$Paul Loya$

Paul Loya

Associate Professor • Ph.D., 1998, Massachusetts Institute of Technology

At Binghamton since	2002
Office	WH 206
Phone	(607) 777-3506
Fax	(607) 777-2450
Email	ploya@binghamton.edu • loya@math.binghamton.edu

Areas of Interest

Global and geometric analysis, Elliptic theory of differential operators on manifolds with singularities, Partial differential equations, General Relativity

Research

The underlying theme of my research is the investigation of topological, geometric, and spectral invariants of (singular) Riemannian manifolds using techniques from partial differential equations. For example, the Euler characteristic of a surface is a topological invariant based its usual definition in terms of a triangulation of the surface. However, it may also be considered geometric in view of the Gauss-Bonnet theorem or spectral in view of the Hodge theorem. I am interested in such relationships on general singular Riemannian manifolds.

Courses

Fall 2026

Course	Section	Title	Schedule	Room
Math 226	06	Integration Techniques and Applications	MWF 9:45–11:15	CW-327
Math 227	06	Infinite Series	MWF 9:45–11:15	CW-327
Math 304	01	Linear Algebra	MWF 12:15–1:15	FA-209
Math 472	01	PDE and Mathematical Analysis	MWF 12:15–1:15	FA-209

Ph.D. Students

Brian Kirby, Spring, 2026 — On Resolving the Singularities of the Reissner-Nordström Penrose Diagram via Method of Blow-Ups
Kunal Sharma, Spring, 2019 — Adiabatic Limit of Calderon Projector on Manifold with Cylindrical End
Binbin Huang, Spring, 2018 — On a Pseudodifferential Calculus with Modest Boundary Condition
Adam Weisblatt, Spring, 2018 — Geometric techniques for Laplace and Dirac Operators

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