|Alma mater||Yale University, MIT|
Salem Prize (2013)|
Clay Research Award (2015)
|Institutions||Stanford, University of Toronto, New York University, MIT|
|Doctoral advisor||Tomasz Mrowka|
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 an invited speaker at the International Congress of Mathematicians in India in 2010, where he spoke about systolic geometry. In 2014 he received a Simons Investigator Award. 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.
- 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, Bibcode:2008InMat.172..477G, 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 (2016). Polynomial Methods in Combinatorics. American Mathematical Society. ISBN 978-1-4704-2890-7.
- Lawrence Guth at the Mathematics Genealogy Project.
- Fall newsletter 2010, Univ. of Toronto mathematics department, retrieved 2011-05-26.
- ICM listing of invited speakers Archived 2011-07-17 at the Wayback Machine., retrieved 2011-05-26.
- "Simons Investigator Awardees". Simons Foundation. Retrieved 11 September 2017.
- Clay Research Award 2015
- Guth's approach to Gromov's systolic inequality, Shmuel Weinberger, July 18, 2009.
- "Distinct Distance Problem in the Plane" Solved, Math In The News, Mathematical Association of America, March 2, 2011.
- Tao, Terence (2018). "Review of Polynomial methods in combinatorics by Larry Guth". 55: 103–107. doi:10.1090/bull/1586.