# Larry Guth

Room 2-278

Phone x3-4326

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Professor of Mathematics

Metric geometry, harmonic analysis, extremal combinatorics

Larry Guth is a Professor of Mathematics. He 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 MIT 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."