I am currently Evarist Giné
Assistant Research Professor at the University of Connecticut.
Before arriving at UConn I was a postdoctoral researcher at the
Instituto de Ciencias Matematicas, Madrid, Spain where I worked with José María Martell.
I did my PhD at the University of Kentucky
with John Lewis in 2014.
I also received postdoctoral researcher fellowship from Institut Mittag-Leffler,
Stockholm, Sweden to attend the Evolutionary Problems semester in the fall of 2013.
During the spring semester of 2017, I was a postdoctoral fellow at the
Mathematical Sciences Research Institute, Berkeley, CA to participate
in the Harmonic Analysis program where my mentor was Tatiana Toro.
My research interests are Analysis of PDEs, Potential Theory, Geometric Measure Theory.
You can find my CV here
or my Google Scholar page.
This year, I am co-organizer for the
Analysis Learning Seminar at UConn.
I am also co-organizing the AMS Special section on Regularity of PDEs on Rough Domains at Northeastern University, Boston, MA April 21-22, 2018.
Publications and Preprints
On the Brunn-Minkowski inequality for nonlinear Logarithmic capacity.
(with Olli Saari)
The Brunn-Minkowski inequality and a Minkowski problem for nonlinear capacity.
(with Jasun Gong, Jay Hineman, John Lewis, and Andrew Vogel).
Submitted (2017), 105 pages.
Absolute continuity of harmonic measure for domains with lower regular boundaries.
(with Jonas Azzam, and Mihalis Mourgoglou).
Submitted (2016), 45 pages.
Rectifiability, interior approximation and Harmonic Measure.
(with Simon Bortz, Steve Hofmann, and José María Martell).
Submitted (2016), 18 pages.
On the absolute continuity of p-harmonic measure and surface measure in Reifenberg flat domains.
Pacific Journal of Math. 286 (2017), no. 1, 25-37.
[Published Version, arXiv, Abstract]
$\sigma$-finiteness of elliptic measures for quasilinear elliptic PDE in space.
(with John Lewis and
Advances in Mathematics 309 (2017), 512-557.
Rectifiability and elliptic measures on 1-sided NTA domains with Ahlfors-David regular boundaries.
(with Matthew Badger, and Steve Hofmann, and José María Martell).
Trans. Amer. Math. Soc. 369 (2017), no. 8, 5711-5745.
Hausdorff dimension and $\sigma$-finiteness of $p$-harmonic measures in space when $p\geq n$.
(with John Lewis and Andrew Vogel).
Nonlinear Anal. 129 (2015), 198-216.
On the dimension of a certain measure in the plane.
Ann. Acad. Sci. Fenn. Math., 39 (2014), 187-209.
Abstract, Slide, Video]
On the logarithm of the minimizing integrand for certain variational problems in two dimensions.
John Lewis and Andrew Vogel),
Analysis and Mathematical Physics, March 2012, Volume 2, Issue 1, pp 79-88.