Publications

Preprints

    1. W. Liu, C-C. Chiang, K. Vilonen and, T. Xue, Cuspidal character sheaves on graded Lie algebras. arXiv:2409.04030
    2. D. Davis and K. Vilonen, Unitary representations of real groups and localization theory for Hodge modules. arXiv:2309.13215.
    3. D. Davis and K. Vilonen, Hodge filtrations of tempered Hodge modules. arXiv:2206.09091.
    4. D. Davis and K. Vilonen, Mixed Hodge modules and real groups. arXiv:2202.08797.
    5. K. Vilonen and T. Xue, Invariant systems and character sheaves for graded Lie algebras. arXiv:2111.08403.
    6. K. Vilonen and T. Xue, A note on Hessenberg varieties. arxiv: 2101.08652.
    7. M. Grinberg, K. Vilonen, and T. Xue, Nearby Cycle Sheaves for Stable Polar Representations, arXiv:2012.14522.
    8. S. Gelfand, R. MacPherson, and K. Vilonen, Microlocal Perverse Sheaves, arXiv:0509440.

Publications

    1. K. Vilonen, and T. Xue, Character sheaves for graded Lie algebras: stable gradings, Adv. Math. 417 (2023), arXiv:2012.08111.
    2. M. Grinberg, K. Vilonen, and T. Xue, Nearby cycle sheaves for symmetric pairs. Amer. J. Math. 145 (2023), no.1, 1-63. arXiv.
    3. K. Vilonen and T. Xue, Character sheaves for symmetric pairs: special linear groups.  Trans. Amer. Math. Soc. 376 (2023) no. 2, 837-853. arXiv.
    4. K. Vilonen, and T. Xue, Character sheaves for classical symmetric pairs. With an appendix by Dennis Stanton. Represent. Theory 26 (2022), 1097-1144.
    5. R. Bezrukavnikov and K. Vilonen, Koszul Duality for Quasi-split Real Groups, Inventiones Mathematicae, 226 (2021),139-193, arXiv:1510.08343.
    6. T.-H. Chen, K. Vilonen and T. Xue, Springer correspondence, Hyperelliptic curves, and cohomology of Fano varieties. Math. Res. Lett. 27 (2020), No. 5, 1281-1323. arXiv.
    7. T.-H. Chen, K. Vilonen and T. Xue, Hessenberg varieties, intersections of quadrics, and the Springer correspondence, Trans. Amer. Math. Soc. 373 (2020), No. 4, 2427-2461. arXiv. MR4069224
    8. J. Taskinen and K. Vilonen, Cartan theorems for Stein manifolds over a discrete valuation base, J. Geom. Anal. 29 (2019), No. 1, 577-615. arXiv. MR3897027
    9. T. -H. Chen, K. Vilonen and T. Xue, Springer correspondence for the split symmetric pair in type A, Compos. Math. 154 (2018), No. 11, 2403-2425. arXiv. MR3867304
    10. I. Mirkovic and K. Vilonen, Erratum for “Geometric Langlands duality and representations of algebraic groups over commutative rings”, Ann. of Math. (2) 188 (2018), No. 3, 1017-1018. MR3866890
    11. T.-H. Chen, K. Vilonen and T. Xue, On the cohomology of Fano varieties and the Springer correspondence, With an appendix by Dennis Stanton. Adv. Math. 318 (2017), 515-533. arXiv. MR3689749
    12. T. Xue and K. Vilonen, The null-cone and cohomology of vector bundles on flag varieties, Represent. Theory 20 (2016), 482-498. MR3589334
    13. W. Schmid and K. Vilonen, Hodge theory and unitary representations, Representations of reductive groups, Progr. Math. 312, Birkhäuser/Springer, Cham (2015), 443-453. MR3495806
    14. M. Kashiwara and K. Vilonen, Microdifferential systems and the codimension-three conjecture, Ann. of Math. (2) 180 (2014), 573-620. MR3224719
    15. K. Vilonen and G. Williamson, Characteristic cycles and decomposition numbers, Math. Res. Lett. 20 (2013), 359-366. MR3151652
    16. W. Schmid and K. Vilonen, Hodge theory and unitary representations of reductive Lie groups, Frontiers of Mathematical Sciences, International Press (2011), 397-420, arXiv. MR3050836
    17. M. Kashiwara and K. Vilonen, On the codimension-three conjecture, Proc. Japan, Acad., Ser. A 86 (2010), 154-158. MR2780007
    18. I. Mirkovic and K. Vilonen, Geometric Langlands duality and representations of algebraic groups over commutative rings, Annals of Math., 166 (2007), 95-143. MR2342692
    19. M. Emerton, D. Nadler, and K. Vilonen, A geometric Jacquet functor, Duke Math. J. 125 (2004), No. 2, 267-278. arXiv. MR2096674
    20. E. Frenkel, D.Gaitsgory, and K. Vilonen, On the geometric Langlands conjecture, Journal of Amer. Math. Soc., 15 (2002), No. 2, 364-417. MR1887638
    21. E. Frenkel, D. Gaitsgory and K. Vilonen, Whittaker patterns in the geometry of moduli spaces of bundles on curves, Annals of Math. 153 (2001), 699-748. arXiv. MR1836286
    22. W. Schmid and K. Vilonen, Characteristic cycles and wave front cycles of representations of reductive groups, Annals of Math. 151 (2000), 1071-1118. arXiv. MR1779564
    23. I. Mirkovic and K. Vilonen, Perverse Sheaves on Affine Grassmannians and Langlands Duality, Mathematical Research Letters 7 (2000), 13-24. MR1748284
    24. W. Schmid and K. Vilonen, On the geometry of nilpotent orbits, Asian J. Math., vol 8, no 1 (1999), 233-274, A Special Volume in Honour of Sir Michael Atiyah.
      Reprinted in – Surveys in differential geometry, Surv. Differ. Geom., VII, Int. Press (2000), 565-623. MR1919437
    25. K. Vilonen, Geometric methods in representation theory, Representation theory of Lie groups, Amer. Math. Soc. (1998), 241-290. MR1737730
    26. K. Vilonen, Topological methods in representation theory, Proceedings of the International Congress of Mathematicians, Vol. II (Berlin, 1998). Doc. Math. 1998, Extra Vol. II, 595–604. MR1648108
    27. W. Schmid and K. Vilonen, Two geometric character formulas for reductive Lie groups, Journal of AMS, 11 (1998), No. 2, 799-876. MR1612634
    28. E. Frenkel, D.Gaitsgory, D. Kazhdan, and K. Vilonen, Geometric realization of Whittaker Functions and the Langlands Conjecture, Journal of AMS, 11 (1998), No. 2, 451-484. MR1484882
    29. S. Gelfand, R. MacPherson, and K. Vilonen, Perverse sheaves and quivers, Duke Math. Journal 83 (1996), 621-643. MR1390658
    30. W. Schmid and K. Vilonen, Characteristic cycles of constructible sheaves, Invent. Math. 124 (1996), 451-502. MR1369425
    31. W. Schmid and K. Vilonen, Characters, characteristic cycles, and nilpotent orbits. Geometry, Topology & Physics (1995), 329-340. MR1358623
    32. W. Schmid and K. Vilonen, Weyl group actions on Lagrangian cycles and Rossmann’s formula. Noncompact Lie groups and some of their applications (San Antonio, TX, 1993), 243–250, NATO Adv. Sci. Inst. Ser. C Math. Phys. Sci., 429, Kluwer Acad. Publ., Dordrecht, 1994. MR1306528
    33. K. Vilonen, Perverse sheaves and finite-dimensional algebras, Trans. Amer. Math. Soc. 341 (1994), 665-676. MR1135104
    34. W. Schmid and K. Vilonen, Characters, fixed points and Osborne’s conjecture, Representation theory of groups and algebras, Amer. Math. Soc. (1993), 287-303. MR1216196
    35. I. Mirkovic, T. Uzawa and K. Vilonen, Matsuki correspondence for sheaves, Invent. Math. 109 (1992), No. 2, 231-245. MR1172690
    36. I. Mirkovic and K. Vilonen, Characteristic varieties of character sheaves, Invent. Math. 93 (1988), No. 2, 405-418. MR0948107
    37. R. MacPherson and K. Vilonen, Perverse sheaves with singularities along the curve y^n=x^m, Comment. Math. Helv. 63 (1988), No. 1, 89-102. MR0928029
    38. R. Mirollo and K. Vilonen, Bernstein-Gel’fand-Gel’fand reciprocity on perverse sheaves, Ann. Sci. Ecole Norm. Sup. (4) 20 (1987), No. 3, 311-323. MR0925719
    39. R. MacPherson and K. Vilonen, Elementary construction of perverse sheaves, Invent. Math. 84 (1986), No. 2, 403-435. MR0833195
    40. K. Vilonen, Intersection homology D-module on local complete intersections with isolated singularities, Invent. Math. 81 (1985), No. 1, 107-114. MR0796193
    41. R. MacPherson and K. Vilonen, Elementary construction of perverse sheaves (French), C.R.Acad. Sci. Paris Ser. I. Math. 299 (1984), No, 10, 443-446. MR0768077