Lawrence David Guth (born 1977) is a professor of mathematics at the

Massachusetts Institute of Technology The Massachusetts Institute of Technology (MIT) is a private land-grant research university in Cambridge, Massachusetts. Established in 1861, MIT has played a key role in the development of modern technology and science, and is one of the ...

Education and career

Guth graduated from Yale in 2000, with BS in mathematics. In 2005, he got his PhD in mathematics from the

, where he studied geometry of objects with random shapes under the supervision of

Tomasz Mrowka Tomasz Mrowka (born September 8, 1961) is an American mathematician specializing in differential geometry and gauge theory. He is the Singer Professor of Mathematics and former head of the Department of Mathematics at the Massachusetts Institu ...

. 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 New York University (NYU) is a private research university in New York City. Chartered in 1831 by the New York State Legislature, NYU was founded by a group of New Yorkers led by then-Secretary of the Treasury Albert Gallatin. In 1832, the ...

Courant Institute of Mathematical Sciences The Courant Institute of Mathematical Sciences (commonly known as Courant or CIMS) is the mathematics research school of New York University (NYU), and is among the most prestigious mathematics schools and mathematical sciences research cente ...

hired Guth as a professor, listing his areas of interest as "

metric geometry In mathematics, a metric space is a set together with a notion of ''distance'' between its elements, usually called points. The distance is measured by a function called a metric or distance function. Metric spaces are the most general settin ...

harmonic analysis Harmonic analysis is a branch of mathematics concerned with the representation of Function (mathematics), functions or signals as the Superposition principle, superposition of basic waves, and the study of and generalization of the notions of Fo ...

, and geometric combinatorics." 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 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 1 ...

and, along with

Nets Katz Nets Hawk Katz is the IBM Professor of Mathematics at the California Institute of Technology. He was a professor of Mathematics at Indiana University Bloomington until March 2013. Katz earned a B.A. in mathematics from Rice University in 1990 at t ...

, found a solution to the

Erdős distinct distances problem In discrete geometry, the Erdős distinct distances problem states that every set of points in the plane has a nearly-linear number of distinct distances. It was posed by Paul Erdős in 1946 and almost proven by Larry Guth and Nets Katz in 2015. ...

. His wide-ranging interests include the Kakeya conjecture and the systolic inequality.

Recognition

Guth won an Alfred P. Sloan Fellowship in 2010. He was an invited speaker at the

International Congress of Mathematicians The International Congress of Mathematicians (ICM) is the largest conference for the topic of mathematics. It meets once every four years, hosted by the International Mathematical Union (IMU). The Fields Medals, the Nevanlinna Prize (to be rename ...

in India in 2010, where he spoke about systolic geometry. In 2013, the

American Mathematical Society The American Mathematical Society (AMS) is an association of professional mathematicians dedicated to the interests of mathematical research and scholarship, and serves the national and international community through its publications, meetings, ...

awarded Guth its annual Salem Prize, citing his "major contributions to geometry and combinatorics." In 2014 he received a

Simons Investigator Award The Simons Foundation is a private foundation established in 1994 by Marilyn and James Harris Simons, Jim Simons with offices in New York City. As one of the largest charitable organizations in the US with assets of over $5 billion in 2022, the ...

. In 2015, he received the

Clay Research Award __NOTOC__ The Clay Research Award is an annual award given by the Oxford-based Clay Mathematics Institute to mathematicians to recognize their achievement in mathematical research. The following mathematicians have received the award: {, class=" ...

. He was included in the 2019 class of fellows of the

"for contributions to harmonic analysis, combinatorics and geometry, and for exposition of high level mathematics". On February 20, 2020, the

National Academy of Sciences The National Academy of Sciences (NAS) is a United States nonprofit, non-governmental organization. NAS is part of the National Academies of Sciences, Engineering, and Medicine, along with the National Academy of Engineering (NAE) and the Nati ...

announced that Guth is the first winner of their new $20,000

Maryam Mirzakhani Maryam Mirzakhani ( fa, مریم میرزاخانی, ; 12 May 1977 – 14 July 2017) was an Iranian mathematician and a professor of mathematics at Stanford University. Her research topics included Teichmüller theory, hyperbolic geometry, ...

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." In 2021, he was elected member of the US

Personal

He is the son of

Alan Guth Alan Harvey Guth (; born February 27, 1947) is an American theoretical physicist and cosmologist. Guth has researched elementary particle theory (and how particle theory is applicable to the early universe). He is Victor Weisskopf Professor of ...

, a physicist known for the theory of

inflation In economics, inflation is an increase in the general price level of goods and services in an economy. When the general price level rises, each unit of currency buys fewer goods and services; consequently, inflation corresponds to a reductio ...

in cosmology.

Work

*Metaphors in systolic geometry
the video
*. *. *. *. *. *. *. * *

References

{{DEFAULTSORT:Guth, Larry Living people 20th-century American mathematicians Massachusetts Institute of Technology School of Science alumni University of Toronto faculty Geometers Courant Institute of Mathematical Sciences faculty 1977 births Simons Investigator Place of birth missing (living people) Fellows of the American Mathematical Society Yale College alumni 21st-century American mathematicians Members of the United States National Academy of Sciences