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David D Ben-Zvi

Department of Mathematics

Frank E. Gerth III Faculty Fellowships (Holder)

Algebraic Geometry, Representation Theory


Phone: 512-471-8151

Office Location
PMA 10.168

Postal Address
AUSTIN, TX 78712

Ph.D., Harvard University (1999)

Research Interests

Algebraic Geometry, Representation Theory.

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.

[1] A Quantization on Riemann Surfaces with Projective Structure (with I. Biswas.) Letters in Mathematical Physics, 54 (2000) 73{82.

[2] Book: Vertex Algebras and Algebraic Curves (with E. Frenkel). Mathematical Surveys and Monographs 88, American Mathematical Society 2001. (Reviewed by Y.-Z. Huang in Bull. AMS Vol. 39 No. 4 (2002) 585-591.) Featured Review MR1849359 (2003f:17036).

[3] Spectral Curves, Opers and Integrable Systems (with E. Frenkel). Pub. Math. IHES 94 (2001) 87{159. Featured Review MR1896178 (2003j:14047).

[4] Theta Functions and Szego Kernels (with I. Biswas). math.AG/0211441. Int. Math. Res. Notices 24 (2003) 1305{1340.

[5] Opers and Theta Functions (with I. Biswas). e-print math.AG/0204301. Adv. Math. 181 (2004) no.2, 368{395.

[6] Cusps and D-modules (with T. Nevins). e-print math.AG/0212094. Jour. Amer. Math. Soc. 17 no.1 (2004) 155{179.

[7] Geometric Realization of the Segal{Sugawara Construction (with E. Frenkel). e-print math.AG/0301206. In: Topology, Geometry and Quantum Field Theory. Proc., 2002 Oxford Symposium in Honour of the 60th Birthday of Graeme Segal. London Math Soc. Lecture Note Series 308, 2004.

[8] Flows of Calogero-Moser Systems (with T. Nevins). e-print math.AG/0603072. Inter. Math Res. Notices 23 (2007).

[9] From Solitons to Many{Body Systems (with T. Nevins). e-print math.AG/0310490. Pure and Applied Math Quarterly, Vol. 4 No.2 (2008), 319{361. (Bogomolov special issue, part I)

[10] Moduli Spaces. In: Princeton Companion to Mathematics, T. Gowers, J. Barrow-Green and I. Leader (Eds). Princeton University Press, Princeton, NJ, 2008.

  • Fellow of the American Mathematical Society, elected in inaugural class, 2012.
  • President's Associates Centennial Teaching Fellowship in Mathematics, University of Texas, 2011-13.