Larry Guth | Academic Influence

Why Is Larry Guth Influential?

By Erik J. Larson, PhD

Guth is the Claude Shannon Professor of Mathematics at MIT. He did his Ph.D. in Mathematics at MIT in 2005. Prior to his appointment at MIT, Guth held appointments at New York University’s Courant Institute of Mathematical Sciences and at the University of Toronto.

Guth has wide ranging interests in mathematics, and has proved a number of important results in diverse areas. In 2015, he solved a conjecture put forth by Paul Erdos in 1946 known as the “distinct distances problem.” He is also working on problems in geometry, like the Kakeya set, a set of points in Euclidean geometry with the property of having a unit line segment in every direction.

Guth won the Salem Prize in 2013, and received an Alfred P. Sloan Fellowship in 2010. As of 2019, Guth is Fellow of the American Mathematical Society.

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According to Wikipedia, Lawrence David Guth is a professor of mathematics at the Massachusetts Institute of Technology.Education and career Guth graduated from Yale in 2000, with B.S. in mathematics.In 2005, he got his Ph.D. in mathematics from the Massachusetts Institute of Technology, where he studied geometry of objects with random shapes under the supervision of Tomasz Mrowka.

Larry Guth's Published Works

On the Erdős distinct distances problem in the plane
Bounds on Oscillatory Integral Operators Based on Multilinear Estimates
On the Erdos distinct distance problem in the plane
Proof of the main conjecture in Vinogradov's mean value theorem for degrees higher than three
Algebraic methods in discrete analogs of the Kakeya problem
A restriction estimate using polynomial partitioning
The endpoint case of the Bennett–Carbery–Tao multilinear Kakeya conjecture
Restriction estimates using polynomial partitioning II
Minimax Problems Related to Cup Powers and Steenrod Squares
Symplectic embeddings of polydisks
Quantum error correcting codes and 4-dimensional arithmetic hyperbolic manifolds
On Falconer’s distance set problem in the plane
Polynomial Methods in Combinatorics
Polynomial partitioning for a set of varieties
Volumes of balls in large Riemannian manifolds
A short proof of the multilinear Kakeya inequality
Metaphors in Systolic Geometry
Sharp estimates for oscillatory integral operators via polynomial partitioning.
Generalizations of the Kolmogorov–Barzdin embedding estimates
POINTWISE CONVERGENCE OF SCHRÖDINGER SOLUTIONS AND MULTILINEAR REFINED STRICHARTZ ESTIMATES
Distinct Distance Estimates and Low Degree Polynomial Partitioning
Systolic Inequalities and Minimal Hypersurfaces
Pants Decompositions of Random Surfaces
The Width-Volume Inequality
Algebraic curves, rich points, and doubly-ruled surfaces
Notes on Gromov’s systolic estimate
A sharp Schrodinger maximal estimate in $\mathbb{R}^2$
A sharp Schrödinger maximal estimate in R[superscript 2]
Strichartz estimates for the Schrödinger equation on irrational tori
Polynomial Wolff axioms and Kakeya‐type estimates in R4
Volumes of balls in Riemannian manifolds and Uryson width
Incidence estimates for well spaced tubes
Contraction of Areas vs. Topology of Mappings
Unexpected Applications of Polynomials in Combinatorics
THE WAIST INEQUALITY IN GROMOV ’ S WORK LARRY GUTH
Degree reduction and graininess for Kakeya-type sets in $\mathbb{R}^3$
Small cap decouplings
Area-contracting maps between rectangles
Lipshitz maps from surfaces
Generalizations of the
On the discretized sum-product problem
2-Complexes with Large 2-Girth
Bounds on oscillatory integral operators
Recent progress in quantitative topology
Ruled Surface Theory and Incidence Geometry
A Few Snapshots from the Work of Mikhail Gromov
Improved decoupling for the parabola
Isoperimetric inequalities and rational homotopy invariants
Homotopically non-trivial maps with small k-dilation
A sharp square function estimate for the cone in $\mathbb{R}^3$
Curves in $$\mathbb {R}^4$$R4 and Two-Rich Points
Curves in R 4 and Two-Rich Points.
Directional isoperimetric inequalities and rational homotopy invariants
Area-expanding embeddings of rectangles
2-complexes with large homological systoles
STRAIGHT LINE ORTHOGONAL DRAWINGS OF COMPLETE TERNERY TREES SPUR FINAL PAPER
A family of maps with many small fibers
Minimal number of self-intersections of the boundary of an immersed surface in the plane
Three Applications of Entropy to Gerrymandering
Degree reduction and graininess for Kakeya-type sets in R[superscript 3]
The Bezout theorem
The Hopf volume and degrees of maps between 3-manifolds
The joints problem for matroids
Strichartz estimates for the Schroedinger equation on non-rectangular two-dimensional tori
The Hopf invariant and simplex straightening
Remembering Jean Bourgain (1954–2018)
Amenable groups and smooth topology of 4-manifolds
The polynomial method in error-correcting codes
Sharp superlevel set estimates for small cap decouplings of the parabola
An incidence bound for lines in three dimensions
The Polynomial Method Professor Larry Guth
Combinatorial structure, algebraic structure, and geometric structure
A pr 2 01 8 On the discretized sum-product problem
Optimal homotopies of curves on surfaces
Contraction of Areas vs. Topology of Mappings Publisher Accessed Terms of Use Contraction of Areas vs. Topology of Mappings
On polynomials and linear algebra in combinatorics
Fundamental examples of the polynomial method
Ruled surfaces and projection theory
Northern California Symplectic Geometry Seminar
The polynomial method in differential geometry
A hardness of approximation result in metric geometry
The polynomial method in number theory
Harmonic analysis and the Kakeya problem
A DECOUPLING INEQUALITY FOR SHORT GENERALIZED DIRICHLET SEQUENCES
Decoupling inequalities for short generalized Dirichlet sequences
Curves in $\mathbb{R}^4$ and two-rich points
Incidence geometry in three dimensions

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