Research

My research interests lie in the intersection of Partial Differential Equations (PDEs) and Differential Geometry. In particular, I am interested in the effect of the curvature on the different PDE models for fluid dynamics and chemotaxis. Here you can check my CV

Papers

Y. Chen and P. Fuster Aguilera and V. Martinez and K. Zhao, Boundary symmetry breaking via logistic damping in a chemotaxis-growth system. (2026 submitted) ArXiv
C. H. Chan and M. Czubak and P. Fuster Aguilera, Thin Shell Limit and the Derivation of the Viscosity Operator on the Ellipsoid. (2025 - submitted) ArXiv
P. Fuster Aguilera and W. Wang and K. Zhao and N. Zhu, Critical mass in a chemotaxis model with spatially dependent sensitivity in dimension two. (2024 - submitted)
P. Fuster Aguilera and K. Zhao, Global stability of a logarithmically sensitive chemotaxis model under dynamic boundary conditions. (2024 - EJAM Journal) ArXiv
P. Fuster Aguilera and V. Martinez and K. Zhao, A PDE model for chemotaxis with logarithmic sensitivity and logistic growth. (Contemporary Research in Mathematical Biology: Modeling, Computation and Analysis) Contemporary Mathematics and its Applications: Monographs, Expositions and Lecture Notes, December 2023, in press. CRMB. ArXiv.
P. Fuster Aguilera, A PDE model for chemotaxis with logarithmic sensitivity and logistic growth. (Ph.D. thesis, Tulane University, May 2021)
C. H. Chan and M. Czubak and P. Fuster Aguilera, The Gauss Formula for the Laplacian: Examples.(2026 in-preparation)

Book Contributions & Articles

P. Fuster Aguilera, s. amethyst, A. Henrich, S. Kara, A. Wooton. Storytelling. MAA Focus. June/July 2024. Read here
P. Fuster Aguilera, R. Brooks, Redefining Math Conferences: A Panel. AMS Notices. March 2024.Read here
P. Fuster Aguilera, S. Kara, A Conversation on Meet a Mathematician and Math For All. Practices and Policies: Advocating For Students of Color in Mathematics. Pamela E. Harris and Aris Winger. CreateSpace 2021.Book here

Posters

P. Fuster Aguilera and V. Martinez and K. Zhao, A PDE model for chemotaxis with logarithmic sensitivity and logistic growth (poster) (AWM poster session at JMM 2021)
P. Fuster Aguilera and R. Cortez and K. Zhao, Singular Limit and Global Stabilization of a PDE Model for Chemotaxis with Dynamic Boundary Conditions (poster) (AWM poster session at SIAM 2021)