Larry Guth

{{Infobox scientist

| name = Larry Guth

| image =

| image_size =

| caption =

| birth_name = Lawrence David Guth

| birth_date = {{birth year and age|1977}}

| birth_place =

| death_date =

| death_place =

| nationality = American

| fields = Mathematics

| workplaces = {{Plainlist|

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| alma_mater = {{Plainlist|

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| doctoral_advisor = Tomasz Mrowka

| doctoral_students = Hong Wang

| thesis_title = Area-contracting maps between rectangles

| thesis_year = 2005

| thesis_url = https://dspace.mit.edu/handle/1721.1/31158

| known_for =

| awards = {{Plainlist|

Salem Prize (2013)
Clay Research Award (2015)
New Horizons in Mathematics Prize (2016)
Bôcher Memorial Prize (2020)
Maryam Mirzakhani Prize (2020)

}}

| parents = Alan Guth {{font|size=90%|(father)}}

| website = {{URL|https://math.mit.edu/~lguth/}}

}}

Lawrence David Guth ({{IPAc-en|g|uː|θ}}; born 1977) is a professor of mathematics at the Massachusetts Institute of Technology.{{cite web|url=https://math.mit.edu/directory/profile.html?pid=1461|title=Larry Guth|work=Directory|publisher=MIT Mathematics|access-date=2025-05-10}}

Education and career

Guth graduated from Yale University in 2000 with a BS in mathematics.{{Cite web | url= https://math.mit.edu/documents/uploads/cv/2015_04_14_CV_lguth.pdf |title=Curriculum Vitae Larry Guth |publisher=MIT Mathematics Department |quote=B.S. Mathematics, Yale University, 2000 |date=2020 |access-date=February 20, 2020}}

In 2005, he received his PhD in mathematics from the Massachusetts Institute of Technology (MIT), where he studied geometry of objects with random shapes under the supervision of Tomasz Mrowka.{{mathgenealogy |name=Lawrence Guth|id=34061}}.

After MIT, Guth went to Stanford as a postdoc and later to the University of Toronto as an assistant professor on a tenure track

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."{{Cite web |url=https://cims.nyu.edu/newsletters/Fall2011.pdf |title=New Faculty: Larry Guth |publisher=Courant Institute of Mathematical Sciences at NYU |quote= He was a postdoc at Stanford and an Assistant Professor at the University of Toronto. He received a Sloan fellowship in 2010. |date=2011 |access-date=February 20, 2020}}

In 2012, Guth moved to MIT, where he is Claude Shannon Professor of Mathematics.

Research

In his research, Guth has strengthened Gromov's systolic inequality for essential manifolds[http://mathandlife.blogspot.com/2009/07/guths-approach-to-gromovs-systolic.html Guth's approach to Gromov's systolic inequality], Shmuel Weinberger, July 18, 2009. and, along with Nets Katz, found a solution to the Erdős distinct distances problem.{{citation|url=http://mathdl.maa.org/mathDL/?pa=mathNews&sa=view&newsId=1062|series=Math In The News|publisher=Mathematical Association of America|title="Distinct Distance Problem in the Plane" Solved|date=March 2, 2011}}. His interests include the Kakeya conjecture and the systolic inequality.

Recognition

Guth won an Alfred P. Sloan Fellowship in 2010.{{Cite web |url=http://www.artsci.utoronto.ca/main/newsitems/five-u-of-t-scientists-awarded-prestigious-sloan-fellowships |title=February 19, 2010 — Five U of T scientists awarded prestigious Sloan Fellowships — Faculty of Arts & Science |access-date=October 23, 2011 |archive-url=https://web.archive.org/web/20120616122908/http://www.artsci.utoronto.ca/main/newsitems/five-u-of-t-scientists-awarded-prestigious-sloan-fellowships |archive-date=June 16, 2012 |url-status=dead }} He was an invited speaker at the International Congress of Mathematicians in India in 2010, where he spoke about systolic geometry.[http://www.math.toronto.edu/cms/assets/MathFiles/Alumni/In-The-News/Newsletters/Files/Newsletter2010.pdf Fall newsletter 2010], Univ. of Toronto mathematics department, retrieved May 26, 2011.[http://www.icm2010.org.in/scientific-program/invited-speakers ICM listing of invited speakers] {{webarchive|url=https://web.archive.org/web/20110717191917/http://www.icm2010.org.in/scientific-program/invited-speakers |date=July 17, 2011 }}, retrieved May 26, 2011.

In 2013, the American Mathematical Society awarded Guth its annual Salem Prize, citing his "major contributions to geometry and combinatorics."{{Cite web |url=https://www.ams.org/notices/201403/rnoti-p296.pdf |title=Guth Awarded 2013 Salem Prize |work=Notices of the AMS |quote=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. |date=2014 |access-date=February 20, 2020}}

In 2014 he received a Simons Investigator Award.{{cite web |url= http://www.simonsfoundation.org/mathematics-and-physical-science/simons-investigators/simons-investigators-awardees |title= Simons Investigator Awardees |publisher= Simons Foundation |access-date= September 11, 2017 |archive-url= https://web.archive.org/web/20170806190912/https://www.simonsfoundation.org/mathematics-and-physical-science/simons-investigators/simons-investigators-awardees/ |archive-date= August 6, 2017 |url-status= dead }}

In 2015, he received the Clay Research Award.[http://www.claymath.org/events/news/2015-clay-research-award Clay Research Award 2015]

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".{{citation|url=https://www.ams.org/profession/ams-fellows/new-fellows|title=2019 Class of the Fellows of the AMS|publisher=American Mathematical Society|access-date=November 7, 2018}}

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."{{cite tweet |author-link= |user=theNASciences |number=1230508007538266112 |date= February 20, 2020|title= The inaugural recipient for the Maryam Mirzakhani Prize in Mathematics, Larry Guth of @MIT|script-title= |trans-title= |language= |retweet= |link= https://twitter.com/theNASciences/status/1230508007538266112|access-date= February 20, 2020}}{{Cite web |url=http://www.nasonline.org/programs/awards/2020-awards/Guth.html |title=2020 Maryam Mirzakhani Prize in Mathematics |publisher=NAS |quote=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 |date=February 20, 2020 |access-date=February 20, 2020}} He was one of three recipients of the 2020 Bôcher Memorial Prize.{{cite journal|title=2020 Bôcher Memorial Prize|date=April 2020 |journal=Notices of the American Mathematical Society|url=https://www.ams.org/journals/notices/202004/rnoti-p546.pdf |volume=67|issue=4|pages=546–549}}. In 2021, he was elected member of the US National Academy of Sciences.{{Cite web|url=http://www.nasonline.org/news-and-multimedia/news/2021-nas-election.html|title=News from the National Academy of Sciences|date=April 26, 2021|access-date=July 2, 2021|quote=Newly elected members and their affiliations at the time of election are: ... Guth, Larry; Claude Shannon Professor, department of mathematics, Massachusetts Institute of Technology, Cambridge}}

Personal

He is the son of Alan Guth, a theoretical physicist known for the theory of inflation in cosmology.{{Cite web |url=https://news.mit.edu/2014/profile-larry-guth-0527 |title=Like father, like son |last=Knight |first=Helen |publisher=MIT News |quote=Guth moved to MIT as a graduate student, where he began studying geometry under the supervision of mathematics professor Tomasz Mrwoka. |date=May 27, 2014 |access-date=February 20, 2020}}

Work

Metaphors in systolic geometry: [http://video.ias.edu/members/guth the video]
{{citation

| last = Guth | first = Larry

| arxiv = math.DG/0610212

| doi = 10.4007/annals.2011.173.1.2

| mr = 2753599

| issue = 1

| journal = Annals of Mathematics

| pages = 51–76

| series = 2nd ser.

| title = Volumes of balls in large Riemannian manifolds

| volume = 173

| year = 2011| s2cid = 1392012

}}.

{{citation

| last1 = Guth | first1 = Larry

| last2 = Katz | first2 = Nets Hawk

| author2link = Nets Hawk Katz

| arxiv = 0812.1043

| doi = 10.1016/j.aim.2010.05.015

| mr = 2680185

| issue = 5

| journal = Advances in Mathematics

| pages = 2828–2839

| title = Algebraic methods in discrete analogs of the Kakeya problem

| volume = 225

| year = 2010| s2cid = 15590454

}}.

{{citation

| last = Guth | first = Larry

| arxiv = 0903.5299

| doi = 10.1007/s00039-010-0052-0

| mr = 2594618

| issue = 6

| journal = Geometric and Functional Analysis

| pages = 1688–1692

| title = Systolic inequalities and minimal hypersurfaces

| volume = 19

| year = 2010| s2cid = 17827200

}}.

{{citation

| last = Guth | first = Larry

| arxiv = 0811.2251

| doi = 10.1007/s11511-010-0055-6

| mr = 2746348

| issue = 2

| journal = Acta Mathematica

| pages = 263–286

| title = The endpoint case of the Bennett–Carbery–Tao multilinear Kakeya conjecture

| volume = 205

| year = 2010| s2cid = 16258342

}}.

{{citation

| last = Guth | first = Larry

| arxiv = math/0702066

| doi = 10.1007/s00039-009-0710-2

| mr = 2491695

| issue = 6

| journal = Geometric and Functional Analysis

| pages = 1917–1987

| title = Minimax problems related to cup powers and Steenrod squares

| volume = 18

| year = 2009| s2cid = 10402235

}}.

{{citation

| last = Guth | first = Larry

| arxiv = 0709.1957

| doi = 10.1007/s00222-007-0103-9

| mr = 2393077

| issue = 3

| journal = Inventiones Mathematicae

| pages = 477–489

| title = Symplectic embeddings of polydisks

| volume = 172

| year = 2008| bibcode = 2008InMat.172..477G

| s2cid = 18065526

}}.

{{citation

| last = Guth | first = Larry

| arxiv = math/0609569

| doi = 10.1007/s00039-007-0628-5

| mr = 2373013

| issue = 4

| journal = Geometric and Functional Analysis

| pages = 1139–1179

| title = The width-volume inequality

| volume = 17

| year = 2007| s2cid = 16014518

}}.

{{citation

| first1 = Larry

| last1 = Guth

| first2 = Nets Hawk

| last2 = Katz

| author2link = Nets Hawk Katz

| journal = Annals of Mathematics

| doi = 10.4007/annals.2015.181.1.2

| title = On the Erdős distinct distance problem on the plane

| year = 2015

| pages = 155–190

| volume = 181

| issue = 1

| arxiv = 1011.4105

| mr=3272924| s2cid = 43051852

}}

{{cite book|last1=Guth|first1=Larry|title=Polynomial Methods in Combinatorics|publisher=American Mathematical Society|year=2016|isbn=978-1-4704-2890-7|url=http://bookstore.ams.org/ulect-64/}}{{cite journal

| last = Tao | first = Terence | author-link = Terence Tao

| date = August 2017

| doi = 10.1090/bull/1586 | doi-access = free

| issue = 1

| journal = Bulletin of the American Mathematical Society

| pages = 103–107

| title = Book Review: Polynomial methods in combinatorics

| volume = 55}}