I am a Professor in the Geometry Research Group of the Mathematics Department, University of Texas, Austin.
I am interested in the interface between representation theory, algebraic geometry and mathematical physics. One focus of my current research is a new approach, joint with David Nadler to the representation theory of real and complex Lie groups built from a combination of the geometric Langlands program, topological field theory and derived algebraic geometry. Another program I am working on, joint with Tom Nevins, applies noncommutative geometry, in particular the geometry of differential operators, to questions concerning integrable systems. I am also interested in the applications of algebraic structures coming from physics (such as conformal field theory and vertex algebras) to the geometry of moduli spaces. This is the subject of my work with my advisor Edward Frenkel; check out our book Vertex Algebras and Algebraic Curves.
My other collaborators are Indranil Biswas, Matt Szczesny (my academic brother), Reimundo Heluani, John Francis, Sam Gunningham, David Helm, David Jordan, Anatoly Preygel, Jonathan Block, Nigel Higson, Adrien Brochier, Andrew Blumberg and Aaron Royer.
My current graduate students are Richard Hughes, Vaibhav Murali, Lee Cohn, Iordan Ganev. My former graduate students are Hendrik Orem (Ph. D. 2015), Pavel Safronov (Ph. D. 2014), Parker Lowrey (Ph.D. 2010), Carl Mautner (Ph.D. 2010),
Slides for lecture at Luminy, July 2012
Course page for Literacy Seminar in Geometry and Topology, Fall 2013.
I miss the nuance of the old topos.
Sunrise on Io by David Ben-Zvi and Paul Burchard. Copyright 1993 by The Geometry Center, University of Minnesota. Used with permission.
More cool fractal pictures I helped make at the Geometry Center
Our Himalayan Adventure, David and friends in Himachal and Ladakh 2003
Click here for some old pictures.
I am an avid movie fan. Check out some lists of movies I've seen.
Some quotes collected from my U.of Chicago Honors Calculus class.
A brief personal history
Image from Outside In:
[Copyright © Summer 1992 by The Geometry Center, Univerity of Minnesota. All rights reserved - see more info]
Department of Mathematics University of Texas, Austin Office 10.168 (512)471-8151 email@example.com