|Thesis||Area-contracting maps between rectangles (2005)|
|Doctoral advisor||Tomasz Mrowka|
Education and career
Guth graduated from Yale in 2000, with B.S. in mathematics.
After MIT, Guth went to Stanford as a postdoc, and later to the University of Toronto as an Assistant Professor.
In 2011, New York University's Courant Institute of Mathematical Sciences hired Guth as a professor, listing his areas of interest as "metric geometry, harmonic analysis, and geometric combinatorics."
In 2012, Guth moved to MIT, where he is Claude Shannon Professor of Mathematics.
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 was included in the 2019 class of fellows of the American Mathematical Society "for contributions to harmonic analysis, combinatorics and geometry, and for exposition of high level mathematics".
On February 20, 2020, the National Academy of Sciences announced that Guth is the first winner of their new $20,000 Maryam Mirzakhani Prize in Mathematics for mid-career mathematicians.The citation states that his award is "for developing surprising, original, and deep connections between geometry, analysis, topology, and combinatorics, which have led to the solution of, or major advances on, many outstanding problems in these fields."
- 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.
- "Curriculum Vitae Larry Guth" (PDF). MIT Mathematics Department. 2020. Retrieved February 20, 2020.
B.S. Mathematics, Yale University, 2000
- Lawrence Guth at the Mathematics Genealogy Project.
- Knight, Helen (May 27, 2014). "Like father, like son". MIT News. Retrieved February 20, 2020.
Guth moved to MIT as a graduate student, where he began studying geometry under the supervision of mathematics professor Tomasz Mrwoka.
- "New Faculty: Larry Guth" (PDF). Courant Institute of Mathematical Sciences at NYU. 2011. Retrieved February 20, 2020.
He was a postdoc at Stanford and an Assistant Professor at the University of Toronto. He received a Sloan fellowship in 2010.
- "Larry Guth". MIT Mathematics Department. 2020. Retrieved February 20, 2020.
In 2020, Larry received the Bôcher Memorial Prize of the AMS, for his "deep and influential development of algebraic and topological methods for partitioning the Euclidean space and multi-scale organization of data, and his powerful applications of these tools in harmonic analysis, incidence geometry, analytic number theory, and partial differential equations." Larry wrote about this technique in his book “Polynomial Methods in Combinatorics.” He also received the newly named Maryam Mirzakhani Prize in Mathematics (formerly the NAS Award in Mathematics)
- 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.
- "Archived copy". Archived from the original on 2012-06-16. Retrieved 2011-10-23.CS1 maint: archived copy as title (link)
- 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.
- "Guth Awarded 2013 Salem Prize" (PDF). Notices of the AMS. 2014. Retrieved February 20, 2020.
Lawrence Guth of the Massachusetts Institute of Technology has been awarded the 2013 Salem Prize for his "major contributions to geometry and combinatorics. His brilliant insights led to the solution of old problems and the introduction of powerful new techniques,” according to the prize citation.
- "Simons Investigator Awardees". Simons Foundation. Archived from the original on 6 August 2017. Retrieved 11 September 2017.
- Clay Research Award 2015
- 2019 Class of the Fellows of the AMS, American Mathematical Society, retrieved 2018-11-07
- @theNASciences (February 20, 2020). "The inaugural recipient for the Maryam Mirzakhani Prize in Mathematics, Larry Guth of @MIT" (Tweet). Retrieved February 20, 2020 – via Twitter.
- "2020 Maryam Mirzakhani Prize in Mathematics". NAS. February 20, 2020. Retrieved February 20, 2020.
Guth is receiving the $20,000 prize 'for developing surprising, original, and deep connections between geometry, analysis, topology, and combinatorics, which have led to the solution of, or major advances on, many outstanding problems in these fields.' The Mirzakhani prize honors exceptional contributions to the mathematical sciences by a mid-career mathematician
- Tao, Terence (2018). "Review of Polynomial methods in combinatorics by Larry Guth". 55: 103–107. doi:10.1090/bull/1586. Cite journal requires