Larry Guth

Lawrence David Guth is a professor of mathematics at the Massachusetts Institute of Technology. He has previously worked at the New York University's Courant Institute of Mathematical Sciences and at the University of Toronto.
Guth received his Ph.D. in 2005 from the Massachusetts Institute of Technology under the supervision of Tomasz Mrowka. He won an Alfred P. Sloan Fellowship in 2010. He was invited speaker at the International Congress of Mathematicians in India in 2010, where he spoke about systolic geometry. In 2015 he received the Clay Research Award. In his research, Guth has strengthened Gromov's systolic inequality for essential manifolds and, along with Nets Katz, found a solution to the Erdős distinct distances problem. His wide-ranging interests include the Kakeya conjecture and the systolic inequality.
He is the son of physicist Alan Guth known for the theory of Inflation in cosmology and the nephew of Lucille Guth, a social worker.

Work

• Metaphors in systolic geometry: the video
• Guth, Larry (2011), "Volumes of balls in large Riemannian manifolds", Annals of Mathematics, 2nd ser., 173 (1): 51–76, arXiv:math.DG/0610212, doi:10.4007/annals.2011.173.1.2, MR 2753599 .
• Guth, Larry; Katz, Nets Hawk (2010), "Algebraic methods in discrete analogs of the Kakeya problem", Advances in Mathematics, 225 (5): 2828–2839, arXiv:0812.1043, doi:10.1016/j.aim.2010.05.015, MR 2680185 .
• Guth, Larry (2010), "Systolic inequalities and minimal hypersurfaces", Geometric and Functional Analysis, 19 (6): 1688–1692, arXiv:0903.5299, doi:10.1007/s00039-010-0052-0, MR 2594618 .
• Guth, Larry (2010), "The endpoint case of the Bennett–Carbery–Tao multilinear Kakeya conjecture", Acta Mathematica, 205 (2): 263–286, arXiv:0811.2251, doi:10.1007/s11511-010-0055-6, MR 2746348 .
• Guth, Larry (2009), "Minimax problems related to cup powers and Steenrod squares", Geometric and Functional Analysis, 18 (6): 1917–1987, arXiv:math/0702066, doi:10.1007/s00039-009-0710-2, MR 2491695 .
• Guth, Larry (2008), "Symplectic embeddings of polydisks", Inventiones Mathematicae, 172 (3): 477–489, arXiv:0709.1957, doi:10.1007/s00222-007-0103-9, MR 2393077 .
• Guth, Larry (2007), "The width-volume inequality", Geometric and Functional Analysis, 17 (4): 1139–1179, arXiv:math/0609569, doi:10.1007/s00039-007-0628-5, MR 2373013 .
• Guth, Larry; Katz, Nets Hawk (2015), "On the Erdős distinct distance problem on the plane", Annals of Mathematics, 181 (1): 155–190, arXiv:1011.4105, doi:10.4007/annals.2015.181.1.2, MR 3272924 
• Guth, Larry. Polynomial Methods in Combinatorics. American Mathematical Society. ISBN 978-1-4704-2890-7.