Kari Vilonen

Professor of Mathematics

Office:

301 Lunt Hall
Department of Mathematics
Northwestern University
Evanston, IL 60208-2730, USA
Tel.: (847) 491-5557
Fax: (847) 491-8906
E-mail: vilonen (followed by @math.northwestern.edu)

Links:
I am involved in running a project on the geometric Langlands program.



Recent Publications*:
Perverse sheaves and quivers, S.Gelfand, R.MacPherson, and K. Vilonen, Duke Math. Journal 83 (1996), 621-643.

Characteristic cycles of constructible sheaves, W. Schmid and K. Vilonen, Inventiones Math. 124 (1996), 451-502.

Geometric realization of Whittaker Functions and the Langlands Conjecture, E. Frenkel, D.Gaitsgory, D. Kazhdan, and K. Vilonen, Journal of AMS, 11 (1998), no. 2, 451-484.

Two geometric character formulas for reductive Lie groups, W. Schmid and K. Vilonen, Journal of AMS, 11 (1998), no. 2, 799-876.

Topological methods in representation theory, K. Vilonen, Documenta Mathematica, Extra Volume for ICM 1998 (1998), vol II, 595-604.

On the geometry of nilpotent orbits, W. Schmid and K. Vilonen, Asian J. Math., vol 8, no 1, 233-274, (1999), a special volume in honor of Michael Atiyah. Reprinted in: Surveys in differential geometry,  565 - 623, Surv. Differ. Geom., VII, Int. Press, Somerville, MA, 2000.

Geometric methods in representation theory, K. Vilonen, Representation theory of Lie groups (J. Adams and D. Vogan, eds.), IAS/Park City Mathematics Series, vol 8, AMS, 2000, pp 241 - 290. [PS file 1,4MB]. The dvi version without pictures [ dvi ].

Perverse Sheaves on Affine Grassmannians and Langlands Duality, I. Mirkovic and K. Vilonen, Mathematical Research Letters 7 (2000), 13 - 24.

Characteristic cycles and wave front cycles of representations of reductive groups, W. Schmid and K. Vilonen, Annals of Math. 151 (2000), 1071 - 1118.

Whittaker patterns in the geometry of moduli spaces of curves, E. Frenkel, D.Gaitsgory, and K. Vilonen, Annals of Math. 153 (2001), 699 - 748.

On the geometric Langlands conjecture, E. Frenkel, D.Gaitsgory, and K. Vilonen, Journal of Amer. Math. Soc., 15 (2002), no 2, 364 - 417.

A geometric Jacquet functor, M. Emerton, D.Nadler, and K. Vilonen, Duke Math. J.  125 (2004), no. 2, 267–278, and also available at math.RT/0311339.

Geometric Langlands duality and representations of algebraic groups over commutative rings, I. Mirkovic and K. Vilonen, preprint, to appear in Annals of Mathematics.

Microlocal Perverse Sheaves, S. Gelfand, R. MacPherson, and K. Vilonen, preprint.

*My research has been partially supported by DARPA and the NSF.