THEMATIC PROGRAMS

November  4, 2025
THEMATIC PROGRAM ON ARITHMETIC GEOMETRY,HYPERBOLIC GEOMETRY AND RELATED TOPICS July-December, 2008

 

Clay Mathematics Institute Senior Scholar

Henri Gillet
Department of Mathematics, Statistics, and Computer Science, University of Illinois at Chicago

Clay Mathematics Institute Public Lecture
November 25, 2008 -- 4pm,
to be held at Fields, Room 230
Supported by the Clay Mathematics Institute and
the Department of Mathematics, University of Toronto
Clay Mathematics Institute CMI Fellows and Scholars Thematic Year Home page

What is infinity factorial (and why might we care)?

Euler, in the 18th century, computed the values for the sums of (divergent) series such as 1+2+3+ … + n + (n+1) + … (which is equal to -1/12). His computations can be interpreted using the Riemann zeta function, (actually first considered by Euler himself). I shall discuss these and other divergent sums and products, including how we can give a value to ∞!=1.2.3. … n.(n+1). … . I shall give some indication of how these kinds of computations are related to results in number theory and geometry. This lecture should be accessible to students who have a good knowledge of calculus, and have some knowledge of complex numbers.

The Clay Mathematics Institute Senior Scholars program aim is to foster mathematical research and the exchange of ideas by providing support for senior mathematicians who will play a central role in a topical program at an institute or university. Senior Scholars will be in residence for a substantial fraction of the program and are expected to interact extensively with the other participants.