PIMS Colloquium: Tom Archibald

Things hypergeometric reach out in various directions that may be a little surprising. In this talk we will look at some nineteenth-century developments. Beginning with some results of Gauss, we will sample from work by E. E. Kummer (who, in providing solutions for the hypergeometric equation, had noticed connections to Legendre's period relations for elliptic integrals); and by L. Fuchs (who characterized the hypergeometric equation among linear DEs of the "Fuchsian" class). These studies are linked to work by Fuchs, Hermite and others on modular equations, and the detailed history reveals some surprising connections in classical mathematics.