Kari Vilonen

Vilonen (left) with Wilfried Schmid at Oberwolfach in 2006

Kari Kaleva Vilonen (born 1955) is a Finnish mathematician, specializing in geometric representation theory.

Vilonen participated as a student in the International Mathematical Olympiad and received in 1973/74 the bronze medal. He received in 1983 his Ph.D from Brown University under Robert MacPherson with thesis The Intersection Homology D-module on Hypersurfaces with Isolated Singularities.[1] Vilonen was an assistant professor at Harvard University from 1986 to 1989. From 1989 to 2000 he was a faculty member at Brandeis University. He is a professor at Northwestern University[2] since 2000 and a professor at the University of Helsinki since 2010.[3]

With Dennis Gaitsgory and Edward Frenkel he proved the geometrical Langlands conjecture for curves over finite fields.

Vilonen was a Guggenheim Fellow for the academic year 1997/98. In 1998 he was an Invited Speaker with talk Topological methods in representation theory at the International Congress of Mathematicians in Berlin. In 2004 he was elected a member of the Finnish Academy of Science and Letters.

Selected publications

  • Mirković, I; Uzawa, T; Vilonen, K (1992). "Matsuki correspondence for sheaves". Inventiones mathematicae. 109 (1): 231–245. Bibcode:1992InMat.109..231M. doi:10.1007/BF01232026.
  • Vilonen, K (1994). "Perverse sheaves and finite-dimensional algebras". Trans. Amer. Math. Soc. 341 (2): 665–676. doi:10.1090/S0002-9947-1994-1135104-3.
  • Frenkel, E; Gaitsgory, D; Kazhdan, D; Vilonen, K (1998). "Geometric realization of Whittaker functions and the Langlands conjecture". J. Amer. Math. Soc. 11 (2): 451–484. doi:10.1090/S0894-0347-98-00260-4.
  • Schmid, Wilfried; Vilonen, Kari (1998). "Two geometric character formulas for reductive Lie groups". J. Amer. Math. Soc. 11 (4): 799–867. doi:10.1090/S0894-0347-98-00275-6.
  • Mirković, I; Vilonen, K (1999). "Perverse sheaves on affine Grassmannians and Langlands duality". arXiv:math/9911050.
  • J. Adams; D. Vogan, eds. (2000). "Geometric methods in representation theory by K. Vilonen". Representation theory of Lie groups. IAS/Park City Mathematics Series 8. American Mathematical Society. pp. 241–290. arXiv:math/0410032. Bibcode:2004math.....10032V.
  • Frenkel, E; Gaitsgory, D; Vilonen, K (2002). "On the geometric Langlands conjecture". J. Amer. Math. Soc. 15 (2): 367–417. doi:10.1090/S0894-0347-01-00388-5.
  • Schmid, Wilfried; Vilonen, Kari (2011). "Hodge theory and the unitary representations of reductive Lie groups". Frontiers in Mathematical Sciences. International Press. pp. 397–420. arXiv:1206.5547. Bibcode:2012arXiv1206.5547S.

References

  1. ↑ Kari Vilonen at the Mathematics Genealogy Project
  2. ↑ Kari Vilonen, Department of Mathematics, Northwestern University
  3. ↑ "Humboldt researcher award winner coming to MPIM". Max Planck Institute for Mathematics.
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