CLE Moore Instructor/NSF Postdoc
Department of Mathematics
Office: 2-174
Email: maxe is my username.


I am a CLE Moore Instructor (and, as of July, 2017, an NSF Postdoc) at MIT broadly interested in applications of harmonic analysis and geometric measure theory to PDE. At MIT, I am working mostly with Professor David Jerison and on problems related to free boundary regularity. I am spending the Spring of 2017 at MSRI as a postdoc in the Harmonic Analysis program.

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).

My CV is available pdf.


Free Boundary Regularity for Almost-Minimizers

with Guy David and Tatiana Toro
Submitted. 2017. ArXiv. 70 pages.
[Abstract ±]

Quantitative Stratification for Some Free-Boundary Problems

with Nick Edelen
Submitted. 2017. ArXiv. 30 pages.
[Abstract ±]

Parabolic NTA Domains in R2

Submitted 2016. ArXiv. 12 pages.
[Abstract ±]

A Free Boundary Problem for the Parabolic Poisson Kernel

Advances in Math. to appear. ArXiv. 91 pages.
[Abstract ±]

Structure of Sets which are Well Approximated by Zero Sets of Harmonic Polynomials

with Matthew Badger and Tatiana Toro
Submitted. 2015. ArXiv. 41 pages.
[Abstract ±]

A Two-Phase Free Boundary Problem For Harmonic Measure

Ann. Sci. de l'ENS. Vol. 49, 2016, pp 859-905. Published Version (behind paywall). ArXiv.
[Abstract ±]

Older Papers (pre-graduate school)

Selected Talks

Parabolic NTA domains in R2. (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 in the Spring of 2017 (I'm at MSRI), and I won't be teaching the 2017-2018 Academic year. However, I am available to supervise MIT undergraduates interested in doing reading/research during the 2017-2018 Academic year. If you want to learn some cool analysis, please feel free to contact me.