Larry Guth

Last updated

Larry Guth
Born
Lawrence David Guth

1977 (age 46–47)
NationalityAmerican
Alma mater
Parent Alan Guth (father)
Awards
Scientific career
FieldsMathematics
Institutions
Thesis Area-contracting maps between rectangles  (2005)
Doctoral advisor Tomasz Mrowka
Website math.mit.edu/~lguth/

Lawrence David Guth (born 1977) is a professor of mathematics at the Massachusetts Institute of Technology. [1]

Contents

Education and career

Guth graduated from Yale in 2000, with BS in mathematics. [2]

In 2005, he got his PhD in mathematics from the Massachusetts Institute of Technology, where he studied geometry of objects with random shapes under the supervision of Tomasz Mrowka. [3] [4]

After MIT, Guth went to Stanford as a postdoc, and later to the University of Toronto as an Assistant Professor. [5]

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." [5]

In 2012, Guth moved to MIT, where he is Claude Shannon Professor of Mathematics. [6]

Research

In his research, Guth has strengthened Gromov's systolic inequality for essential manifolds [7] and, along with Nets Katz, found a solution to the Erdős distinct distances problem. [8] His interests include the Kakeya conjecture and the systolic inequality.

Recognition

Guth won an Alfred P. Sloan Fellowship in 2010. [9] He was an invited speaker at the International Congress of Mathematicians in India in 2010, where he spoke about systolic geometry. [10] [11]

In 2013, the American Mathematical Society awarded Guth its annual Salem Prize, citing his "major contributions to geometry and combinatorics." [12]

In 2014 he received a Simons Investigator Award. [13] In 2015, he received the Clay Research Award. [14]

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". [15]

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." [16] [17] He was one of three recipients of the 2020 Bôcher Memorial Prize. [18] In 2021, he was elected member of the US National Academy of Sciences . [19]

Personal

He is the son of Alan Guth, a theoretical physicist known for the theory of inflation in cosmology. [4]

Work

Related Research Articles

<span class="mw-page-title-main">Timothy Gowers</span> British mathematician

Sir William Timothy Gowers, is a British mathematician. He is Professeur titulaire of the Combinatorics chair at the Collège de France, and director of research at the University of Cambridge and Fellow of Trinity College, Cambridge. In 1998, he received the Fields Medal for research connecting the fields of functional analysis and combinatorics.

<span class="mw-page-title-main">Kakeya set</span> Shape containing unit line segments in all directions

In mathematics, a Kakeya set, or Besicovitch set, is a set of points in Euclidean space which contains a unit line segment in every direction. For instance, a disk of radius 1/2 in the Euclidean plane, or a ball of radius 1/2 in three-dimensional space, forms a Kakeya set. Much of the research in this area has studied the problem of how small such sets can be. Besicovitch showed that there are Besicovitch sets of measure zero.

<span class="mw-page-title-main">Jean Bourgain</span> Belgian mathematician (1954–2018)

Jean Louis, baron Bourgain was a Belgian mathematician. He was awarded the Fields Medal in 1994 in recognition of his work on several core topics of mathematical analysis such as the geometry of Banach spaces, harmonic analysis, ergodic theory and nonlinear partial differential equations from mathematical physics.

<span class="mw-page-title-main">Terence Tao</span> Australian–American mathematician (born 1975)

Terence Chi-Shen Tao is an Australian mathematician. He is a professor of mathematics at the University of California, Los Angeles (UCLA), where he holds the James and Carol Collins chair. His research includes topics in harmonic analysis, partial differential equations, algebraic combinatorics, arithmetic combinatorics, geometric combinatorics, probability theory, compressed sensing and analytic number theory.

<span class="mw-page-title-main">Ben Green (mathematician)</span> British mathematician (born 1977)

Ben Joseph Green FRS is a British mathematician, specialising in combinatorics and number theory. He is the Waynflete Professor of Pure Mathematics at the University of Oxford.

<span class="mw-page-title-main">Systolic geometry</span> Form of differential geometry

In mathematics, systolic geometry is the study of systolic invariants of manifolds and polyhedra, as initially conceived by Charles Loewner and developed by Mikhail Gromov, Michael Freedman, Peter Sarnak, Mikhail Katz, Larry Guth, and others, in its arithmetical, ergodic, and topological manifestations. See also Introduction to systolic geometry.

<span class="mw-page-title-main">Maryam Mirzakhani</span> Iranian mathematician (1977–2017)

Maryam Mirzakhani was an Iranian mathematician and a professor of mathematics at Stanford University. Her research topics included Teichmüller theory, hyperbolic geometry, ergodic theory, and symplectic geometry. On 13 August 2014, Mirzakhani was honored with the Fields Medal, the most prestigious award in mathematics, becoming the first woman to win the prize, as well as the first Iranian. The award committee cited her work in "the dynamics and geometry of Riemann surfaces and their moduli spaces".

In the mathematical field of Riemannian geometry, M. Gromov's systolic inequality bounds the length of the shortest non-contractible loop on a Riemannian manifold in terms of the volume of the manifold. Gromov's systolic inequality was proved in 1983; it can be viewed as a generalisation, albeit non-optimal, of Loewner's torus inequality and Pu's inequality for the real projective plane.

<span class="mw-page-title-main">Introduction to systolic geometry</span> Non-technical introduction to systolic geometry

Systolic geometry is a branch of differential geometry, a field within mathematics, studying problems such as the relationship between the area inside a closed curve C, and the length or perimeter of C. Since the area A may be small while the length l is large, when C looks elongated, the relationship can only take the form of an inequality. What is more, such an inequality would be an upper bound for A: there is no interesting lower bound just in terms of the length.

In mathematics, arithmetic combinatorics is a field in the intersection of number theory, combinatorics, ergodic theory and harmonic analysis.

<span class="mw-page-title-main">Leon Simon</span> Australian mathematician (born 1945)

Leon Melvyn Simon, born in 1945, is a Leroy P. Steele Prize and Bôcher Prize-winning mathematician, known for deep contributions to the fields of geometric analysis, geometric measure theory, and partial differential equations. He is currently Professor Emeritus in the Mathematics Department at Stanford University.

Mikhail "Mischa" Gershevich Katz is an Israeli mathematician, a professor of mathematics at Bar-Ilan University. His main interests are differential geometry, geometric topology and mathematics education; he is the author of the book Systolic Geometry and Topology, which is mainly about systolic geometry. The Katz–Sabourau inequality is named after him and Stéphane Sabourau.

The Maryam Mirzakhani Prize in Mathematics is awarded by the U.S. National Academy of Sciences "for excellence of research in the mathematical sciences published within the past ten years." Named after the Iranian mathematician Maryam Mirzakhani, the prize has been awarded every four years since 1988.

Alex Eskin is an American mathematician. He is the Arthur Holly Compton Distinguished Service Professor in the Department of Mathematics at the University of Chicago. His research focuses on rational billiards and geometric group theory.

Nets Hawk Katz is the W.L. Moody Professor of Mathematics at Rice University. He was a professor of mathematics at Indiana University Bloomington until March 2013 and the IBM Professor of Mathematics at the California Institute of Technology until 2023.

Andrea Malchiodi is an Italian mathematician who is active in the fields of partial differential equations and calculus of variations, with several contributions to geometric analysis.

<span class="mw-page-title-main">Tamar Ziegler</span> Israeli mathematician

Tamar Debora Ziegler is an Israeli mathematician known for her work in ergodic theory, combinatorics and number theory. She holds the Henry and Manya Noskwith Chair of Mathematics at the Einstein Institute of Mathematics at the Hebrew University.

<span class="mw-page-title-main">Xiaonan Ma</span> Chinese mathematician

Xiaonan Ma is a Chinese mathematician working in global analysis and local index theory.

In mathematics, the polynomial method is an algebraic approach to combinatorics problems that involves capturing some combinatorial structure using polynomials and proceeding to argue about their algebraic properties. Recently, the polynomial method has led to the development of remarkably simple solutions to several long-standing open problems. The polynomial method encompasses a wide range of specific techniques for using polynomials and ideas from areas such as algebraic geometry to solve combinatorics problems. While a few techniques that follow the framework of the polynomial method, such as Alon's Combinatorial Nullstellensatz, have been known since the 1990s, it was not until around 2010 that a broader framework for the polynomial method has been developed.

References

  1. ↑ https://math.mit.edu/directory/profile.php?pid=1461 MIT Math Department profile of Larry Guth
  2. ↑ "Curriculum Vitae Larry Guth" (PDF). MIT Mathematics Department. 2020. Retrieved February 20, 2020. B.S. Mathematics, Yale University, 2000
  3. ↑ Lawrence Guth at the Mathematics Genealogy Project.
  4. 1 2 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.
  5. 1 2 "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.
  6. ↑ "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)
  7. ↑ Guth's approach to Gromov's systolic inequality, Shmuel Weinberger, July 18, 2009.
  8. ↑ "Distinct Distance Problem in the Plane" Solved, Math In The News, Mathematical Association of America, March 2, 2011.
  9. ↑ "February 19, 2010 — Five U of T scientists awarded prestigious Sloan Fellowships — Faculty of Arts & Science". Archived from the original on June 16, 2012. Retrieved October 23, 2011.
  10. ↑ Fall newsletter 2010, Univ. of Toronto mathematics department, retrieved May 26, 2011.
  11. ↑ ICM listing of invited speakers Archived July 17, 2011, at the Wayback Machine , retrieved May 26, 2011.
  12. ↑ "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.
  13. ↑ "Simons Investigator Awardees". Simons Foundation. Archived from the original on August 6, 2017. Retrieved September 11, 2017.
  14. ↑ Clay Research Award 2015
  15. ↑ 2019 Class of the Fellows of the AMS, American Mathematical Society , retrieved November 7, 2018
  16. ↑ @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.
  17. ↑ "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
  18. ↑ "2020 Bôcher Memorial Prize" (PDF). Notices of the American Mathematical Society. 67 (4): 546–549. April 2020..
  19. ↑ "News from the National Academy of Sciences". April 26, 2021. Retrieved July 2, 2021. 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
  20. ↑ Tao, Terence (August 2017). "Book Review: Polynomial methods in combinatorics". Bulletin of the American Mathematical Society. 55 (1): 103–107. doi: 10.1090/bull/1586 .
This page is based on this Wikipedia article
Text is available under the CC BY-SA 4.0 license; additional terms may apply.
Images, videos and audio are available under their respective licenses.