Department of Mathematics |

My current research focuses on elliptic and parabolic integro-differential problems. In recent years this area has seen an increased number of publications with tools ranging from probability to analysis. My contributions belong to the analytical perspective but I am also very interested in learning new techniques. I wrote my PhD thesis on 2013 at the University of Texas in Austin under the supervision of Luis Caffarelli. I have worked on regularity estimates for viscosity solutions of fully nonlinear integro-differential parabolic equations, variational problems involving free boundaries and asymptotic shape theorems for queueing models.

- with Nestor Guillén
**From the free boundary condition for Hele-Shaw to a fractional parabolic equation**. - with Dennis Kriventsov
**Further Time Regularity for Non-Local, Fully Non-Linear Parabolic Equations**. (CPAM) - with Dennis Kriventsov
**Further time regularity for fully non-linear parabolic equations**. (Math. Research Letters). - with Gonzalo Dávila
**estimates for concave, non-local parabolic equations with critical drift**. (J. of Integral Equations and Applications) - with Gonzalo Dávila
**Hölder estimates for non-local parabolic equations with critical drift**. (J. of Differential Equations). - with François Baccelli and Sergey Foss
**Shape Theorems for Poisson Hail on a Bivariate Ground**. (Advances in Applied Probability). - with Mark Allen
**Free Boundaries on Two-Dimensional Cones**. (J. of Geometric Analysis). - with Gonzalo Dávila
**Regularity for solutions of nonlocal parabolic equations II**. (J. of Differential Equations). **Regularity for fully non linear equations with non local drift**.- with Gonzalo Dávila
**Regularity for solutions of non local parabolic equations**. (Calculus of Variations and Partial Differential Equations). - with Gonzalo Dávila
**Regularity for solutions of nonlocal, non symmetric equations**. (Ann. Inst. H. Poincaré Anal. Non Linéaire).