Metric geometry, harmonic analysis, extremal combinatorics
Larry Guth is a Claude E. Shannon Professor of Mathematics, as of July 2019. and a 2021 MacVicar Fellow. Guth did his PhD at MIT in 2005 under the supervision of Tom Mrowka. Following a postdoctoral position at Stanford and a junior faculty appointment at the University of Toronto, he was appointed professor at the Courant Institute in 2011, and joined the MIT math faculty as professor in 2012.
Guth's research interests are in metric geometry, harmonic analysis, and extremal combinatorics. Metric geometry means the study of inequalities involving lengths, areas, and volumes. Some main examples are isoperimetric inequalities and systolic inequalities. The systolic inequality is one focus of Guth's work. Another focus is to find connections between geometric inequalities and topology.
More recently, Guth has done work in harmonic analysis and combinatorics. A lot of this work is related to the Kakeya problem - an open question in Euclidean geometry that connects with restriction-type estimates in Fourier analysis and with
estimates about incidences of lines in extremal combinatorics.
Guth received an Alfred P. Sloan Fellowship in 2010. In 2014, he received the Salem Prize in Mathematics, for outstanding contributions to analysis. He was also named a Simons Investigator by the Simons Foundation. In summer 2015, Guth received the Teaching Prize in Graduate Education by MIT's School of Science, and the Research Prize of the Clay Mathematics Institute. In the fall, Larry was awarded the New Horizons in Mathematics Prize "for ingenious and surprising solutions to long standing open problems in symplectic geometry, Riemannian geometry, harmonic analysis, and combinatorial geometry." In 2018, Larry was elected Fellow of the American Academy of Arts and Sciences. In 2019 he was also selected to be a Fellow of the AMS, and in 2020, 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), “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 Larry was selected for the Margaret MacVicar Faculty 10-year Fellowship, MIT's highest honor for undergraduate teaching. He was also elected Member of the National Academy of Sciences.
In 2010 Larry gave an Invited Address (geometry section) at the International Congress of Mathematicians (ICM); and a Plenary Address at ICM2022.