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 the interplay between harmonic analysis, geometric measure theory, the calculus of variations and 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

Click to See My: [CV [Updated Oct. 8th 2018] |Research| Teaching/Organizing | Slides and Reports | Travel| Old Materials ]

with Luca Spolaor and Bozhidar Velichkov

*Geometry & Topology,* to appear. ArXiv. 19 pages.

[Abstract ±]

with Nick Edelen

*Transactions of the AMS.* **Vol 371**, 2019, pp 2043-2072. ArXiv. 30 pages.

[Abstract ±]

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.

- Geometry and the Dirichlet Problem in Any Co-Dimension (An Introduction to Harmonic Measure for Physcists and Engineers)
- Simon's Foundation Collaboration on the Localization of Waves, Workshop on the Spectral Properties of Disordered Systems, January 2019.
- An Epiperimetric Approach to Isolated Singularities (Oberwolfach Extended Abstract)
- Oberwolfach, Calculus of Variations Workshop, July-August 2018.
- Regularized Distance and Harmonic Measure in Co-Dimension Greater than One (Seminar Talk)
- PCMI, Harmonic Analysis Research Program Seminar, July 2018.
- 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.

In the fall of 2018 I am teaching 18.100Q, Communications Intensive Real Analysis at MIT. Please check the stellar site here for more info (MIT login required).

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 Mark Allen,
Spencer Becker-Kahn
and Mariana Smit Vega Garcia, I am co-organizing the AMS Special Section on *Interactions between Geometric Measure Theory, PDE, and Harmonic Analysis* at the University of Hawaii, Manoa, HI March 22-24, 2019.

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

- Workshop on Spectral Properties of Disordered Systems
- Paris, France January 9th-11th, 2019.
- Geometric and Harmonic Analysis (giving a minicourse)
- University of Connecticut, CT March 29th-31st, 2019.

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.