I've spent the past few years studying objects called minimal surfaces. The word "minimal" should hint that these things actually appear in nature, and, indeed, this is the case. Soap films are examples of minimal surfaces and so, arguably, anyone who has ever played with soap bubbles or taken a sud-filled bath has studied these objects, too. (Speaking of playing, self-proclaimed "professional nerd" Andrew Lipson has a gallery of minimal (and other) surfaces built out of legos.)

If you're new to math in general or minimal surfaces in particular, there are a number of excellent resources available to you, but before jumping straight in, you should keep in mind a few things. First, the concept of a surface requires advanced or upper level mathematics to properly define (specifically topology and/or differential geometry), but the notion of a surface one encounters, say, in a multivariable calculus course will suffice for a first pass at the subject. Second, the concept of being minimal or, equivalently, of minimizing area, can be understood from a variety of perspectives. My preferred approach uses Complex Analysis and Differential Geometry, but other mathematicians use the language of Partial Differential Equations and Geometric Measure Theory, for instance. For more details of an introductory nature, please consult Professor Michael Dorff's website. You may also wish to peruse Professor Frank Morgan's website, someone who also has spent a great deal of time getting undergraduates involved with minimal surface related research.

For a more detailed explanation of my research interests and thesis results, please consult my research statement. My advisor, Mike Wolf, has a great website. The MSRI maintains a fairly exhaustive database of known (and conjectured!) minimal surfaces, complete with computer animations and tons of pictures. In case that isn't enough, Professor Matthias Weber has a wonderful gallery of minimal surfaces available at his website.

I have been fortunate enough to work with Francisco Martin, and I am looking forward to working with my newest best friends, Magdalena Rodriuez and Adam Weyhaupt. Pictures of myself with all three of these wonderful mathematicians are featured at the top of this page.

This year, I will also be working with a wonderful team of undergraduate students at St. Mary's. Click here for more details.

If you have any questions, comments, concerns or ideas, please feel free to e-mail me!