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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 th ...
.


Education and career

Guth graduated from Yale in 2000, with BS in mathematics. In 2005, he got his PhD in mathematics from 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 th ...
, 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 Institut ...
. 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, th ...
's
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 functions or signals as the superposition of basic waves, and the study of and generalization of the notions of Fourier series and Fourier transforms (i.e. an ex ...
, and
geometric combinatorics Geometric combinatorics is a branch of mathematics in general and combinatorics in particular. It includes a number of subareas such as polyhedral combinatorics (the study of faces of convex polyhedra), convex geometry (the study of convex sets ...
." 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 and, along with Nets Katz, 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 rena ...
in India in 2010, where he spoke about
systolic 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 o ...
. 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, meeting ...
awarded Guth its annual
Salem Prize The Salem Prize, in memory of Raphael Salem, is awarded each year to young researchers for outstanding contributions to the field of analysis. It is awarded by the School of Mathematics at the Institute for Advanced Study in Princeton and was fou ...
, citing his "major contributions to geometry and combinatorics." In 2014 he received a Simons Investigator Award. 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
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, meeting ...
"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 Nat ...
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." In 2021, he was elected member of the US
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 Nat ...
.


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 reduct ...
in cosmology.


Work

*Metaphors in
systolic 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 o ...

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