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. K. Vilonen and T. Xue, Invariant systems and character sheaves for graded Lie algebras. arXiv:2111.08403.
    5. K. Vilonen and T. Xue, A note on Hessenberg varieties. arxiv: 2101.08652.
    6. M. Grinberg, K. Vilonen, and T. Xue, Nearby Cycle Sheaves for Stable Polar Representations, arXiv:2012.14522.
    7. S. Gelfand, R. MacPherson, and K. Vilonen, Microlocal Perverse Sheaves, arXiv:0509440.

Publications

    1. D. Davis and K. Vilonen, Mixed Hodge modules and real groups.Adv. Math. 470 (2025), Paper No. 110255, 78 pp. arXiv:2202.08797.
    2. K. Vilonen, and T. Xue, Character sheaves for graded Lie algebras: stable gradings, Adv. Math. 417 (2023), Paper No. 108935, 59 pp. arXiv:2012.08111.
    3. M. Grinberg, K. Vilonen, and T. Xue, Nearby cycle sheaves for symmetric pairs. Amer. J. Math. 145 (2023), no.1, 1-63. arXiv.
    4. K. Vilonen and T. Xue, Character sheaves for symmetric pairs: special linear groups.  Trans. Amer. Math. Soc. 376 (2023) no. 2, 837-853. arXiv.
    5. K. Vilonen, and T. Xue, Character sheaves for classical symmetric pairs. With an appendix by Dennis Stanton. Represent. Theory 26 (2022), 1097-1144.
    6. R. Bezrukavnikov and K. Vilonen, Koszul Duality for Quasi-split Real Groups, Inventiones Mathematicae, 226 (2021),139-193, arXiv:1510.08343.
    7. 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.
    8. 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
    9. 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
    10. 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
    11. 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
    12. 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
    13. T. Xue and K. Vilonen, The null-cone and cohomology of vector bundles on flag varieties, Represent. Theory 20 (2016), 482-498. MR3589334
    14. W. Schmid and K. Vilonen, Hodge theory and unitary representations, Representations of reductive groups, Progr. Math. 312, Birkhäuser/Springer, Cham (2015), 443-453. MR3495806
    15. M. Kashiwara and K. Vilonen, Microdifferential systems and the codimension-three conjecture, Ann. of Math. (2) 180 (2014), 573-620. MR3224719
    16. K. Vilonen and G. Williamson, Characteristic cycles and decomposition numbers, Math. Res. Lett. 20 (2013), 359-366. MR3151652
    17. 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
    18. M. Kashiwara and K. Vilonen, On the codimension-three conjecture, Proc. Japan, Acad., Ser. A 86 (2010), 154-158. MR2780007
    19. I. Mirkovic and K. Vilonen, Geometric Langlands duality and representations of algebraic groups over commutative rings, Annals of Math., 166 (2007), 95-143. MR2342692
    20. M. Emerton, D. Nadler, and K. Vilonen, A geometric Jacquet functor, Duke Math. J. 125 (2004), No. 2, 267-278. arXiv. MR2096674
    21. E. Frenkel, D.Gaitsgory, and K. Vilonen, On the geometric Langlands conjecture, Journal of Amer. Math. Soc., 15 (2002), No. 2, 364-417. MR1887638
    22. 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
    23. 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
    24. I. Mirkovic and K. Vilonen, Perverse Sheaves on Affine Grassmannians and Langlands Duality, Mathematical Research Letters 7 (2000), 13-24. MR1748284
    25. 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
    26. K. Vilonen, Geometric methods in representation theory, Representation theory of Lie groups, Amer. Math. Soc. (1998), 241-290. MR1737730
    27. 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
    28. W. Schmid and K. Vilonen, Two geometric character formulas for reductive Lie groups, Journal of AMS, 11 (1998), No. 2, 799-876. MR1612634
    29. 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
    30. S. Gelfand, R. MacPherson, and K. Vilonen, Perverse sheaves and quivers, Duke Math. Journal 83 (1996), 621-643. MR1390658
    31. W. Schmid and K. Vilonen, Characteristic cycles of constructible sheaves, Invent. Math. 124 (1996), 451-502. MR1369425
    32. W. Schmid and K. Vilonen, Characters, characteristic cycles, and nilpotent orbits. Geometry, Topology & Physics (1995), 329-340. MR1358623
    33. 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
    34. K. Vilonen, Perverse sheaves and finite-dimensional algebras, Trans. Amer. Math. Soc. 341 (1994), 665-676. MR1135104
    35. 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
    36. I. Mirkovic, T. Uzawa and K. Vilonen, Matsuki correspondence for sheaves, Invent. Math. 109 (1992), No. 2, 231-245. MR1172690
    37. I. Mirkovic and K. Vilonen, Characteristic varieties of character sheaves, Invent. Math. 93 (1988), No. 2, 405-418. MR0948107
    38. 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
    39. 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
    40. R. MacPherson and K. Vilonen, Elementary construction of perverse sheaves, Invent. Math. 84 (1986), No. 2, 403-435. MR0833195
    41. K. Vilonen, Intersection homology D-module on local complete intersections with isolated singularities, Invent. Math. 81 (1985), No. 1, 107-114. MR0796193
    42. 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