Research Interests:

My research interests lie primarily in the geometry and analysis of non-linear partial differential equations arising in fluid dynamics and other areas of mathematical physics. The bulk of this work takes place in the setting of infinite-dimensional Riemannian geometry and hence incorporates tools from finite-dimensional geometry, functional and harmonic analysis as well as partial differential equations.

Publications:

[4] M. Bauer, P. Heslin, G. Misiołek, S.C. Preston, Geometric Analysis of the Generalized Surface Quasi-Geostrophic Equations, Math. Ann. (to appear) (arXiv link).

[3] M. Bauer, P. Heslin, C. Maor, Completeness and geodesic distance properties for fractional Sobolev metrics on spaces of immersed curves, J. Geom. Anal., (to appear)  (arXiv link).

[2] P. Heslin, Two-Point Boundary Value Problems on Diffeomorphism Groups, Int. Mat. Res. Not. IMRN, Volume 2023, Issue 23, December 2023, Pages 19902–19931 (link).

[1] P. Heslin, Two-Point Boundary Value Problems on Diffeomorphism Groups, Ph.D. Dissertation, University of Notre Dame, 2021 (link).