Kari Vilonen

Office:

158 Peter Hall Building

School of Mathematics and Statistics

University of Melbourne

Parkville, Victoria 3010 Australia

Tel.: +61 3 8344 1100

E-mail: kari.vilonen (followed by @unimelb.edu.au)

Recent publications

• M. Grinberg, K. Vilonen, T. Xue, Nearby cycle sheaves for symmetric pairs, arXiv: 1805.02794.
  
  
• J. Taskinen and K. Vilonen, Cartan theorems for Stein manifolds over a discrete valuation base, arXiv: 1609.03658.
  
  
• T.-H. Chen, Kari Vilonen and T. Xue, Springer correspondence for the split symmetric pair in type A, arXiv: 1608.06034.
  
  
• T.-H. Chen, Kari Vilonen and T. Xue, Hessenberg varieties, intersections of quadrics, and the Springer correspondence, arXiv: 1511.00617.
  
  
• T.-H. Chen, Kari Vilonen and T. Xue, Springer correspondence for symmetric spaces, arXiv: 1510.05986.
  
  
• T.-H. Chen, T. Xue and K. Vilonen, On the cohomology of Fano varieties and the Springer correspondence, With an appendix by Dennis Stanton. Adv. Math. 318 (2017) 515-533. MR3689749 arXiv: 1602.03052.
  
  
• T. Xue and K. Vilonen, The null-cone and cohomology of vector bundles on flag varieties, Represent. Theory 20 (2016) 482-498. MR3589334
  
  
• W. Schmid and K. Vilonen, Hodge theory and unitary representations Representations of reductive groups, 443-453, Progr. Math. 312, Birkhäuser/Springer, Cham, 2015. MR3495806
  
  
• M. Kashiwara and K. Vilonen, Microdifferential systems and the codimension-three conjecture, Ann. of Math. (2) 180 (2014) 573-620. MR3224719 arXiv:1209.5124.
  
  
• K. Vilonen and G. Williamson, Characteristic cycles and decomposition numbers, Math. Res. Lett. 20 (2013) 359-366. MR3151652 arXiv:1208.1198
  
  
• W. Schmid and K. Vilonen, Hodge theory and unitary representations of reductive Lie groups, Frontiers of Mathematical Sciences, International Press 2011, 397-420. MR3050836 arXiv:1206.5547
  
  
• M. Kashiwara and K. Vilonen, On the codimension-three conjecture, Proc. Japan, Acad., Ser. A 86 (2010), 154-158. MR2780007
  
  
• Geometric Langlands duality and representations of algebraic groups over commutative rings, I. Mirkovic and K. Vilonen, Annals of Math., 166 (2007) 95-143.
  
  
• Microlocal Perverse Sheaves, S. Gelfand, R. MacPherson, and K. Vilonen, http://arxiv.org/abs/math/0509440
  
  
• 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.
  
  
• On the geometric Langlands conjecture, E. Frenkel, D.Gaitsgory, and K. Vilonen, Journal of Amer. Math. Soc., 15 (2002), no 2, 364 - 417.
  
  
• Whittaker patterns in the geometry of moduli spaces of curves, E. Frenkel, D. Gaitsgory and K. Vilonen, Annals of Math. 153 (2001), 699 - 748.
  
  
• Characteristic cycles and wave front cycles of representations of reductive groups, W. Schmid and K. Vilonen, Annals of Math. 151 (2000), 1071 - 1118.
  
• Perverse Sheaves on Affine Grassmannians and Langlands Duality, I. Mirkovic and K. Vilonen, Mathematical Research Letters 7 (2000), 13 - 24.
  
  
• 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 ].
  
  
• 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.
  
  
• Topological methods in representation theory, K. Vilonen, Documenta Mathematica, Extra Volume for ICM 1998 (1998), vol II, 595-604.
  
  
• Two geometric character formulas for reductive Lie groups, W. Schmid and K. Vilonen, Journal of AMS, 11 (1998), no. 2, 799-876.
  
  
• 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.
  
  
• Characteristic cycles of constructible sheaves, W. Schmid and K. Vilonen, Inventiones Math. 124 (1996) 451-502.
  
  
• Perverse sheaves and quivers, S. Gelfand, R. MacPherson, and K. Vilonen, Duke Math. Journal 83 (1996) 621-643.
  
  

Activities and funding:

I was involved in running a project on the geometric Langlands program.

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