Journal articles and Preprints
Current research supported in part by the National Science Foundation through Award # DMS-2144232.
- • The fuzzy Landau equation: global well-posedness and Fisher information.
Preprint (2025) [arXiv]. Joint with Maria Gualdani, Natasa Pavlovic, Maja Taskovic, and Nicola Zamponi.
- • The Landau equation and Fisher information.
Expository note (2025), submitted to Notices of the AMS [arXiv]. Joint with Luis Silvestre.
- • The Landau equation does not blow up.
Acta Mathematica (2025) [Journal]. Joint with Luis Silvestre.
- • Regularization estimates of the Landau-Coulomb diffusion.
Nonlinear Analysis (2025)[Journal]. Joint with Rene Cabrera and Maria Gualdani.
- • A Convex Optimization Framework for Regularized Geodesic Distances.
SIGGRAPH 2023 (conference) [Conference]. Joint with Michal Edelstein, Justin Solomon, and Mirela Ben-Chen.
- • Hardy's inequality and the isotropic Landau equation.
Journal of Functional Analysis (2022)[Journal]. Joint with Maria Gualdani.
- • A Hele-Shaw limit without monotonicity.
Archive for Rational Mechanics and Analysis (2022)[Journal]. Joint with Inwon Kim and Antoine Mellet.
- • Optimal transport and the Gauss curvature equation.
Methods and Applications of Analysis (2020)[Journal]. Joint with Jun Kitagawa.
- • Geometry of Graph Partitions via Optimal Transport.
SIAM Journal on Scientific Computing (2020)[Journal]
Joint with Tara Abrishami, Parker Rule, Zachary Schutzman, Justin Solomon, Thomas Weighill, and Si Wu.
- • Min-max formulas for nonlocal elliptic operators on Euclidean space.
Nonlinear Analysis (2019)[Journal]. Joint with Russell Schwab.
- • Some free boundary problems recast as nonlocal parabolic equations.
Nonlinear Analysis (2019)[Journal]. Joint with Hector Chang-Lara and Russell Schwab.
- • Coupling Levy measures and comparison principles for viscosity solutions.
Transactions of the AMS (2019)[Journal]. Joint with Chenchen Mou and Andrzej Swiech.
- • Estimates for Dirichlet-to-Neumann maps as integro-differential operators.
Potential Analysis (2019)[Journal]. Joint with Russell Schwab and Jun Kitagawa.
- • On $A_p$ weigths and the Landau equation.
Calculus of Variations and Partial Differential Equations (2019) [Journal]. Joint with Maria Gualdani.
- • Min-max formulas for nonlocal elliptic operators.
Calculus of Variations and Partial Differential Equations (2019)[Journal]. Joint with Russell Schwab.
- • From the free boundary condition for Hele-Shaw to a fractional parabolic equation.
Unpublished manuscript. Joint with Héctor Chang-Lara.
- • Neumann Homogenization via Integro-Differential Operators, Part 2: singular gradient dependence.
SIAM Journal on Mathematical Analysis (2018)[Journal]. Joint with Russell Schwab.
- • Pointwise estimates and regularity in geometric optics and other Generated Jacobian Equations.
Communications on Pure and Applied Mathematics (2017)[Journal]. Joint with Jun Kitagawa.
- • Estimates for radial solutions of the homogeneous Landau equation with Coulomb potential.
Analysis & PDE (2016)[Journal]. Joint with Maria Gualdani.
- • Neumann Homogenization via Integro-Differential Operators.
Discrete and Continuous Dynamical Systems (2016)[Journal]. Joint with Russell Schwab.
- • Mean curvature, threshold dynamics, and phase field theory on finite graphs.
Milan Journal of Mathematics (2014)[Journal]
Joint with Andrea Bertozzi, Yves Van Gennip, and Braxton Osting.
- • Quasistatic droplets in randomly perforated domains.
Archive for Rational Mechanics and Analysis (2015)[Journal]. Joint with Inwon Kim.
- • On the local geometry of maps with c-convex potentials.
Calculus of Variations and Partial Differential Equations (2012)[Journal]. Joint with Jun Kitagawa.
- • Aleksandrov-Bakelman-Pucci type estimates for integro-differential equations.
Archive for Rational Mechanics and Analysis (2012)[Journal]. Joint with Russell Schwab.
- • Regularity for non-local almost minimal boundaries and applications.
Unpublished manuscript. Joint with Cristina Caputo.
- • Optimal regularity for the Signorini problem.
Calculus of Variations and Partial Differential Equations (2009)[Journal]
Presentations
- • Optimal transport problems with interaction effects
ICERM workshop, Optimal Transport in Data Science (May 2023) [Slides] [video] - • Aleksandrov's estimate and its generalizations (and lack thereof)
Midwest Geometry Conference (March 2022) [Slides] - • Free boundary problems as Hamilton-Jacobi-Bellman equations
Online Analysis and PDE Seminar (March 2021) [Slides] - • Recent advances in the theory of prescribed Jacobian equations
Texas State University (January 2019) [Slides] - • Free boundary problems as parabolic Integro-differential equations
BIRS workshop, Advanced Developments for Surface and Interface Dynamics (June 2018) [Slides] [video] - • A rapid course on generated Jacobian equations
Banff workshop, Generated Jacobian Equations: from geometric optics to economics (April 2017) [Slides] [video]
Lecture notes
- • The Landau equation and Fisher information.
Expository note (2025), submitted to Notices of the AMS [arXiv]. Joint with Luis Silvestre.
- • A primer on Generated Jacobian Equations: geometry, optics, economics.
Notices of the American Mathematical Society (2019). [Article] - • Five lectures on optimal transportation: geometry, regularity and applications.
Joint with Robert McCann.
Analysis and Geometry of Metric Measure Spaces: Lecture Notes of the Séminaire de Mathématiques Supérieure (SMS), Montréal (2012). [Book]