AUSTIN, Texas—A University of Texas at Austin professor will try to strengthen the relationship between geometry and algebra with a $400,000 Early Career Development (CAREER) award from the National Science Foundation.
The CAREER awards are prestigious grants for young teacher-scholars expected to be future academic leaders.
Dr. David Ben-Zvi, assistant professor of mathematics, also will use the grant to post a series of lectures and other resources on the World Wide Web in order to raise interest in the connection between geometry and algebra among students.
Ben-Zvi works in Geometric Representation Theory, a part of mathematics whose goal is to apply geometric techniques to problems in algebra, using geometric intuition to find conceptual approaches to problems that would otherwise require long calculations.
With the project, Ben-Zvi is addressing a small portion of the geometric Langlands program. Robert Langlands, a professor at the Institute for Advanced Study at Princeton University, has proposed that all of mathematics is under one umbrella, that problems and solutions in one area can be represented in another.
Ben-Zvi calls it an “exciting and varied but potentially intimidating and inaccessible area.”
“Very beautiful ideas and constructions are coming out of this area,” Ben-Zvi said. “It’s an area that’s got a relatively large amount of buzz in the math community. People are talking about it, but most people have no idea what it’s about.”
He hopes to provide a grounding in the area with videotaped lectures that can seen by streaming video, audio and lecture notes that are being posted to the GRASP Web site.
The Web site is aimed at beginning graduate students in math and is designed to make the subject area more accessible.
“The fancy machinery of the Langlands program, when looked at in simple cases, boils down to questions that are very familiar in algebra,” Ben-Zvi said. “The hope is that the more general point of view the Langlands philosophy provides will shed new light on these familiar questions while giving us a concrete test case to see the Langlands story in action.”
The algebraic structures in which Ben-Zvi is interested are related to areas of mathematical physics such as string theory.
For more information contact: Tim Green, 512-475-6596.
