Abstract: The golden ratio is one of the most intriguing constants in mathematics. It has a beautiful description in terms of a continued fraction. In his first letter to G. H. Hardy, Ramanujan hinted at a theory of continued fractions, which greatly expands on this classical observation. He offered shocking evaluations which Hardy described as...

"These formulas defeated me completely...they could only be written down by a mathematician of the highest class. They must be true because no one would have the imagination to invent them". - G. H. Hardy

Ramanujan had a secret device, two power series identities which were independently discovered previously by Rogers. The two Rogers-Ramanujan identities are now ubiquitous in mathematics.

It turns out that these identities and Ramanujan´s theory of evaluations are hints of a much larger theory. In joint work with Michael Griffin and Ole Warnaar, the author has discovered a rich framework of Rogers-Ramanujan identities, one which comes equipped with a beautiful theory of algebraic numbers. The story blends the theory of Hall-Littlewood polynomials, modular forms, and the representation theory of Kac-Moody affine Lie algebras.

About Ken Ono

Ken Ono received his BA from the University of Chicago in 1989, and his PhD in 1993 at UCLA where his advisor was Basil Gordon.

Ono´s contributions include several monographs and over 140 research and popular articles in number theory, combinatorics, and algebra. He is considered to be an expert in the theory of integer partitions and modular forms. In 2000 he ´greatly´ expanded Ramanujan´s theory of partition congruences, and in work with Kathrin Bringmann he has made important contributions to the theory of Maass forms, functions which include Ramanujan´s mock theta functions as examples. In 2007 Don Zagier gave a Seminar Bourbaki address on the work of Bringmann, Ono, and Zwegers on the mock theta functions. The 2009 SASTRA Ramanujan Prize, awarded to a young mathematician under the age of 32, has been awarded to Kathrin Bringmann for this joint work with Ono. In 2012 Ono made world news for his work proving the last open conjectures contained in Ramanujan´s enigmatic death-bed letter to G. H. Hardy.

Ono has received many awards for his research. In April 2000 he received the Presidential Career Award (PECASE) from Bill Clinton in a ceremony at the White House, and in June 2005 he received the National Science Foundation Director´s Distinguished Teaching Scholar Award at the National Academy of Science. He has also won a Sloan Fellowship, a Packard Fellowship, and a Guggenheim Fellowship. In 2012 he became a fellow of the American Mathematical Society.