Alex Kontorovich

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Alex Kontorovich, Oberwolfach 2011

Alex V. Kontorovich (born September 22, 1980 in the Soviet Union ) is an American mathematician who deals with analytic number theory, automorphic forms and representation theory, L-functions , harmonic analysis and homogeneous dynamics.

Life

Kontorovich studied from 1998 at Princeton University with Jakow Sinai , among others , where he also took jazz and saxophone studies and obtained a bachelor's degree in mathematics in 2002, and at Columbia University with a doctorate with Dorian Goldfeld (and Peter Sarnak ) in 2007 ( The Hyperbolic Lattice Point Count in Infinite Volume with Applications to Sieves ). From 2007 to 2010 he was Tamarkin Assistant Professor at Brown University , 2010/11 Assistant Professor at the State University of New York at Stony Brook and thereafter Assistant Professor and from 2014 Associate Professor at Yale University . From 2014 he is an Associate Professor at Rutgers University .

He was visiting scholar at Harvard, at the ETH Zurich and at the Institute for Advanced Study (2009–2010, 2013–2014).

plant

In 2011 he proved with Jean Bourgain a presumption of Zaremba of 1971 on continued fractions , whether any natural number appears as the denominator of a rational number whose continued fraction partial counter has, from a natural upward limited amount numbers (. B. from the set (1.2 , 3,4,5)). Zaremba suspected this to be so, and Kontorovich and Bourgain proved it.

In 2008 he proved with Hee Oh a theorem about the fractal dimension of plane Apollonian circle packings (fractal dimension , number of circles with a radius greater than r: where the constant C depends on the first three mutually touching circles). In doing so, they used number-theoretical and dynamic aspects of the problem that Jeffrey Lagarias , Peter Sarnak , Allan Wilks and Ronald Graham had previously explored.

In 2014 he received the Levi L. Conant Prize for the essay From Apollonius to Zaremba: Local-global phenomena in thin orbits . In it he suggested surprising connections between number theoretic and geometric problems. The number theoretic problem is the Zaremba problem mentioned above. The geometrical problem is about what he calls integer Soddy spherical packings (named after the chemist Frederick Soddy ), generalizations of Apollonian circular packings on three dimensions, with the curvatures being integers. Kontorovich proved that sufficiently large natural numbers that satisfy certain congruence conditions of the problem (are permissible ) can be represented as curvature in such a spherical packing.

He also deals with the Collatz problem (3x + 1 problem) and developed stochastic models for predicting the dynamics involved with Jeffrey Lagarias . Here and in a problem of the distribution of the values ​​of L-functions, he and Steven J. Miller showed the validity of Benford's law .

Others

From 2013 to 2015 he was a Sloan Research Fellow. He is a fellow of the American Mathematical Society .

He is also active and composes in various Klezmer music bands as a saxophonist (and clarinetist). He is a founding member of the Klez Dispensers and played with the Klezmatics . Kontorovich also plays jazz and classical music.

He is a US citizen.

Fonts

  • From Apollonius to Zaremba: Local-global phenomena in thin orbits , Bulletin AMS, Vol. 50, 2013, pp. 187–228, Arxiv
  • with Jean Bourgain : On the Local-Global Conjecture for Apollonian Gaskets, Inventiones Mathematicae, Volume 196, 2014, pp. 589–650, Arxiv
  • with Jean Bourgain: On Zaremba´s Conjecture, Annals of Mathematics, Volume 180, 2014, pp. 137–196, Arxiv Preprint, 2011
  • with Hee Oh : Apollonian Packings and Horospheres on Hyperbolic 3-manifolds, Journal of the AMS, Volume 24, 2011, pp. 603-648, Arxiv
  • with Hee Oh: Almost Prime Pythagorean Triples in Thin Orbits, J. Reine Angew. Math., Volume 667, 2012, pp. 89-131, Arxiv

Web links

Individual evidence

  1. ↑ Alex Kontorovich in the Mathematics Genealogy Project (English)Template: MathGenealogyProject / Maintenance / id used
  2. ↑ See Dana Mackenzie A tisket, a tasket, an Apollonian basket , American Scientist, Volume 98, 2010, pp. 10-14. The essay won the Chauvenet Prize
  3. ^ Levi Conant Prize for Kontorovich, Notices AMS April 2014, pdf
  4. ↑ Kontorovich, Lagarias, Stochastic Models for the 3x + 1 and 5x + 1 Problems , in: The Ultimate Challenge: The 3x + 1 problem, Amer. Math. Soc .: Providence 2010, pp. 131--188
  5. ^ Kontorovich, Steven J. Miller: Benford's Law, Values ​​of L-functions and the 3x + 1 problem, Acta Arith., Volume 120, 2005, pp. 269-297, Arxiv
  6. ↑ Article on Zaremba in All About Jazz
personal data
SURNAME Kontorovich, Alex
ALTERNATIVE NAMES Kontorovich, Alex V.
BRIEF DESCRIPTION American mathematician
DATE OF BIRTH September 22, 1980
PLACE OF BIRTH Soviet Union