# Ivan Mirkovic

Professor Emeritus

Location

LGRT 1680

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Education

Ph.D. University of Utah, 1986

M.S. University of Zagreb, 1981

B.S. University of Zagreb, 1977

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RESEARCH INTERESTS

Representation theory, algebraic geometry

Geometric Representation Theory, Quantum Field Theory, Number Theory, Algebraic Geometry

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Selected Publications

- Linear Koszul duality. Compos. Math. 146 (2010), no. 1, 233ñ258. with S.Riche
- Localization of modules for a semisimple Lie algebra in prime characteristic. With an appendix by Bezrukavnikov and Simon Riche. Ann. of Math. (2) 167 (2008), no. 3, 945ñ991. with R. Bezrukavnikov, D. Rumynin.
- Geometric Langlands duality and representations of algebraic groups over commutative rings. Ann. of Math. (2) 166 (2007), no. 1, 95ñ143. with K. Vilonen
- Singular localization and intertwining functors for reductive Lie algebras in prime characteristic. Nagoya Math. J. 184 (2006) (Lusztig issue). with R. Bezrukavnikov, D. Rumynin.
- Equivariant homology and
-theory of affine Grassmannians and Toda lattices. Compos. Math. 141 (2005), no. 3, with R. Bezrukavnikov; M. Finkelberg**K** - Character sheaves on reductive Lie algebras. Mosc. Math. J. 4 (2004), no. 4, 897ñ910, 981.
- Tilting exercises. Mosc. Math. J. 4 (2004), no. 3, 547ñ557, 782. with Beilinson, A.; Bezrukavnikov, R.
- Some results about geometric Whittaker model. Adv. Math. 186 (2004), no. 1, 143ñ152. with Bezrukavnikov, Roman; Braverman, Alexander.
- On quiver varieties and affine Grassmannians of type
. C. R. Math. Acad. Sci. Paris 336 (2003), no. 3, 207ñ212, with Vybornov, Maxim**A** - Intersection cohomology of Drinfeld's compactifications. Selecta Math. (N.S.) 8 (2002), no. 3, 381ñ418. with Braverman, A.; Finkelberg, M.; Gaitsgory, D.
- Semi-infinite flags. II. Local and global intersection cohomology of quasimaps' spaces. Differential topology, infinite-dimensional Lie algebras, and applications, 113ñ148, Amer. Math. Soc. Transl. Ser. 2, 194, Amer. Math. Soc., Providence, RI, 1999. with Feigin, Boris; Finkelberg, Michael; Kuznetsov, Alexander
- Semi-infinite flags. I. Case of global curve
. Differential topology, infinite-dimensional Lie algebras, and applications, 81ñ112, Amer. Math. Soc. Transl. Ser. 2, 194, Amer. Math. Soc., Providence, RI, 1999. with Finkelberg, Michael**boldP**^{1} - Centers of reduced enveloping algebras. Math. Z. 231 (1999), no. 1, 123ñ132. with Rumynin, Dmitriy
- A note on a symplectic structure on the space of
-monopoles. Comm. Math. Phys. 201 (1999), no. 2, 411ñ421. with Finkelberg, Michael; Kuznetsov, Alexander; Markarian, Nikita*G* - Evens, SamCharacteristic cycles for the loop Grassmannian and nilpotent orbits. Duke Math. J. 97 (1999), no. 1, 109ñ126. with Evens, Sam
- The singular supports of IC sheaves on spaces of quasimaps are irreducible. Topics in quantum groups and finite-type invariants, 85ñ93, Amer. Math. Soc. Transl. Ser. 2, 185, Amer. Math. Soc., Providence, RI, 1998, with Finkelberg, M.; Kuznetsov, A.
- Fourier transform and the Iwahori-Matsumoto involution. Duke Math. J. 86 (1997), no. 3, 435ñ464, with Evens, Sam
- Matsuki correspondence for sheaves. Invent. Math. 109 (1992), no. 2, 231ñ245. with Uzawa, T.; Vilonen, K.
- Characteristic varieties of character sheaves. Invent. Math. 93 (1988), no. 2, 405ñ418. with Vilonen, K.
- CLASSIFICATION OF IRREDUCIBLE TEMPERED REPRESENTATIONS OF SEMISIMPLE GROUPS. Thesis (Ph.D.)ñThe University of Utah. 1986. 86 pp,