J. H. Andrade — IME-USP

About

I am an Associate Professor (Livre Docente) at the Department of Mathematics, IME-USP, and a permanent member of the graduate program PPGMAT.

I received my B.S. (2016) and Ph.D. (2020) in Mathematics from the Federal University of Paraíba, under the supervision of João Marcos do Ó and co-supervision of Fernando Codá Marques (Princeton). During my doctorate I spent a research period at Princeton University (2019–2020) with support from the Fulbright Commission. I held postdoctoral positions at the University of São Paulo (2021–2023) and the University of British Columbia (2022–2023), funded by FAPESP.

My research concerns qualitative properties of solutions to nonlinear elliptic equations arising in Differential Geometry — multiplicity, regularity, symmetry, bifurcation, and classification of asymptotic behavior.

Nonlinear PDEs Conformal Geometry Geometric Analysis Geometric Measure Theory

Statistics

22 Papers 29 Talks 10 Students 37 Collaborators 9 Countries

Interests

My work lies at the intersection of nonlinear analysis and differential geometry. The main research lines are outlined below.

Q-curvature and Higher-Order Conformal Geometry

Classification and asymptotic analysis of singular solutions to higher-order conformally invariant equations (GJMS/Paneitz operators), compactness phenomena, Delaunay-type metrics, and stability of Q-curvature functionals.

Fractional Yamabe Problem

Complete, conformally flat metrics with constant fractional Q-curvature on punctured spheres. Pohozaev-type invariants and rigidity results for nonlocal conformal operators.

Allen–Cahn Systems and Phase Transitions

Diffuse interface models for isoperimetric clusters, multiphasic Allen–Cahn–Hilliard systems on Riemannian manifolds, connections with minimal surfaces, and Conley index methods.