Davide Parise
S.E.W. Visiting Assistant Professor
University of California San Diego
Email: dparise@ucsd.edu
Address: Applied Physics & Mathematics
9500 Gilman Drive #0112,
La Jolla, CA 92093-0112, USA
Office: AP&M 6321
About me
I am currently S.E.W. Visiting Assistant Professor at the University of California San Diego, mentored by Prof. Luca Spolaor. During Fall 2024, I was SLMath Postdoc at the Simons Laufer Mathematical Institute (formerly MSRI), taking part in the special program Special Geometric Structures and Analysis mentored by Profs. Henri Guenancia and Tristan Rivière. Previously, I completed my Ph.D. in Mathematics at the University of Cambridge, advised by Prof. Neshan Wickramasekera.
Research interests: Differential Geometry, Partial Differential Equations, Calculus of Variations, and Geometric Measure Theory.
Publications
- Nonabelian Yang-Mills-Higgs and Plateau's Problem in Codimension Three. Joint work with Alessandro Pigati, and Daniel Stern.
- Almost minimizing Yang-Mills fields: log-epiperimetric inequality, non-concentration, and uniqueness of tangents. Joint work with Riccardo Caniato.
- Rectifiability of the singular set and uniqueness of tangent cones for semicalibrated currents. Joint work with Paul Minter, Anna Skorobogatova, and Luca Spolaor.
- Quantitative Stability of Sobolev Inequalities on Compact Riemannian manifolds. Joint work with Francesco Nobili.
- Boundary behavior of limit-interfaces for the Allen-Cahn equation on Riemannian manifolds with Neumann boundary condition. Joint work with Martin Li, and Lorenzo Sarnataro.
- The Parabolic U(1)-Higgs Equations and Codimension-two Mean Curvature Flows. Joint work with with Alessandro Pigati, and Daniel Stern.
- Convergence of the self-dual U(1)-Yang-Mills-Higgs energies to the (n - 2)-area functional. Joint work with Alessandro Pigati, and Daniel Stern.
- Warped Tori with Almost Non-Negative Scalar Curvature. Joint work with with Brian Allen, Lisandra Hernandez, Alec Payne, and Shengwen Wang.
Submitted.
Submitted.
Submitted.
Int. Math. Res. Not. Volume 2025, Issue 1, January 2025, rnae269.
Arch. Ration. Mech. Anal. 248, 124, (2024)
Geom. Funct. Anal. 34 (2024), no. 4, 1171–1225.
Comm. Pure Appl. Math. 77 (2024), no. 1, 670–730.
Geom. Dedicata, 200 (2019), no.1, 153-171.
Teaching
- Winter 2025, Math 142A Introduction to Analysis I;
- Spring 2025, Math 142B Introduction to Analysis II;