A Hele-Shaw problem with interior and free boundary oscillation: well-posedness and homogenization. With Y. P. Zhang. (2025) Preprint: arXiv:2508.13441.
The incompressible limit of an inhomogeneous model of tissue growth. With A. Sulak. (2025) Preprint: arXiv:2503.19849.
Well-posedness for viscosity solutions of the one-phase Muskat problem in all dimensions. With R. Schwab and S. Tu. (2024) Preprint: arXiv: 2404.1097.
Nonlocal Approximation of Slow and Fast Diffusion. With K. Craig and M. Jacobs. Journal of Differential Equations Vol 426 (2025), 782-852.
Speed-up of traveling waves by negative chemotaxis. With Q. Griette and C. Henderson. Journal of Functional Analysis 285 (2023), no.10, Paper No. 110115, 67 pp.
A blob method for inhomogeneous diffusion with applications to multi-agent control and sampling. With K. Craig, K. Elamvazhuthi, M. Haberland. Mathematics of Computation 92 (2023), no.344, 2575–2654.
Non-local competition slows down front acceleration during dispersal evolution. With V. Calvez, C. Henderson, S. Mirrahimi; numerical appendix by T. Dumont. Annales Henri Lebesgue, Volume 5 (2022), pp. 1-71.
Decentralized, Deterministic Robot Swarm Control using Blob Methods for PDEs. With M. Haberland, K. Craig, K. Elamvazhuthi. July 2020. Refereed conference proceeding, SciPy 2020. DOI 10.25080/Majora-342d178e-018.
Quantifying Swarm Coverage. With B. Anderson, E. Loeser, M. Gee, F. Ren, S. Biswas, M. Haberland, A. L. Bertozzi. Springer Lecture Notes in Electrical Engineering, vol. 613, 2020, arXiv:1905.07655.
Quantitative Assessment of Robotic Swarm Coverage. With B. Anderson, E. Loeser, M. Gee, F. Ren, S. Biswas, M. Haberland, A. L. Bertozzi. Proc. 15th Int. Conf. on Informatics in Control, Automation, and Robotics (ICINCO 2018), vol. 2, pp. 91-101, 2018.
Uniform convergence for the incompressible limit of a tumor growth model. With I. Kim. Ann. Inst. H. Poincaré Anal. Non Linéaire, Volume 35, Issue 5, August 2018, pp 1321-1354; available online.
On a model of a population with variable motility. Mathematical Models and Methods in Applied Sciences. Vol 25, 2015, Issue 10, pp 1961-2014; available online.
Error estimates for approximations of nonhomogeneous nonlinear uniformly elliptic equations. Calc. Var. & PDE, 2015, Volume 54, Issue 3, pp 2939–2983; available online.
Error estimates for approximations of nonlinear uniformly parabolic equations. Nonlinear Differential Equations and Applications, 2015, Vol 22, Issue 3, pp 345-389; available online.
The Spiral Index of Knots. With C. Adams, W. George, R. Hudson, R. Morrison, L. Starkston, S. Taylor. Math. Proc. Cambridge Philos. Soc. 149, 2010, no. 2, 297-315; available online.
Particle approximation of diffusion with applications to sampling, BIRS workshop, May 2025.
Particle approximation of diffusion, IMSI workshop, December 2024.
Effect of Repelling Chemotaxis on Propagation , BIRS workshop, October 2024.
Nonlocal approximation of linear and nonlinear diffusion, ICERM workshop, May 2024.
A Particle Method for Degenerate Diffusion, and Applications to Robotic Swarming, Simons Institute for the Theory of Computing workshop (virtual), October 2021.
Front propagation in a nonlocal reaction-diffusion equation, IAS seminar talk, March 2019.
Front propagation in a nonlocal reaction-diffusion equation, IAS short colloquial talk, October 2018.
The cane toads PDE -- a model of a population with variable motility, BIRS CMO workshop, August 2016.