Specific current interests: the combination of ideas from
derived algebraic geometry, topological quantum field theory
and noncommutative geometry
to geometric representation theory, the geometric Langlands
correspondence and integrable systems.
National Science Foundation CAREER Award 2005-2010
National Science Foundation DMS Grant 2004-2007
University of Texas Summer Research Assignment, 2004
National Science Foundation Postdoctoral
Research Fellowship, 1999-2001
National Science Foundation Graduate Fellowship
1994-97
Princeton University Mathematics Department Brown Prize (Junior Prize, 1993),
Covington Prize
(Senior Prize, 1994) and Miller Prize (Thesis Prize, 1994).
Recipient, Barry M. Goldwater Scholarship, 1993-4.
Recipient, B'nai Brith Scholarship, 1990-4.
Professional Experience:
Associate Professor in Mathematics, U. of Texas Austin, 2008-present.
Member, Institute for Advanced Study, Spring 2008.
Visiting Assistant Professor, Northwestern University, Fall 2004.
Assistant Professor in Mathematics, U. of Texas Austin, 2003-2008.
L. E. Dickson Instructor in Mathematics. U. of
Chicago, 1999-2003.
Postdoctoral Fellow, MSRI, Spring Semester 2002.
Visitor, Technische Universit\"at Berlin, July 1998.
Exchange Scholar, UC Berkeley. September 1997-June
1999.
Visitor, Institute for Advanced Study, February-June
1997.
Teaching Experience:
(UT Austin unless otherwise stated)
Lie Groups (Graduate Course). Fall 2009.
Literacy Seminar in Geometry (Graduate Course). Spring 2009.
Math 408L: Differential and Integral Calculus. Fall 2008.
Geometric Langlands (Graduate Course). Fall 2007.
Complex Geometry (Graduate Course). Spring 2007.
Math 408L: Differential and Integral Calculus. Fall 2006.
Math 341: Linear Algebra. Spring 2006.
Riemannian Geometry (Graduate Course). Fall 2005.
Representation Theory of SL_2 (Graduate Course). Spring 2005.
Math 408C - Differential and Integral Calculus, 1st semester.
Spring 2004.
Math 408D - Differential and Integral Calculus, 2nd semester.
Fall 2003.
Graduate Course: Conformal Field Theory and Representation Theory.
Spring Quarter 2003, U. of Chicago.
Math 161-162 - Honors Calculus. Fall-Winter Quarters
2000-2001, U. of Chicago.
Math 162 - Honors Calculus. Winter Quarter 2000,
U. of Chicago.
Math 54W -- Linear Algebra and Differential
Equations (section for
A. Givental), Berkeley 1998.
Teaching Preparation Course (Math 300) at Berkeley,
1998.
Teaching Apprenticeship Program at Harvard, 1995.
Service:
Associate Editor, Advances in Mathematics, 2005-present.
Referee for journals, including Inventiones
Mathematicae, Duke Mathematical Journal, Compositio Mathematica,
Advances in Mathematics, Journal of Algebraic
Geometry, Communications in Mathematical Physics,
Transformation Groups, and Moscow
Mathematical Journal.
Organizer, Mathematics Department Colloquia.
U. of Chicago, 1999-2003.
The Geometry Center:
Visitor (1991,1994), Summer Student (1992) and Apprentice
(March--August 1993) at the Geometry Center (University of Minnesota).
Animator and Script Writer (1991-1993) for video production
``Outside In''. Honors for ``Outside In'': First Place in 1998
International Congress of Mathematicians VideoMath Contest. Shown at
SIGGRAPH 94 Electronic Theater, won awards at NICOGRAPH, London
Effects and Animation Festival, Prix Pixel Imagina, and Prix Ars
Electronica, and was featured on the cover of Scientific American.
[1] Vertex Algebras and Algebraic Curves (with
E. Frenkel). First Edition: Mathematical Surveys and Monographs 88, American
Mathematical Society 2001. (Reviewed by Y.-Z. Huang
in
Bull. AMS Vol. 39 No. 4 (2002) 585-591.)
Second Edition: American Mathematical Society 2004.
Featured Review MR1849359 (2003f:17036).
Papers:
(see the
arXiv search for abstracts and texts of the papers. )
[2]
Spectral Curves, Opers and Integrable
Systems (with E. Frenkel). Publications Math\`ematiques de
l'Institut des Hautes \'Etudes Scientifiques no. 94 (2001) 87-159.
Featured Review MR1896178 (2003j:14047).
[4]
Theta Functions and Szeg\"o
Kernels (with I. Biswas). e-print math.AG/0211441.
International Math. Research Notices no. 24 (2003) 1305--1340.
[5]
Opers and Theta Functions (with
I. Biswas). e-print math.AG/0204301. Advances in Mathematics 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 Society Lecture Note Series 308, 2004.
[8]
From Solitons to Many--Body Systems (with T. Nevins). e-print
math.AG/0310490. Pure and Applied Math
Quarterly Vol. 4 No.2, 2008 (Bogomolov special issue, part I)
[9] Moduli Spaces. Expository article, to appear in Princeton Companion
to Mathematics, ed. T. Gowers, 2005.
The Geometric Langlands Program. Invited Lecture Series,
Winter School, Mathematisches Institut G\"ottingen. January 2007.
Geometry of Derived Categories. Minicourse, Graduate Student Warmup
Workshop for AMS Summer Institute in Algebraic Geometry. U. of Washington
Seattle. July 2005.
Vertex, Chiral and Factorization Algebras I-III. Workshop on Vertex Algebras
and their Applications. E.Schr\"odinger Institute, Vienna. June 2005.
Solitons and Many-Body Systems. U. of Minnesota.
January 2003.
Solitons and Many-Body Systems. U.C. Davis.
January 2003.
Solitons and Many-Body Systems. U. of
Massachusetts, Amherst. December 2002.
Differential Solitons and Algebraic
Geometry. U. of Michigan. October 2002.
Geometric Langlands for Beginners. Special
Departmental Colloquium, U. of Chicago. May 2001.
Moduli spaces and vertex algebras. SUNY
Stony-Brook. April 2000.
Geometry of Integrable Systems. UC
Riverside. March, 1999.
Conference Talks:
Langlands duality for 3d gauge theories. Gauge Theory and Representation Theory.
Institute for Advanced Study, November 2007.
Langlands duality for character sheaves. Fourier-Mukai and Nahm transforms. CRM
Montreal, August 2007.
Langlands duality and topological field theory. Quantum Geometry.
Aspen Center for Physics, July 2007.
Loop Spaces and Langlands Parameters. Noncommutative Geometry. Northwestern U., May 2007.
Geometric Langlands. Workshop on Moduli of Vector Bundles.
Clay Foundation, October 2006.
Langlands Duality and Real Groups.
Michigan/Ohio State Algebraic Geometry Workshop. Ohio State U., April 2006.
Langlands Duality and Real Groups. Texas Geometry
and Topology Conference, U. of Texas Austin. October 2005.
What's the deal with Geometric Langlands? AMS
Algebraic Geometry Boot Camp, U. of Washington. July 2005.
Hilbert Schemes, Perverse Bundles and D Bundles.
Session on Noncommutative Geometry, AMS Sectional Meeting, U.C. Santa Barbara.
March 2005.
The Langlands Program. Loop
Spaces and Elliptic Cohomology, in honor of Jack Morava. U. of
Toronto, October 2004.
Calogero-Moser Spaces, Perverse Bundles and D-Bundles. Infinite-Dimensional Aspects of Representation Theory
and Applications, University of Virginia. May 2004.
Calogero-Moser, KP and D-Bundles. AMS Southeast Regional Meeting, Florida State University.
March 2004.
Geometric Langlands and Hitchin Systems. Special Meeting on Geometric Langlands
and String Theory. Institute for Advanced Study. March 2004.
Noncommutative Geometry and Soliton Equations. Noncommutative
Algebraic Geometry, Mittag-Leffler Institute. January 2004.
Noncommutative Geometry and Soliton Equations.
Geometric Methods in Algebra and Number Theory. U. of Miami,December 2003.
$\D$--bundles and Grassmannians.
Representations of infinite-dimensional Lie algebras
and applications, University of California, Santa Barbara. October 2003.
Geometry and the Sugawara Construction.
Representations of Loop Groups Conference, UCLA. November 2001.
Affine Springer Fibers and Cartans of Loop Groups.
AMS Regional Meeting at Providence College. October, 1999.
Formal Higgs Bundles and Integrable Systems.
Vector Bundles on Algebraic Curves '99. Salamanca, June 1999.
Cartan Subgroups of Loop Groups.
Lie Groups, Lie Algebras and their
Representations, UCLA. December, 1998.
KdV and Algebraic Geometry.
Generalized
Kac-Moody Algebras, Oberwolfach. July, 1998.
Grassmannians, Connections and Integrable Systems.
AMS Regional Meeting at UC Davis. April, 1998.
Everting the Sphere.
Smith College Regional Geometry
Institute. August 1993.
Regular Homotopy and Sphere Eversions.
MSRI Conference on Visualization of
Geometric Structures. October 1992.
Invited Seminar Talks:
Real Groups and Derived Algebraic Geometry. Algebraic Topology Seminar, MIT.
April 2008.
Real Groups and Topological Field Theory. Lie Groups and Quantum Math Seminar,
Rutgers. March 2008.
Character Sheaves and Real Groups. Derived Algebraic
Geometry Seminar, Institute for Advanced Study. February 2008.
Langlands Duality and Real Groups. Algebra Seminar,
Caltech. April 2006.
Langlands Duality and Real Groups. Algebraic
Geometry Seminar, Stanford U. November 2005.
The Segal-Sugawara Construction. Dutch Intercity Seminar AG, U.v.Amsterdam.
June 2005.
Calogero-Moser Systems. Algebra Seminar, U.v. Amsterdam. June 2005.
Hilbert Schemes, Perverse Bundles and D Bundles.
Mathematical Physics Seminar, Northwestern U. December 2004.
Real Groups and Langlands Duality. Topology Seminar,
Notre Dame U. November 2004.
Real Groups and Langlands Duality. Algebra Seminar, U. Illinois
Chicago. November 2004.
From Solitons to Many-Body Systems via Noncommutative Geometry.
Algebraic Geometry Seminar, U. of Chicago. April 2003.
Solitons and Many-Body Systems. Joint Math/Physics "Everyperson"
Seminar, Brandeis U. March 2003.
Solitons and Many-Body
Systems. Algebraic Geometry Seminar, Columbia University, February
2003.
Solitons and Many-Body Systems. Integrable Systems Seminar, Institute
for Advanced Studies, February 2003.
Solitons and Many-Body Systems. Geometry Seminar, UT
Austin. January 2003.
Differential Solitons and Algebraic Geometry. Algebra Seminar,
Notre Dame University. December 2002.
Solitons and $\D$--modules. Algebra Seminar, U. of Washington Seattle.
December 2002.
Solitons and Particles in Algebraic Geometry. Algebraic Geoemtry
Seminar, U. of Illinois Chicago. November 2002.
Solitons and $\D$--modules. Algebra Seminar, Northwestern
U. November 2002.
Cusps, $\D$-Modules and Vertex Algebras.
Lie Theory Seminar, U. of Wisconsin Madison. November 2002.
Differential Solitons and Algebraic Geometry.
Mathematical Physics Seminar, U. of Wisconsin Madison. November 2002.
Cusps, $\D$-Modules and Solitons. Algebra
Seminar, U. of Pennsylvania. September 2002.
Integrable Systems and Bundles on Curves. California
Institute of Technology. November 2001.
Isomonodromy on Riemann Surfaces. Algebra Geometry and Physics
Seminar, SUNY Stony-Brook. September 2001.
Calogero-Moser and Hitchin Systems I-IV. Geometric
Langlands Seminar, U. of Chicago. October, 2000.
Moduli spaces and vertex algebras. Algebraic Geometry Seminar,
Northwestern U. May 2000.
Moduli of curves and bundles via vertex algebras. Algebra Seminar,
U. of Pennsylvania. April 2000.
Moduli of curves and bundles via vertex algebras. Algebraic
Geometry Seminar, Duke U. April 2000.
Moduli of curves and bundles via vertex
algebras. Mathematical Physics Seminar, U. of Michigan. April 2000.
Solitons and Algebraic Geometry I-II. Algebraic Geometry Seminar, U. of
Chicago. October 1999.