Research

I am mainly interested in geometric analysis, differential geometry, calculus of variations, and elliptic partial differential equations (PDEs). Within these broad fields of research, I am particularly driven towards problems arising from theoretical physics.

Currently, my research concentrates on the analytical aspects of elliptic geometric variational problems, with a particular focus on harmonic maps, gauge theory, and minimal surfaces.

• Area rigidity for the regular representation of surface groups.

Join work with Xingzhe Li and Antoine Song.

Submitted.

• Symmetric log-epiperimetric inequality for harmonic maps with analytic target and applications.

Join work with Davide Parise.

Submitted.

• Coulomb Gauges and Regularity for Stationary Weak Yang–Mills Connections in Supercritical Dimension.

Joint work with Tristan Rivière.

Submitted.

• Almost minimizing Yang–Mills fields: log-epiperimetric inequality, non-concentration, and uniqueness of tangents.

Joint work with Davide Parise.

Submitted.

• Weak and strong L^p-limits of vector fields with finitely many integer singularities in dimension n.

Joint work with Filippo Gaia.

Ann. Sc. Norm. Sup. Pisa Cl. Sci., to appear.

• The unique tangent cone property for weakly holomorphic maps into projective algebraic varieties.

Joint work with Tristan Rivière.

Duke Mathematical Journal, 172.13 (2023), 2471 – 2536.

• The strong L^p-closure of vector fields with finitely many integer singularities on B^3.

Journal of Functional Analysis, 281.6 (2021), paper no. 109095.

• Jun. 2026: International Geometric Analysis Conference in Milan II, Bocconi University, Milan, Italy.

• Apr. 2026: Graduate Student Topology and Geometry Conference 2026, Rutgers University, New Brunswick, NJ, USA.

• Nov. 2025: Geometric Analysis Seminar, Yale University, New Haven, CT, USA.

• Oct. 2025: Geometry Seminar, University of California San Diego, La Jolla, CA, USA.

• Oct. 2025: Geometric Analysis Seminar, University of Chicago, Chicago, IL, USA.

• Oct. 2025: Geometry Seminar, Stanford University, Stanford, CA, USA.

• Oct. 2025: Geometric Analysis Seminar, Brown University, Providence, RI, USA.

• Sep. 2025: Differential Geometry Seminar, University of Wisconsin–Madison, Madison, WI, USA.

• May 2025: Rutgers Gauge Theory, Low-Dimensional Topology, and Geometric Analysis Conference 2025, Rutgers University, New Brunswick, NJ, USA.

• May 2025: CUNY Geometric Analysis Seminar, CUNY, New York City, NY, USA.

• Apr. 2025: Gauge Theory Learning Seminar, Rutgers University, online.

• Apr. 2025: Geometric Analysis Seminar, Johns Hopkins University, Baltimore, MD, USA.

• Mar. 2025: Geometry and Topology Seminar, University of Toronto, Toronto, Canada. 

• Oct. 2024: GMT and Minimal Surfaces Seminar, SLMath, Berkeley, USA. 

• Jun. 2024: Conference CHANGE – CHallenges in ANalysis and GEometry, ETH Zürich, Zürich, Switzerland.

• May 2024: Geometry Seminar, University of California San Diego, La Jolla, CA, USA. 

• May 2024: Differential Geometry and Geometric Analysis Seminar, Princeton University, Princeton, NJ, USA. 

• Apr. 2024: Caltech Postdocs Launch, California Institute of Technology, Pasadena, USA.

• Jul. 2023: Seminari di Analisi Matematica dell’Università e del Politecnico, Politecnico di Torino, Torino, Italy.

• Jun. 2023: Seminario di Analisi, Sapienza Università di Roma, Roma, Italy.

• May 2023: Seminaire de Geometrie, Institut de Mathématiques de Jussieu - Paris Rive Gauche, Paris, France.

• Apr. 2023: Analysis and Geometric Analysis Seminar, Cornell University, online.

• Jun. 2022: Workshop/Summer School "Geometric analysis and calibrated geometries", ETH Zürich, Zürich, Switzerland.

• Oct. 2021: Analysis Seminar, ETH Zürich, Zürich, Switzerland.

• Jun. 2025: International Geometric Analysis Conference in Milan, Bocconi University, Milan, Italy.

• Apr. 2025: Perspectives in Modern Mathematics: The Fifth Duke Mathematical Journal Conference, Duke University, Durham, NC, USA.

• Feb. 2025: The 30th Souther California Geometric Analysis Seminar, University of California Irvine, Irvine, CA, USA.

• Nov. 2024: Workshop "Geometry and analysis of special structures on manifolds", SLMath, Berkeley, CA, USA.

• Oct. 2024: Workshop "Recent progresses on geometric analysis and Riemannian geometry", SLMath, Berkeley, CA, USA.

• Sep. 2024: Introductory Workshop: Special Geometric Structures and Analysis, SLMath, Berkeley, CA, USA.

• Mar. 2024: MAGEC (Meeting on Analysis and noncommutative Geometry for Early Career researchers) 2024, Pasadena, CA, USA.

• Jul. 2023: Minicourse "Regularity of Area Minimizing Hypersurfaces, generically" by Prof. Otis Chodosh, UCL, London, UK.

• Jun. 2023: Summer School "Vito Volterra Meeting", Sapienza Università di Roma, Roma, Italy.

• Jan. 2022: Conference "Variational Aspect of Minimal Surfaces", Institut Henri Poincaré and University of Paris, Paris, France.

• Dec. 2021: Conference "Geometric PDEs in Freiburg", University of Freiburg, Freiburg, Germany.