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.

- 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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