University of Hawaii Mathematics Department

Distinguished Lecture Series

February 25, 26, 27, 2009


The Distinguished Lecture Series is a series of three lectures. The first lecture is intended for a general audience. This year the lectures will be given by:


Ken Ono

Solle P. and Margaret Manasse Professor of Letters and Science
and the Hilldale Professor of Mathematics
University of Wisconsin - Madison


A poster advertising the event created by Blake Ann Antida.


GENERAL AUDIENCE LECTURE
UNEARTHING THE VISIONS OF A MASTER:
THE WEB OF RAMANUJAN'S MOCK THETA FUNCTIONS IN NUMBER THEORY

Wednesday, February 25, 2009 - 4:30 pm - Bilger 150
Reception 3:30 pm - Campus Center 203E

The legend of Ramanujan is one of the most romantic stories in the modern history of mathematics. It is the story of an untrained mathematician, from south India, who brilliantly discovered tantalizing examples of phenomena well before their time. Indeed, the legacy of Ramanujan's work (as a whole) is well documented and includes direct connections to some of the deepest results in modern number theory such as the proof of the Weil Conjectures and the proof of Fermat's Last Theorem. However, one final problem remained, the enigma of the functions which Ramanujan discovered on his death bed. Here we tell the story of Ramanujan and this final mystery.


FREEMAN DYSON'S CHALLENGE FOR THE FUTURE:
THE MOCK THETA FUNCTIONS I, II

Thursday, February 26, 2009 - 3:30 pm - Keller 401
Friday, February 27, 2009 - 3:30 pm - Keller 401

Refreshments each day 3:00 pm - Keller 418

In his last letter to Hardy (written on his death bed), Ramanujan gave examples of 17 functions he referred to as "mock theta functions". Without a definition and without good clues, number theorists were unable to make any real sense out of these peculiar functions. Nevertheless, these examples make important appearances in many disparate areas of mathematics, a fact which inspired Freeman Dyson to proclaim:

"Mock theta-functions give us tantalizing hints of a grand synthesis still to be discovered. Somehow it should be possible to build them into a coherent group-theoretical structure... This remains a challenge for the future. My dream is that I will live to see the day when our young physicists, struggling to bring the predictions of superstring theory into correspondence with the facts of nature, will be led to enlarge their analytic machinery to include not only theta-functions but mock theta-functions." --Freeman Dyson, 1987

In this lecture I will describe the solution to this challenge and give an indication of some of the open problems which have now been solved as a result.


The Speaker:

Ken Ono received his Ph.D from UCLA in 1993 under the guidance of Basil Gordon. Upon graduation, he held positions at the University of Georgia, the University of Illinois (Urbana- Champaign), the Institute of Advanced Studies, and Penn State University, where he was named the Louis P. Martarano Professor in 1999. He is presently the Manasse Professor of Letters and Science and the Hilldale Professor of Mathematics at the University of Wisconsin at Madison.

He has authored over 100 research papers, as well as the CBMS monograph entitled The Web of Modularity. His work includes ground-breaking results on partition congruences, coefficients of modular forms, traces of singular moduli, Borcherds products, mock- theta functions, and much more. He has advised 16 doctoral students to date and sits on the editorial boards of eleven journals. He has received numerous awards and honors, including a Sloan Fellowship, a Presidential Early Career Award, a Packard Fellowship, and a Guggenheim Fellowship.

In addition to his research accomplishments, Ono is also a master lecturer and teacher as evidenced by his receipt of the 2005 National Science Foundation Director's Distinguished Teaching Scholar Award and the 2007 Favorite Instructor Award from the University of Wisconsin Residence Halls.


Location:

For the location of the relevant buildings (Keller Hall, Campus Center, Bilger Hall) consult the campus map.


The Sponsors:

The lectures are sponsored by the National Science Foundation, and the Department of Mathematics and the College of Natural Sciences of the University of Hawaii, Manoa.