Xiangjin Xu

Xiangjin Xu is an Associate Professor in the Department of Mathematical Sciences at Binghamton University (SUNY), part of Harpur College. He has been affiliated with Binghamton since 2007. His research focuses on Harmonic Analysis on Manifolds and Nonlinear Partial Differential Equations (PDEs), with a particular emphasis on eigenfunction estimates, geometric PDEs, and control theory. He holds a Ph.D. in Mathematics from Johns Hopkins University (2004) and a Master’s degree from Nankai Institute of Mathematics (1999).

Education:

• Ph.D., Mathematics, Johns Hopkins University, 2004
• Master’s Thesis: Periodic solutions of Hamiltonian systems, Nankai Institute of Mathematics, 1999

Research Interests:

Xiangjin’s work spans two primary areas:

1. Harmonic Analysis on Manifolds: Studies eigenfunction growth estimates, nodal sets, and applications to PDE well-posedness on compact manifolds. This includes work on Hörmander multiplier theorems, Bochner-Riesz means, and spectral projectors.
2. Nonlinear Differential Equations: Focuses on Harnack inequalities, Liouville-type theorems, and gradient estimates for equations on manifolds with Ricci curvature conditions. Explores stabilization/observability of PDEs via Carleman estimates and periodic solutions in Hamiltonian systems.

Grants & Funding:

• NSF-DMS 0602151 (2006–2008), NSF-DMS-0852507 (2008–2010)
• Harpur College Research Grants (2010–2011, 2012–2013, 2019–2020)
• NYS/UUP Individual Development Award (2013–2014)
• AMS-NSF Travel Grants for international conferences (2010–2025)

Labs/Teams: Collaborates on projects involving geometric analysis, spectral theory, and PDE control. Active in seminars like the Analysis Seminar (Math 564).