# Introduction

Paul Loya Associate Professor Department of Mathematics at Binghamton University. At Binghamton since 2002. |

Office: |
WH 206 phone: (607) 777-3506, fax: (607) 777-2450 |

Address: |
Dept. of Mathematics,
Binghamton University Vestal Parkway East Binghamton, NY 13902 |

# Teaching

**Spring office hours:**TBD.

Classes: |
Atiyah-Singer Index Theorem.
Differential Equations. Real Analysis. |

# Research

**
Summary of research interests:
** Global and Geometric Analysis,
Partial Differential Equations on Manifolds with Singularities,
Index Theory, Mathematical Physics, Differential Geometry. (The celebrated
Gauss-Bonnet Theorem gives
the basic gist of some of what interests me. 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.