Larry Guth's homepage
Fall 2017, I am teaching 18.118, a topics course in Fourier analysis about decoupling theory.
Spring 2016, I am teaching 18.156,
Real Analysis. See also the Open Courseware website for the course 18.156 on OCW.
I am also teaching a unit on decoupling in Math 158: Topics in analysis. There is a little webpage for the unit here: Decoupling unit.
Fall 2015, I am teaching 18.103,
Spring 2015, I am teaching 18.156,
Fall 2014, I am teaching 18.103,
Spring 2014, I am teaching 18.156,
Real Analysis, and 18.979,
Geometry Seminar (a reading course on classic papers in
Fall 2013, I am teaching 18.821, Math Project Lab. If you
are in the course, you can access the course info on Stellar.
Spring 2013, I am
teaching 18.966 Geometry
Fall 2012, I am teaching a topics class on the
polynomial method. See also the Open Courseware website for the course Polynomial methods in combinatorics on OCW. I wrote a book developing the notes for this course, which is available through the AMS here Polynomial methods in combinatorics .
In Fall 2014, I am teaching a mini-course / seminar on decoupling and multilinear estimates in harmonic analysis.
Here is a short webpage related to the seminar: Decoupling seminar .
My research interests are in metric geometry, combinatorial
geometry, and harmonic analysis.
Metric geometry refers to estimates about lengths, areas,
volumes, distances, etc. It includes
the study of isoperimetric inequalities and systolic
inequalities. I'm particularly interested in
quantitative geometric estimates that are related to
topology. In combinatorial geometry, I'm
interested in estimates about the intersection patterns of
simple shapes like lines and circles.
This area includes the Szemeredi-Trotter theorem, and the unit
distance problem. In harmonic
analysis, I'm interested in Kakeya-type inequalities about how
simple shapes like cylinders can
overlap in Euclidean space, and in related estimates in Fourier
analysis or PDE.
My papers are available on the arxiv here.
systolic geometry This is a survey paper on systolic
geometry that I gave at the 2010 ICM. There's also a slightly
longer version which you can read here.
waist inequality in Gromov's work This is a short
expository essay that I contributed to a survey about Gromov's
work in an Abel prize volume. It discusses some of his
recent work. The waist inequality is a fundamental
geometric inequality that I think deserves to be more popular.
Recent progress in quantitative
topology This paper discusses the problem of understanding the most efficient way of
contracting a contractible map, where efficiency is measured using the Lipschitz constant of a map.
It describes a recent breakthrough by Chambers, Dotterrer, Ferry, Manin, and Weinberger.
of polynomials in combinatorics This is an expository
essay about recent applications of the `polynomial method' in
combinatorics. I wrote it as a contribution to the new
edition of the book The
Mathematics of Paul Erdos, edited by R. Graham and J.
Namboodiri Lectures. I am giving the 2015 Namboodiri lectures at the University of Chicago on ``Polynomial methods in combinatorics and Fourier analysis''. Here are notes for the lectures. There are separate files with the figures for each lectures.
Lecture 1: Introduction to the polynomial method and incidence geometry. Figures for Lecture 1.
Lecture 2: The distinct distance problem . Figures for Lecture 2.
Lecture 3: Incidence geometry and polynomials in Fourier analysis. Figures for Lecture 3.