# David Jerison

## David Jerison

Principal Investigator (WAVE), Department of Mathematics (MIT)### Contact

### Affiliations

#### Biography

David Jerison is Professor of Mathematics at MIT. His research interests are in Fourier analysis and partial differential equations. Jerison has written one dozen articles in top journals (Acta Math, Annals of Math, Inventiones, and Journal of the AMS). With Carlos Kenig, he made fundamental contributions to the theory of Harnack inequalities and harmonic measure in nonsmooth and fractal domains and to the theory of Carleman inequalities.

With John M. Lee, he proved extremal inequalities on the Heisenberg group and solved the CR Yamabe problem on Cauchy-Riemann (CR) manifolds. He developed new estimates for the Monge-Amp`ere equation and for harmonic measure in convex domains to resolve the problem of finding a polyhedron given the normals to the faces and their harmonic measures. This led him to inverse problems, analogous to the Minkowski problem, for first variation of capacity or the ground state Dirichlet eigenvalue of a convex domain in place of the volume functional used in the Minkowski problem. In 2012, with Lionel Levine and Scott Sheffield, he resolved a 25-year old problem concerning the fluctuations of a growth process related to Brownian motion and harmonic measure known as internal Diffusion-Limited Aggregation (internal DLA). A large fraction of his work is dedicated to understanding the shape of Neumann and Dirichlet eigenfunctions and related questions concerning the regularity, geometry, and topology of free boundaries and minimal surfaces.

Jerison was awarded an Alfred P. Sloan Research Fellowship, 1985-87, and an NSF Presidential Young Investigator Award, 1985-90. He was elected a Fellow of the American Academy of Arts and Sciences in 1999. He was selected as a MacVicar Faculty Fellow 2004-14 and MIT Class of 1960 Fellow, 2014-16. He became a Fellow of the American Mathematical Society (AMS) in 2012. He and Lee received the Bergman Prize of 2012, awarded by a committee of the AMS for their work in CR geometry. In 2018, he was awarded a Simons Fellowship in Mathematics. He has delivered many named lecture series, most recently the Ordway Distinguished Lectures at U. Minnesota in 2016 and the Zhu Khezhen Lectures at Zhejiang University in 2017. He gave an invited address at the AMS summer meeting in Salt Lake City in 1987 and an invited address at the International Congress of Mathematicians in Zurich in 1994. He was an editor of Inventiones 2000-2009 and is currently an editor of the Cambridge Journal of Mathematics and an associate editor of the Duke Mathematical Journal. He served on the 2010 Advisory Board for Mathematics of the Ministry of Education of Israel. He has served on many AMS committees and is currently Vice President of the AMS.

Read more on Dr. Jerison's MIT homepage.

- Fourier analysis and partial differential equations
- Free boundary problems.
- Recently working on internal Diffusion Limited Aggregation (internal DLA), a stochastic growth model.

#### Honors and Awards

See biography for this information

#### Selected Publications

- 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