Max Engelstein

CLE Moore Instructor/NSF Postdoc

Department of Mathematics

MIT

Office: 2-174

Email: username@mit.edu. maxe is my username.

About

I am a CLE Moore Instructor and an NSF Postdoc at MIT broadly interested in applications of harmonic analysis and geometric measure theory to PDE. At MIT my sponsoring scientist is Professor David Jerison and most of my research here has been on problems related to free boundary regularity. I spent the Spring of 2017 at MSRI as a postdoc in the Harmonic Analysis program, where my mentor was Professor Svitlana Mayboroda.

Up until June of 2016, I was a graduate student at the University of Chicago and my advisor was Professor Carlos Kenig. You can find my thesis, on free boundary problems for harmonic and caloric measure, here (and you can see a picture of me defending said thesis to the right). While in graduate school I spent several months at the University of Washington, working with Professor Tatiana Toro

My CV is available pdf.

with Matthew Badger and Tatiana Toro

*Analysis & PDE.* **Vol. 10**, 2017, pp 1455-1495. Published Version (behind paywall). ArXiv.

[Abstract ±]

- The Least-Perimeter Partition of a Sphere into Four Equal Areas,
*J. Disc. Comp. Geom.***44**, 2010, pp 645-653. Published Version (behind paywall). arXiv:0903.4097. - Asymptotics of Perimeter-Minimizing Partitions (with Quinn Maurmann et al.),
*Can. Math. Bull.***53**, 2010, pp 516-525. Published Version (behind paywall). - Isoperimetric Problems on the sphere and on surfaces with density (with Anthony Marcuccio et al.),
*NYJM***15**, 2009, pp 97-123. Published Version.

- Parabolic NTA domains in
**R**^{2}. (AMS Sectional Meeting Talk) - AMS Sectional Meeting, Special Session on Geometric Aspects of Harmonic Analysis, September 2016.
- The structure of the singular set of a two-phase free boundary problem for harmonic measure. (AMS Sectional Meeting Talk)
- AMS Sectional Meeting, Special Session on Geometric Measure Theory and Its Applications, March 2016.
- A Two-Phase Problem for Harmonic Measure (Seminar Talk)
- Seattle Rainwater Seminar. University of Washington, Seattle. Seattle, WA. March 2015.

I am not teaching the 2017-2018 Academic year. However, if you are an MIT undergraduate interested in doing a reading/research project and want to learn some cool analysis, please feel free to contact me.

Together with Murat Akman, I am co-organizing the AMS Special Section on *PDE in Rough Domains* at Northeastern University, Boston, MA April 21-22, 2018.

While applying to the NSF Postdoc, I found it very helpful to read several previous proposals which other mathematicians made available on their websites. In that spirit, here is my NSF Summary and NSF Description from my sucessful NSF Postdoc Application in the Fall of 2016. I also applied unsucessfully for the NSF postdoc in the fall of 2015, but seem to have lost those materials.