Mark Allen

Office Hours: N/A

Class Schedule: No Classes Spring/Summer 2023

Research Interests: Partial Differential Equations

Degrees: Brigham Young University, BS in Mathematics (2007), Purdue University, MA in Mathematics (2009), PhD in Mathematics (2013)

Prizes and Awards:

1. BYU math department Distinguished Research Award
2. Simons Foundation Collaboration Grant recipient
3. NSF postdoc recipient.
4. Research support award from Purdue Research Foundation.

Publications:

1. Rectifiability and uniqueness of blow-ups for points with positive Alt-Caffarelli-Friedman limit, with D. Kriventsov and R. Neumayer, submitted [arXiv:2210.03552].
2. Sharp quantitative Faber-Krahn inequalities and the Alt-Caffarelli-Friedman monotonicity formula, with D. Kriventsov and R. Neumayer, submitted [arXiv:2107.03505].
3. Linear Stability Implies Nonlinear Stability for Faber-Krahn Type Inequalities, with D. Kriventsov and R. Neumayer, accepted in Interfaces Free Bound. [arXiv:2107.03495].
4. The Inhomogeneous Boundary Harnack Principle for Fully Nonlinear and p-Laplace equations, accepted in Annales De l’IHP (C)-ANL, [arxiv:2010.11854].