introduction

Picture here Paul Loya
Associate Professor
Department of Mathematics at Binghamton University.
Ph.D., 1998, M.I.T. My thesis advisor was Richard Melrose.
At Binghamton since 2002.

Office: LN 2224
phone: (607) 777-3506, fax: (607) 777-2450
E-mail: paul at math.binghamton.edu
Address: Dept. of Mathematics, Binghamton University
Vestal Parkway East
Binghamton, NY 13902

teaching

I'm an advisor for the Binghamton University Math Club.
Fall office hours: M F 3:30 - 4:30, R 4:30-5 and whenever you pass my office, you're welcome to step in.
Classes: Fall: Calc III (Math 323): MWF 2:20-3:20, R 2:50-4:15.
Fall: Functional analysis (Math 590F):.
Spring: Intro to Proofs (Math 330): MWF 12-1, R 8:30-9:55.
Spring: Graduate Analysis (Math 505): MWF 10:50-11:50.
Spring: Hodge Theory (Math 590F).

research

Summary of research interests: Global and Geometric Analysis, Partial Differential Equations on Manifolds with Singularities, Index Theory, Mathematical Physics, Differential Geometry. (If these words are incomprehensible, the celebrated Gauss-Bonnet Theorem gives the basic gist of some of what I do. The Atiyah-Singer Index Theorem is a more precise description of my research.)

The Atiyah-Singer index theorem


Here are the slides on the Atiyah-Singer index theorem "for beginners" that I gave at the MSRI (Mathematical Sciences Research Institute) during the fall of 2008:

The Atiyah-Singer index theorem I.
The Atiyah-Singer index theorem II.
Index theory on singular manifolds I.
Index theory on singular manifolds II.