About me
I am an associate professor of mathematics at Virginia Commonwealth University. My research interests are in the calculus of variations, partial differential equations and geometric measure theory, with a focus on problems arising from materials science, biology and physics.
I obtained my PhD from Indiana University under the supervision of Peter Sternberg. Before joining VCU, I was a Fields-Ontario postdoctoral fellow at the Fields Institute and at McMaster University working with Stan Alama and Lia Bronsard. Prior to that, I spent two years at McGill University working with Rustum Choksi and Gantumur Tsogtgerel.
During the spring and summer of 2024 I visited Ludwig Maximilian University of Munich as a Humboldt Research Fellow.
My research is supported by funds from Alexander von Humboldt Foundation, National Science Foundation and Simons Foundation.
Publications
Journal Articles
with L. Bronsard and K. DeMason
The liquid drop model with a Yukawa potential: Existence of minimizers and sharp stability of the ball
submitted (2026) [pdf][arXiv]
with D. Carazzato and A. Pratelli
Particle approximation of nonlocal interaction energies
Nonlinear Anal. 263, 113974 (2026) [pdf][arXiv][doi]
with M. Bonacini
Stability and minimality of the ball for attractive-repulsive energies with perimeter penalization
to appear in Interfaces Free Bound. [pdf][arXiv][doi]
with M. Bonacini and R. Cristoferi
A stability inequality for the planar lens partition
to appear in Proc. R. Soc. Edinb. A: Math. [pdf][arXiv][doi]
with D. Carazzato and A. Pratelli
On the existence of minimizing sets for a weakly-repulsive non-local energy
Pure Appl. Anal. 6, 995-1015 (2024) [pdf][arXiv][doi]
with A. Burchard and D. Carazzato
Maximizers of nonlocal interactions of Wasserstein type
ESAIM: COCV 30, 80 (2024) [pdf][arXiv][doi]
with M. Bonacini and R. Cristoferi
Stability of the ball for attractive-repulsive energies
SIAM J. Math. Anal. 56, 588-615 (2024) [pdf][arXiv][doi]
with M. Schwitzerlett and H. R. Ogrosky
A long-wave model for film flow inside a tube with slip
J. Fluid Mech. 974, A22 (2023) [pdf][doi]
with M. Novack and R. Venkatraman
Least Wasserstein distance between disjoint shapes with perimeter regularization
J. Funct. Anal. 284, 109732 (2023) [pdf][arXiv][doi]
with R. Choksi and R. Neumayer
Anisotropic liquid drop models
Adv. Calc. Var. 15, 109-131 (2022) [pdf][arXiv][doi]
with M. Bonacini and R. Cristoferi
Riesz-type inequalities and overdetermined problems for triangles and quadrilaterals
J. Geom. Anal. 32, 48 (2022) [pdf][arXiv][doi]
with O. Misiats and O. Stanzhytskyi
On global existence and blowup of solutions of stochastic Keller-Segel type equation
Nonlinear Differ. Equ. Appl. 29, 3 (2022) [pdf][arXiv][doi]
with M. Bonacini and R. Cristoferi
Minimality of polytopes in a nonlocal anisotropic isoperimetric problem
Nonlinear Anal. 205, 112223 (2021) [pdf][arXiv][doi]
with S. Alama, L. Bronsard, and A. Zuniga
A nonlocal isoperimetric problem with density perimeter
Calc. Var. PDEs 60, 1 (2021) [pdf][arXiv][doi]
with O. Misiats
On minimizers of an anisotropic liquid drop model
ESAIM: COCV 27, S20 (2021) [pdf][arXiv][doi]
with O. Misiats and D. Vasiliu
Singular perturbation of an elastic energy with a singular weight
Physica D 406, 132422 (2020) [pdf]arXiv][doi]
with K. Craig
Aggregation-diffusion to constrained interaction: Minimizers & gradient flows in the slow diffusion limit
Ann. Inst. Henri Poincare (C) Anal. Non Lineaire 37, 239-279 (2020) [pdf][arXiv][doi]
with S. Alama, L. Bronsard, and R. Choksi
Droplet phase in a nonlocal isoperimetric problem under confinement
Comm. Pure Appl. Anal. 19, 175-202 (2020) [pdf][arXiv][doi]
with S. Alama, L. Bronsard, and R. Choksi
Droplet breakup in the liquid drop model with background potential
Commun. Contemp. Math. 21, 1850022 (2019) [pdf][arXiv][doi]
with R. C. Fetecau and M. Kovacic
Swarming in domains with boundaries: approximation and regularization by nonlinear diffusion
Discrete Contin. Dyn. Syst. Ser. B 24, 1815-1842 (2019) [pdf][arXiv][doi]
with A. Burchard and R. Choksi
Nonlocal shape optimization via interactions of attractive and repulsive potentials
Indiana Univ. Math. J. 67, 375-395 (2018) [pdf][arXiv][doi]
with S. Alama, L. Bronsard, and R. Choksi
Ground-states for the liquid drop and TFDW models with long-range attraction
J. Math. Phys. 58, 103503 (2017) [pdf][arXiv][doi]
with S. Alama and L. Bronsard
Sharp interface limit of an energy modelling nanoparticle-polymer blends
Interfaces Free Bound. 18, 263-290 (2016) [pdf][arXiv][doi]
with K. Craig
Convergence of regularized nonlocal interaction energies
SIAM J. Math. Anal. 48, 34-60 (2016) [pdf][arXiv][doi]
with R. Simione and D. Slepcev
Existence of ground states of nonlocal-interaction energies
J. Stat. Phys. 159, 972-986 (2015) [pdf][arXiv][doi]
with R. Choksi and R. C. Fetecau
On minimizers of interaction functionals with competing attractive and repulsive potentials
Ann. Inst. Henri Poincare (C) Anal. Non Lineaire 32, 1283-1305 (2015) [pdf][doi]
with R. Choksi and G. Tsogtgerel
Axisymmetric critical points of a nonlocal isoperimetric problem on the two-sphere
ESAIM: COCV 21, 247-270 (2015) [pdf][arXiv][doi]
On a nonlocal isoperimetric problem on the two-sphere
Comm. Pure Appl. Anal. 12, 597-620 (2013) [pdf][doi]
with P. Sternberg
On the global minimizers of a nonlocal isoperimetric problem in two dimensions
Interfaces Free Bound. 13, 155-169 (2011) [pdf][doi]
with A. Eden
Standing waves for a generalized Davey-Stewartson system: Revisited
Appl. Math. Lett. 21, 342-347 (2008) [pdf][doi]
Review Articles and Reports
with M. Bonacini and R. Cristoferi
Alexandrov's Soap Bubble Theorem for Polygons
Am. Math. Mon. 132, 666-675 (2025) [pdf][arXiv][doi]
Nonlocal variational problems on polygons
Oberwolfach Rep. 19, 2171-2174 (2022) [pdf][doi]
with R. Choksi and C. B. Muratov
An old problem resurfaces nonlocally: Gamow's liquid drops inspire today's research and applications
Notices Amer. Math. Soc. 64, 1275-1283 (2017) [pdf][doi]
Teaching
I regularly teach courses in calculus, multivariable calculus, advanced calculus, probability theory, ordinary differential equations, partial differential equations, real analysis, and measure theory.