UBC Math Distinguished Lecture Series Ken Ono (Emory University)

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PIMS- UBC Math Distinguished Lecture Series Ken Ono (Emory University) Nov 9, 2017 University of British Columbia Room: ESB 2012 Vancouver, BC 3:30pm Polya’s Program for the Riemann Hypothesis and Related Problems In 1927 Polya proved that the Riemann Hypothesis is equivalent to the hyperbolicity of Jensen polynomials for Riemann’s Xi-function. This hyperbolicity has only been proved for degrees d=1, 2, 3. We prove the hyperbolicity of 100% of the Jensen polynomials of every degree. We obtain a general theorem which models such polynomials by Hermite polynomials. This theorem also allows us to prove a conjecture of Chen, Jia, and Wang on the partition function. This is joint work with Michael Griffin, Larry Rolen, and Don Zagier. KEN ONO is the Asa Griggs Candler Professor of Mathematics at Emory University. He is considered to be an expert in the theory of integer partitions and modular forms. His contributions include several monographs and over 150 research and popular articles in number theory, combinatorics and algebra. He received his Ph.D. from UCLA and has received many awards for his research in number theory, including a Guggenheim Fellowship, a Packard Fellowship and a Sloan Fellowship. He was awarded a Presidential Early Career Award for Science and Engineering (PECASE) by Bill Clinton in 2000 and he was named the National Science Foundation’s Distinguished Teaching Scholar in 2005. He serves as Editor-in-Chief for several journals and is an editor of The Ramanujan Journal. Visit his web page at http://www.mathcs.emory.edu/~ono/ Light refreshments will be served in ESB 4133 from 3:00pm For more details please visit the PIMS Webpage at: https://www.pims.math.ca/scientific-event/171109-pumdcko www.pims.math.ca @pimsmath facebook.com/pimsmath .

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A Life Inspired by an Unexpected Genius
Quanta Magazine A Life Inspired by an Unexpected Genius The mathematician Ken Ono believes that the story of Srinivasa Ramanujan — mathematical savant and two-time college dropout — holds valuable lessons for how we find and reward hidden genius. By John Pavlus The mathematician Ken Ono in his office at Emory University in Atlanta. For the first 27 years of his life, the mathematician Ken Ono was a screw-up, a disappointment and a failure. At least, that’s how he saw himself. The youngest son of first-generation Japanese immigrants to the United States, Ono grew up under relentless pressure to achieve academically. His parents set an unusually high bar. Ono’s father, an eminent mathematician who accepted an invitation from J. Robert Oppenheimer to join the Institute for Advanced Study in Princeton, N.J., expected his son to follow in his footsteps. Ono’s mother, meanwhile, was a quintessential “tiger parent,” discouraging any interests unrelated to the steady accumulation of scholarly credentials. This intellectual crucible produced the desired results — Ono studied mathematics and launched a promising academic career — but at great emotional cost. As a teenager, Ono became so desperate https://www.quantamagazine.org/the-mathematician-ken-onos-life-inspired-by-ramanujan-20160519/ May 19, 2016 Quanta Magazine to escape his parents’ expectations that he dropped out of high school. He later earned admission to the University of Chicago but had an apathetic attitude toward his studies, preferring to party with his fraternity brothers. He eventually discovered a genuine enthusiasm for mathematics, became a professor, and started a family, but fear of failure still weighed so heavily on Ono that he attempted suicide while attending an academic conference.
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Arxiv:1906.07410V4 [Math.NT] 29 Sep 2020 Ainlpwrof Power Rational Ftetidodrmc Ht Function Theta Mock Applications
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Sixth Ramanujan Colloquium
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Vitae Ken Ono Citizenship
Vitae Ken Ono Citizenship: USA Date of Birth: March 20,1968 Place of Birth: Philadelphia, Pennsylvania Education: • Ph.D., Pure Mathematics, University of California at Los Angeles, March 1993 Thesis Title: Congruences on the Fourier coefficients of modular forms on Γ0(N) with number theoretic applications • M.A., Pure Mathematics, University of California at Los Angeles, March 1990 • B.A., Pure Mathematics, University of Chicago, June 1989 Research Interests: • Automorphic and Modular Forms • Algebraic Number Theory • Theory of Partitions with applications to Representation Theory • Elliptic curves • Combinatorics Publications: 1. Shimura sums related to quadratic imaginary fields Proceedings of the Japan Academy of Sciences, 70 (A), No. 5, 1994, pages 146-151. 2. Congruences on the Fourier coefficeints of modular forms on Γ0(N), Contemporary Mathematics 166, 1994, pages 93-105., The Rademacher Legacy to Mathe- matics. 3. On the positivity of the number of partitions that are t-cores, Acta Arithmetica 66, No. 3, 1994, pages 221-228. 4. Superlacunary cusp forms, (Co-author: Sinai Robins), Proceedings of the American Mathematical Society 123, No. 4, 1995, pages 1021-1029. 5. Parity of the partition function, 1 2 Electronic Research Annoucements of the American Mathematical Society, 1, No. 1, 1995, pages 35-42 6. On the representation of integers as sums of triangular numbers Aequationes Mathematica (Co-authors: Sinai Robins and Patrick Wahl) 50, 1995, pages 73-94. 7. A note on the number of t-core partitions The Rocky Mountain Journal of Mathematics 25, 3, 1995, pages 1165-1169. 8. A note on the Shimura correspondence and the Ramanujan τ(n)-function, Utilitas Mathematica 47, 1995, pages 153-160.
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Arxiv:1911.05264V3 [Math.NT]
A NOTE ON THE HIGHER ORDER TURAN´ INEQUALITIES FOR k-REGULAR PARTITIONS WILLIAM CRIAG AND ANNA PUN Abstract. Nicolas [8] and DeSalvo and Pak [3] proved that the partition function p(n) is log concave for n 25. Chen, Jia and Wang [2] proved that p(n) satisfies the third order ≥ Turán inequality, and that the associated degree 3 Jensen polynomials are hyperbolic for n 94. Recently, Griffin, Ono, Rolen and Zagier [5] proved more generally that for all d, ≥ the degree d Jensen polynomials associated to p(n) are hyperbolic for sufficiently large n. In this paper, we prove that the same result holds for the k-regular partition function pk(n) for k 2. In particular, for any positive integers d and k, the order d Turán ≥ inequalities hold for pk(n) for sufficiently large n. The case when d = k = 2 proves a conjecture by Neil Sloane that p2(n) is log concave. 1. Introduction and Statement of results The Turán inequality (or sometimes called Newton inequality) arises in the study of real entire functions in Laguerre-Pólya class, which is closely related to the study of the Riemann hypothesis [4, 12]. It is well known that the Riemann hypothesis is true if and only if the Riemann Xi function is in the Laguerre-Pólya class, where the Riemann Xi function is the entire order 1 function defined by 1 2 1 iz 1 iz 1 1 Ξ(z) := z π 2 − 4 Γ + ζ iz + . 2 − − 4 − 2 4 − 2 A necessary condition for the Riemann Xi function to be in the Laguerre-Pólya class is that the Maclaurin coefficients of the Xi function satisfy both the Turán and higher order Turán inequalities [4, 11].
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Lecture Topics
Ken Ono, Ph.D. Thomas Jefferson Professor of Mathematics, University of Virginia Vice President, American Mathematical Society Chair of Mathematics, American Association for the Advancement of Science Ken Ono is a research mathematician who has a strong interest in issues related to the college experience. He is known for his research in mathematics, and his work in television and film. He was the Associate Producer of the Hollywood film “The Man Who Knew Infinity” about the self-trained Indian mathematical genius Srinivasa Ramanujan, and he starred in an episode of Star Talk hosted by Neil deGrasse Tyson. Public Lecture Option 1: Title: Why does Ramanujan, “The Man Who Knew Infinity,” matter? “Dear Sir…I beg to introduce myself to you as a clerk… of the Port Trust Office at Madras… I have been employing the spare time at my disposal to work at Mathematics…I have not trodden through the conventional regular course…but I am striking out a new path...” What followed in the letter were astonishing mathematical formulas, so otherworldly the letter's recipient could not help but believe they were true. Written in 1913, it has taken mankind one century to understand their meaning; along the way, the pursuit has led to solutions of ancient mathematical mysteries, breakthroughs in modern physics, and ideas which help power the internet. A major motion picture based on the life of the letter’s author, THE MAN WHO KNEW INFINITY, starring Dev Patel and Jeremy Irons, was released in 2016 (Ken Ono is an Associate Producer of the film). The mysterious “clerk of the Port Trust Office of Madras” has been in the air a lot recently.
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