David Ben-Zvi

My slides and video from plenary talk ``Representation Theory as Gauge Theory" at the 2016 Clay Research Conference.

Course page for Algebra II, Spring 2017.

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 Rustam Antia, 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),

ASPECTS of Topology - conference in honor of Graeme Segal's 70th birthday

Categorical Representation Theory:

Slides for lecture at Luminy, July 2012

Course page for Literacy Seminar in Geometry and Topology, Fall 2013.

• Mirror Symmetry and Hodge Theory: six-part Perspectives in Geometry lecture series by Tony Pantev (U. Penn)
• The Fundamental Lemma - a gentle introduction to the ideas surrounding Ngo's proof of the Fundamental Lemma
• Index Theory and K-Homology - a beautiful four-part Perspectives in Geometry Lecture Series by Nigel Higson (Penn State).

• GRASP (Geometry, Representations, And Some Physics) -- an electronic source for expository streaming--video lectures, notes, and references for beginning graduate students (funded by an NSF CAREER grant). [Not to be confused with Greece Residents Assisting Stray Pets and other GRASP pages]

• My Geometric Langlands page contains various links to introductory lectures, survey papers, notes and other references for the geometric Langlands program and related areas.

• GRASP notes page, containing a (growing) collection of lecture notes, including many on geometric Langlands topics.

• Publications and Preprints and Annotated Bibliography (see also the arXiv search for my papers.)

• My outdated Math Page contains some informal essays and links.

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
benzvi@math.utexas.edu