K. Soundararajan

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Soundararajan 2010 in Stanford

K. Soundararajan ( Kannan Soundararajan ; born December 27, 1973 in Chennai , Tamil Nadu ) is an Indian - American mathematician who deals with analytical number theory.

Soundararajan grew up in Chennai (Madras) and won the silver medal at the International Mathematical Olympiad in 1991 as part of the Indian team . From 1991 he studied mathematics at the University of Michigan , graduating in 1995. As a student he won the first Morgan Prize of the American Mathematical Society for work in analytical number theory. Among other things, he proved with Ramachandran Balasubramanian a conjecture of the combinatorial number theory of Ronald Graham . In 1995 he went on a scholarship as a Sloan Fellow at the Princeton University , where he in 1998 Peter Sarnak with the thesis " Quadratic twists of Dirichlet L-functions received his doctorate." In it he proved that more than 7/8 of the quadratic L-functions have zeros at the critical point s = 1/2. As a post-doctoral student , he was a fellow of the American Institute of Mathematics at the Institute for Advanced Study, among others . He was a professor at the University of Michigan and has been a professor at Stanford University and director of the Mathematics Research Center (MRC) at Stanford since 2006 .

It was first published in 1992 in the Journal of Number Theory and had its roots in work he did as a student at Padma Seshadri High School in Chennai. He deals with multiplicative number theory such as the distribution of zeros of the Riemann zeta function , related to this also with the theory of random matrices , and with Dirichlet L functions and the analytical theory of automorphic forms (Katz-Sarnak theory of symmetry groups associated with automorphic forms ). Together with Jeffrey Lagarias, he formulated an xyz conjecture for smooth solutions (without large prime factors in a, b, c) of the abc equations, analogous to the abc conjecture . With Persi Diaconis he investigated various card shuffling problems (with riffle shuffle ).

In 2008, with Roman Holowinsky from Ohio State University , he solved an important special case of the quantum unique ergodicity conjecture (QUE) by Sarnak and Zeev Rudnick for module surfaces.

With Andrew Granville , he introduced a new approach to analytical number theory ( pretentious approach ) in the 2010s , based on earlier work by Gábor Halász .

In 2016 he discovered Robert Lemke Oliver a surprising symmetry deviation in the prime numbers. Prime numbers (except 2.5) can only end on the digits 1,3,7 or 9. As can be shown, these are evenly distributed among the prime numbers (see Siegel-Walfisz's theorem ). Soundararajan and Lemke found, however, for successive prime numbers that if the first ends on 1, the following in the final digit is not evenly distributed over 1,3,7,9 (i.e. 25 percent probability each), but with 18, 30, 30, 22 percent. There are similar unequal distributions if you look at the other three final digits instead of the 1. The authors examined the first billion prime numbers. They also gave a possible explanation about the Hardy-Littlewood conjecture .

In 2003 he was awarded the Salem Prize for work on Dirichlet L-functions and related character sums. In 2005 he received the first SASTRA Ramanujan Prize with Manjul Bhargava . In 2011 he received the Infosys Prize and in 2012 the Ostrowski Prize . In 2010 he was invited speaker at the International Congress of Mathematicians in Hyderabad ( Quantum Unique Ergodicity and Number Theory ).

Fonts

  • Non vanishing of quadratic Dirichlet L functions at s = 1/2 , Annals of Mathematics, Volume 152, 2000, pp. 447–448, Preprint Arxiv (part of his dissertation)
  • with Ken Ono Ramanujan's ternary quadratic form , Inventiones mathematicae, Volume 130, 1997, pp. 415–454
  • with Andrew Granville, The spectrum of multiplicative functions , Annals of Mathematics, Volume 153, 2001, pp. 407-470
  • with Holowinsky Mass equidistribution of Hecke eigenforms , Annals of Mathematics, Volume 172, 2010, p. 1517, Preprint, Arxiv
  • Quantum unique ergodicity of , Annals of Mathematics, Volume 172, 2010, p. 1529, Preprint Arxiv (uniform distribution of the zeros of the Maass waveform for high eigenvalues ​​in the module area)
  • with Balasubramanian On a conjecture of RL Graham , Acta Arithmetica, Volume 75, 1996, p. 1
  • with Brian Conrey Real zeroes for quadratic Dirichlet L functions , Inventiones mathematicae, Volume 150, 2002, pp. 1-44, Preprint, Arxiv

Web links

Individual evidence

  1. ↑ http://ibnlive.in.com/news/making-math-easy-k-soundarajan/218206-62-128.html
  2. ↑ http://www.imo-official.org/participant_r.aspx?id=2755
  3. ↑ Kannan Soundararajan in the Mathematics Genealogy Project (English)Template: MathGenealogyProject / Maintenance / name used
  4. ↑ Lagarias, Soundararajan Smooth solutions to the abc equation: the xyz conjecture , J. Theory des Nombres Bordeaux, Volume 23, 2011, p. 209
  5. ^ Patrick Illinger, mathematicians find surprising patterns in prime numbers, Süddeutsche Zeitung, March 16, 2016
  6. ↑ Soundararajan, Oliver, Unexpected biases in the distribution of consecutive primes , Arxiv 2016
  7. ↑ First SASTRA Ramanujan Prize ( Memento of the original from July 26, 2011 in the Internet Archive ) Info: The archive link was inserted automatically and has not yet been checked. Please check the original and archive link according to the instructions and then remove this notice.  @1@ 2Template: Webachiv / IABot / www.math.ufl.edu
personal data
SURNAME Soundararajan, K.
ALTERNATIVE NAMES Soundararajan, Kannan
BRIEF DESCRIPTION Indian-American mathematician
DATE OF BIRTH December 27, 1973
PLACE OF BIRTH Chennai , Tamil Nadu