Max Engelstein

Assistant Professor

Department of Mathematics

University of Minnesota-Twin Cities

Office: Vincent Hall 230

Email: username@umn.edu. mengelst is my username.

About

I am an Assistant Professor (Tenure Track) at the University of Minnesota, Twin-Cities broadly interested in the interplay between harmonic analysis, geometric measure theory, the calculus of variations and PDE.

Previously, I was a CLE Moore Instructor and an NSF Postdoc at MIT, where my sponsoring scientist is Professor David Jerison. Before that, 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 I spent the Spring of 2017 at MSRI as a postdoc in the Harmonic Analysis program, where my mentor was Professor Svitlana Mayboroda.

Click to See My: [CV [Updated Oct. 22nd 2019] |Research| Teaching/Organizing | Slides and Reports | Travel| Old Materials ]

with Simon Bortz, Max Goering,
Tatiana Toro and Zihui Zhao

*Preprint.* 2019. ArXiv. 42 pages.

[Abstract ±]

with Aapo Kauranen, Martí Prats, Georgios Sakellaris and Yannick Sire

*Submitted.* 2019. ArXiv. 43 pages.

[Abstract ±]

with Luca Spolaor and Bozhidar Velichkov

*Geometry & Topology,* **Vol 23**, 2019, pp 513-540. ArXiv.

[Abstract ±]

with Luca Spolaor and Bozhidar Velichkov

*Duke Math. J. to appear.* 2018. ArXiv. 36 pages.

[Abstract ±]

with Simon Bortz

*Not For Publication. Superseceded by BEGTZ above.* 2017. ArXiv. 25 pages.

[Abstract ±]

with Guy David and Tatiana Toro

*Advances in Math.* **350**, 2019, pp 1109-1192. ArXiv. 70 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.

In the Academic Year of 2019-2020 I am not teaching (and splitting time between Chicago and Minneapolis). If you are a graduate student at UMN interested in the math that I do, please email me.

Together with Mark Allen,
Spencer Becker-Kahn
and Mariana Smit Vega Garcia, I co-organized 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.

- Prairie Analysis Seminar
- Kansas State University, Manhattan, Kansas November 8th-9th, 2019.
- ``Harmonic Analysis and PDE", May 18-22, 2020 at Yonsei University in Seoul, South Korea.
- Special session on elliptic PDEs and geometric variational problems
- AIMS Conference on Dynamical Systems, Differential Equations and Applications, Atlanta June 5-9th, 2020.

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.

**Support/Disclaimer:** I'm partially supported by an NSF Postdoctoral Fellowship and am an Affiliate Scientist with the Simons Collaboration on Waves. Of course, all of the opinions expressed here are my own and don't necessarily represent the views of either the NSF, the Simons Foundation or my employer the University of Minnesota.