Larry Guth

Lawrence David "Larry" Guth (* 1976 ) is an American mathematician who studies metric geometry, combinatorics and harmonic analysis .

Life

Guth, the son of astrophysicist Alan Guth , studied at the Massachusetts Institute of Technology (MIT) with his doctorate in 2005 with Tomasz Mrowka ( Area contracting maps between rectangles ). He was a post-doctoral student at Stanford University and the University of Toronto . In 2011 he became Professor at the Courant Institute of Mathematical Sciences of New York University and in 2012 Professor at MIT.

Among other things, he dealt with systolic inequalities (based on the fundamental work of Michail Leonidowitsch Gromow ) and the relationship between geometric inequalities and topology. He also deals with the Kakeya problem (generalizations of a geometric problem originally from Sōichi Kakeya ) and the related restriction problem (according to Elias Stein ) of harmonic analysis.

In 2010, with Nets Katz , he solved the problem of different distances from Paul Erdős (1946). They showed that N points in the plane have at least different distances. They used high-degree polynomials. In the higher dimensions the problem is unsolved. The continuous analogue is Falconer's conjecture , which Guth also researched. ${\displaystyle {\frac {N}{\log(N)}}}$

In 2015, together with Jean Bourgain and Ciprian Demeter , he proved the main conjecture in Vinogradov's mean theorem .

In 2010 he was a Sloan Fellow and also in 2010 he was invited speaker at the International Congress of Mathematicians in Hyderabad (Metaphors in systolic geometry). In 2013 he received the Salem Prize . In 2014 he became Simons Investigator of the Simons Foundation. In 2015 he received the Clay Research Award and in 2018 he was elected to the American Academy of Arts and Sciences . For 2020, Guth was awarded the Bôcher Memorial Prize and the Maryam Mirzakhani Prize in Mathematics .

Fonts

• Volumes of Balls in large Riemannian Manifolds , Annals of Mathematics, 173, 2011, 51–76
• with Nets Katz: Algebraic methods in discrete analogues of the Kakeya problem , Advances in Mathematics, 225, 2010, 2828–2839
• Systolic inequalities and minimal hypersurfaces , Geometric and Functional Analysis 19, 2010, 1688-1692
• Notes on Gromov's systolic inequality, Geometriae Dedicata 123, 2006, 113-129
• Width-volume inequality, Geom. Funct. Anal. 17, 2007, 1139-1179, Arxiv
• with Jean Bourgain : Bounds on oscillatory integral operators based on multilinear estimates , Geometric and Functional Analysis 21, 2011, 1239–1295
• Minimax problems related to cup powers and Steenrod squares , Geometry and Functional Analysis, 18, 2009, 1917-1987
• The endpoint case of the Bennett-Carbery-Tao multilinear Kakeya conjecture , Acta Mathematica, 205, 2010, 263-286
• Symplectic embeddings of polydisks , Inventiones Mathematicae, 172, 2008, 477-489
• with Jean Bourgain, Ciprian Demeter: Proof of the main conjecture in Vinogradov's mean value theorem for degrees higher than three , Annals of Mathematics, 184, 2016, 633–682
• Polynomial methods in combinatorics, AMS 2016

Web links

• Homepage at MIT

Individual evidence

1. ↑ Larry Guth in the Mathematics Genealogy Project (English)
2. ^ Terry Tao The Bourgain-Guth argument for proving restriction theorems
3. ↑ Guth, Katz, On the Erdös distinct distances problem in the plane , Annals of Mathematics, Volume 181, 2015, pp. 155–190, Arxiv 2010
4. ↑ Janos Pach on Guth and Katz's solution, 2010
5. ↑ Iosevich, What is Falconer's conjecture?, Notices AMS, April 2019
6. ^ Bourgain, Demeter, Guth: Proof of the main conjecture in Vinogradov's mean value theorem for degrees higher than three, Arxiv 2015 , appears in Annals of Mathematics
7. ↑ Arxiv
8. ↑ 2015 Clay Research Award
9. ↑ Book of Members 1780 – present, Chapter G. (PDF; 931 kB) In: American Academy of Arts and Sciences (amacad.org). Accessed October 7, 2018 (English).