## Héctor A. Chang-Lara

Department of Mathematics
Columbia University

Office: Math 415
Office hours: Fridays 10-noon
Phone: (212) 854-4354
E-Mail: changlara at math dot columbia dot edu

CV

### Research Interest:

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.

### Publications and preprints (arXiv, MathSciNet)

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