Welcome to Paul Loya's Home Page

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.

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.)

Research Publications and Preprints

Undergraduate Mathematics Publications and Preprints

› Bored? Want some challenging "Problems of the Month/Week"?

Check out University of Colorado, Stony Brook, Bilkent University, Purdue University. The problems by Purdue are especially challenging!

› Want to write beautiful mathematics papers on your Windows computer?

Just follow the step-by-step procedures on how to install an a Latex system using WinEdt. (WinEdt costs $40. However, you can instead use TeXnicCenter, which is free.) A (Not So) Short Introduction to LaTeX2e is a free book on how to use Latex.

› Want to do power-point presentations using Latex?

Check out Prosper, a package for Latex that makes great pdf presentations.

› Want to do cool undergraduate mathematical research?

Check out the many summer REU's (research experience for undergrads) and start applying!

› Grad school in mathematics?

Here are some Group Descriptions of math graduate schools in the US, which might give you some feel of what levels of schools where you might fit.

› What can you do with a Mathematics degree?

Of the "Top Ten Jobs in the US", TWO are in the Math Department! (See Jobs Rated Almanac by Les Krantz, Barricade Books, 2002. Jobs are rated in terms of low stress, high compensation, lots of autonomy, tremendous hiring demand, and several other key criteria.)

• Actuary: The job "actuary" was rated the second best job in the US. Only "biologist" rated higher. Click here to read more and here to read about Binghamton's actuary program.
• Statistics: Rated 9th most desirable job in the US and first in the category of "Best Working Environment". Click here, read especially the Sep. 2002 article, for more information.

• The National Security Agency is supposedly the leading employer of mathematicians in the US (although the exact number of mathematicians working for the NSA is classified). It carries out a number of the country's most important and sensitive intelligence activities. John Nash of "A Beautiful Mind" did some work with the NSA as seen in the movie.
• Amy Langville's Operations Research page. OR uses mathematics to analyze problems and make important decisions. It forecasts the outcomes of various alternatives and determines which choice is the best --- the science of better.
• Many consulting firms, e.g. Metron, Wagner Assoc., or Applied Mathematics, Inc., need mathematicians to solve very challenging technology and computer related problems.
• Wall street needs mathematicians to research risk management and quantitative investments, where mathematical models are used to make important financial decisions.
• The Government has a great need to develop mathematical methods to solve scientific, engineering, economic, and military problems. Search for "mathematician" and you might be surprized with the number of positions open. Also check out The Job Page.

› Young mathematician?

Here is some practical advice from the late Gian-Carlo Rota.