Finding Truth in Lie Algebras

Names: David Vella, Ph.D., Associate Professor, Math and Computer Science
David Wiygul, ‘04

Project Title: “An Exploration of Lie Algebras: Structure, Representation, and Orbits”

Project Description: Lie algebras and Lie Groups are mathematical structures first explored and developed over 80 years ago by Sophus Lie (Norwegian), Wilhelm Killing (German), and Elie Cartan (French). While conceptually challenging for the non-mathematician, Lie groups and Lie algebras play a fundamental role in both modern math and in particle physics. David’s and David’s (D² in math terms) project involved extending what was known about orbits of nilpotent elements of the Lie algebra under the action of the ambient Lie group G to orbits of these elements under certain subgroups B of G, known as Borel subgroups.

Project Genesis: Having taken a number of advanced math courses early in his Skidmore career, David W. enrolled in an independent study as a sophomore – essentially a graduate level course – with David V., where his interest in Lie algebras grew. It was only a matter of time until their research interests merged in this field where a large number of important yet unsolved questions remain.

Project Outcome: In April 2004, the team will deliver a presentation on their work during a conference at Mount Holyoke College. In the interim, they’ll continue to explore the topic and may likely publish their findings.

Quote: “The opportunity to focus on both teaching and research is one of the primary reasons I was attracted to Skidmore. Clearly, teaching is very important to me, and engaging students outside the classroom, as well as within it, is extraordinarily satisfying. Outside enrichment outlets for students in which I’m involved include the annual Putnam Exam, Skidmore’s chapter of Pi Mu Epsilon, and the Hudson River Undergraduate Mathematics Conference.” – David Vella.

Student Background: David Wiygul
Home: New York City
Class: 2004
Major: Math & Physics
Minor: Classics
Activities: Tennis, learning guitar
After Skidmore: Graduate school
On collaborative research at Skidmore: “Working closely with professor Vella on an extended project like this has been very rewarding and one of the highlights of my Skidmore experience!”

Faculty Background: David Vella
Courses taught: Calculus; Serious Games: Conflict, Voting, and Power; Problem Solving in Mathematics; Geometry, Topology, Abstract Algebra; Senior Seminar
Academic Background: Ph.D., University of Virginia
Research focus: Algebra and representation theory, game theory, combinatorics
Non-academic interests: Collecting music, spending time with wife and two daughters

Learn more?
http://www.skidmore.edu/academics/mcs/putnam.htm
http://www.skidmore.edu/academics/mcs/pmeframe.htm
http://www.skidmore.edu/academics/mcs/hrumc.htm