Professor of Mathematics, Massachusetts Institute of Technology

Massachusetts Institute of Technology

77 Massachusetts Ave, Room E17-308

Cambridge, MA 02139-4307

USA

(617) 253-4394

jerison (at) math (dot) mit (dot) edu

This site is under construction. For now, Dec, 2014, a few preprints are available under publications.

My main research interests are Fourier analysis and partial differential equations. I am especially interested in free boundary problems. Recently, I have also been working on internal Diffusion Limited Aggregation (internal DLA), a stochastic growth model.

- Structure of one-phase free boundaries in the plane , joint with Nikola Kamburov, Posted 12 December, 2014 arXiv:1412.4106
- Optimal function spaces for continuity of the Hessian determinant as a distribution , joint with Eric Baer, Posted 19 November, 2014 arXiv:1411.5303
- Singularities of the wave trace for the Friedlander model , joint with Yves Colin de Verdiere and Victor Guillemin, Posted 24 Dec 2014 arXiv:1412.7592
- Some remarks on stability of cones for the one-phase free boundary problem , joint with Ovidiu Savin, Posted 28 October, 2014 arXiv:1410.7463
- A free boundary problem for the localization of eigenfunctions , joint with Guy David, Marcel Filoche, and Svitlana Mayboroda, Posted 25 June, 2014 arXiv:1406.6596
- Quantitative stability for the Brunn-Minkowski inequality , joint with Alessio Figalli; to be posted to arXiv 25 Dec, 2014, arXiv:xx
- Quantitative stability for sumsets in R^n , joint with Alessio Figalli, to appear in JEMS; Posted 24 Dec, 2014, arXiv:1412.7586
- Existence and regularity of higher critical points in elliptic free boundary problems , joint with Kanishka Perera, Posted 26 Dec, 2014 arXiv:1412.7976
- How to recognize convexity of a set from its marginals , joint with Alessio Figalli, (Journal Func. Anal. 266, no. 3, 1685-1701, 2014) to be posted to arXiv 25 Dec, 2014 arXiv:xx
- Internal DLA for cylinders , joint with Lionel Levine and Scott Sheffield, Posted to arXiv 18 Oct, 2013, (to appear in the book Advances in Analysis: The Legacy of Elias M. Stein) arXiv:1310.5063
- A gradient bound for free boundary graphs , joint with Daniela De Silva (to appear in Comm. Pure and Appl. Math. 2011). Posted 23 Sept, 2010 arXiv:1009.4694
- Singularities of the wave trace near cluster points of the length spectrum , joint with Yves Colin de Verdiere and Victor Guillemin. Posted 30 Dec, 2010 arXiv:1101.0099
- Logarithmic fluctuations for internal DLA , joint with Lionel Levine and Scott Sheffield. Posted 12 Oct, 2010 arXiv: 1010.2483
- Internal DLA and the Gaussian free field , joint with Lionel Levine and Scott Sheffield. This is a draft posted on arXiv Dec 31, 2010. A newer, better version was posted Jan 3, 2011 arXiv:1101.0596
- Internal DLA in higher dimensions , joint with Lionel Levine and Scott Sheffield. Posted 15 Dec, 2010, arXiv: 1012.3453

The next preprint concerning internal diffusion-limited aggregation (internal DLA) on a cylinder is the color version of the published text. I would like to correct the record on one point (and will later append a corrected version of the manuscript). On page 28, the preprint mentions that Cyrille Lucas used internal DLA to establish a beautiful result, the existence of the so-called heat ball, a set that gives the mean value property for solutions to heat equation. But the text implicitly downplays the discovery by saying that Lucas carried out a program already known to a number of researchers. In fact, not only were those researchers not able to complete the program, but Lucas found this question and resolved it independently.

18.03 - Differential Equatiions Spring 2013

18.103 - Fourier Analysis and Applications Fall 2013

Open Courseware Single Variable Calculus, 18.01 (Notes problem sets from Fall 2006; videos from Fall 2007)

Open Courseware Multivariable Calculus, 18.02 (Notes and problem sets from Spring 2006)

18.155 Differential Analysis, Fall 2008

RSI - Research Science Institute for high school students, for which I organize the math section

SPUR - Summer Program for Undergraduate Research. I direct this program, which is for MIT undergraduates only.