# Ken Ono

**Ken Ono** (born 20 March 1968) is a Japanese-American mathematician who specializes in number theory, especially in integer partitions, modular forms, Umbral moonshine, the Riemann Hypothesis and the fields of interest to Srinivasa Ramanujan. He was the Manasse Professor of Letters and Science and the Hilldale Professor of Mathematics at the University of Wisconsin–Madison.

Ken Ono | |
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Ken Ono in 2015 at the Toronto International Film Festival | |

Born | 20 March 1968 |

Nationality | United States |

Alma mater | UCLA University of Chicago |

Scientific career | |

Fields | Mathematics |

Institutions | University of Virginia^{[1]}Emory University University of Wisconsin–Madison |

Doctoral advisor | Basil Gordon |

Notable students | Daniel Kane Karl Mahlburg Robert Schneider Gwynneth Coogan |

He is currently the Thomas Jefferson Professor of Mathematics at the University of Virginia, the Asa Griggs Candler Professor of Mathematics at Emory University, and the Vice President of the American Mathematical Society.

## Contents

## Early life and educationEdit

Ono is the son of mathematician Takashi Ono, who emigrated from Japan to the United States after World War II. His older brother, immunologist and university president Santa J. Ono, was born while Takashi Ono was in Canada working at the University of British Columbia, but by the time Ken Ono was born the family had returned to the US for a position at the University of Pennsylvania.^{[2]} In the 1980s, Ono attended Towson High School, but he dropped out. He later enrolled at the University of Chicago without a high school diploma. There he raced bicycles, and he was a member of the Pepsi–Miyata Cycling Team.

He received his BA from the University of Chicago in 1989, where he was a member of the Psi Upsilon fraternity. He earned his PhD in 1993 at UCLA where his advisor was Basil Gordon.^{[3]} Initially he planned to study medicine, but later switched to mathematics. He attributes his interest in mathematics to his father.^{[4]}

## Career and researchEdit

Ono's contributions include several monographs and over 160 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, was awarded to Kathrin Bringmann for this joint work with Ono.

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.^{[5]}

In 2011 and 2015 Ono gave TED talks.^{[6]}^{[7]}

In a joint work with Jan Bruinier, he discovered a finite algebraic formula for computing partition numbers.^{[8]}

He stars in the 2013 docudrama "The genius of Srinivasa Ramanujan".^{[9]}

He is profiled in the May 2014 issue of Scientific American.^{[10]} He was an Associate Producer and the mathematical consultant for the movie *The Man Who Knew Infinity* based on Ramanujan's biography written by Robert Kanigel.^{[11]} Ken Ono was chaired, on June 7th 2019, as Thomas Jefferson Professor of Mathematics, at the University of Virginia.^{[12]}

## A framework for the Rogers–Ramanujan identitiesEdit

In April 2014 Ono announced that he and two others had found a framework for the Rogers–Ramanujan identities and their arithmetic properties, solving a long-standing mystery stemming from the work of Ramanujan. The findings yield a treasure trove of algebraic numbers and formulas to access them. Ono's co-authors for this work were S. Ole Warnaar of the University of Queensland and Michael Griffin, an Emory University graduate student. Their work made world news that year and was ranked 15th among the top 100 stories of 2014 in science in *Discover* magazine.^{[13]}

After 15 years of focusing on the Rogers–Ramanujan identities, Warnaar had found a way to embed them into a much larger class of similar identities using representation theory. When Ono saw Warnaar's work, "It just clicked," Ono recalls. "Now we can extract infinitely many functions whose values are algebraic numbers."^{[14]}

## Proof of the Umbral Moonshine ConjectureEdit

In a joint paper (co-authored with John Duncan and Michael Griffin),^{[15]} Ono proved the Umbral moonshine Conjecture. This conjecture was formulated by Miranda Cheng, John Duncan, and Jeff Harvey, and is a generalization of the Monstrous Moonshine Conjecture proved by Fields medalist Richard Borcherds.

## Work on the Riemann HypothesisEdit

In May 2019 Ono published a joint paper (co-authored with Don Zagier and two former students) in the Proceedings of the National Academy of Sciences^{[16]} on the Riemann Hypothesis. Their work proves a large portion of the Jensen-Polya criterion for the Riemann Hypothesis. However, the Riemann Hypothesis remains unsolved. Their work also establishes the Gaussian Unitary Ensemble random matrix condition in derivative aspect for the derivatives of the Riemann Xi function. Fields medalist
Enrico Bombieri published a commentary in the Proceedings of the National Academy of Sciences, USA^{[17]} explaining the significance of this work.

## Personal lifeEdit

In recent years, Ono has resumed athletic training as a runner, swimmer and cyclist; since 2012, he has competed in triathlons as a member of Team USA.

## Honors and awardsEdit

- National Security Agency Young Investigator (1997)
- National Science Foundation CAREER Award (1998)
- Alfred P. Sloan Foundation Research Fellowship (1999)
- David and Lucile Packard Research Fellowship (1999)
- Presidential Early Career Award (awarded by Clinton) (2000)
- National Science Foundation CBMS Distinguished Lecturer (2003)
- John S. Guggenheim Fellowship (2003)
- Manasse Professor of Letters and Science, U. Wisconsin (2004–2011)
- National Science Foundation Director's Distinguished Teaching Scholar Award (2005)
- Hilldale Professor of Mathematics, U. Wisconsin (2008–2011)
- Candler Professor of Mathematics, Emory University (2010–present)
- Fellow of the American Mathematical Society (2013)
- Albert E. Levy Award for Scientific Research (2014)
- MAA George Pólya Distinguished Lecturer (2016–2017)
- International Science Film Festival Technical Award (2017)
- Eleanor Main Graduate Mentor Award (2017)
- Prose Award (Best Scholarly Book in Mathematics), Awarded by the American Publishers, (2018)
- Thomas Jefferson Professor of Mathematics, University of Virginia (Fall 2019-)

## Editorial boardsEdit

Ono is on the editorial board of several journals:

- Annals of Combinatorics
- Bulletin of the American Mathematical Society
- Communications in Number Theory and Physics
- Integers
- International Journal of Modern Mathematics
- The International Journal of Number Theory
- The International Mathematical Forum
- Involve
- Journal of Combinatorics and Number Theory
- The Ramanujan Journal
- Research in the Mathematical Sciences (Editor-in-Chief)
- Research in Number Theory (Editor-in-Chief)

## See alsoEdit

## ReferencesEdit

**^**Fall 2019, Thomas Jefferson Professor of Mathematics: https://math.virginia.edu/people/ono/**^**Bach, John (April 2013), "Getting to know Ono",*UC Magazine*. Although primarily a profile of Ono's brother, this article also includes some details of Ono's early family life.**^**Ken Ono at the Mathematics Genealogy Project**^**Saikia, Manjil (23 February 2015). "In conversation with Prof. Ken Ono: Gonit Sora".*Gonit Sora*. Retrieved 16 March 2015.**^**List of Fellows of the American Mathematical Society, retrieved 2013-03-20.**^**"-Infinity to Infinity, TED".**^**"Live mathematically, but not by the numbers, TED".**^**Kavassalis, Sarah. "Finite formula found for partition numbers".*The Language of Bad Physics*. Retrieved 1 March 2011.**^**"The genius of Srinivasa Ramanujan, IMDB.com".**^**Bleicher, Ariel (2014). "The Oracle, Scientific American".*Scientific American*.**310**(5): 70–75. doi:10.1038/scientificamerican0514-70.**^**Saikia, Manjil (23 February 2015). "In conversation with Prof. Ken Ono: Gonit Sora".*Gonit Sora*. Retrieved 16 March 2015.**^**Fall 2019, Thomas Jefferson Professor of Mathematics: https://math.virginia.edu/people/ono/**^**"Mother lode of mathematical identities discovered, Discover".**^**Griffin, Michael J.; Ono, Ken; Warnaar, S. Ole (2014). "A framework of Rogers–Ramanujan identities and their arithmetic properties".*Duke Mathematical Journal*. arXiv:1401.7718. doi:10.1215/00127094-3449994.**^**Duncan, John; Griffin, Michael J.; Ono, Ken (2015). "Proof of the Umbral Moonshine Conjecture".*Research in the Mathematical Sciences*. arXiv:1503.01472.**^**Griffin, Michael J.; Ono, Ken; Rolen, Larry; Zagier, Don (2019). "Jensen polynomials for the Riemann zeta function and other sequences".*Proceedings of the National Academy of Sciences, USA*.**^**Bombieri, Enrico (2019). "New progress on the zeta function: From old conjectures to a major breakthrough".*Proceedings of the National Academy of Sciences, USA*.

## External linksEdit

- Ken Ono's homepage
- Conversation with Ken Ono at Gonit Sora.
- Ken Ono on
*The Man Who Knew Infinity*and why Ramanujan Matters - Ono, Ken; Aczel, Amir D. (2016-04-13).
*My Search for Ramanujan: How I Learned to Count*. Springer. ISBN 978-3319255668.