hours will be a regular lecture, the last one an exercise class.
Homework: This will be assigned every two weeks and graded.
Exams: The final grade will be the average of a final exam(60%) and the home work assignments (40%).

Material covered: