Home Page
Ivan Mirkovi\'c
Office: LGRT 1235I,
E-mail:
mirkovic@math.umass.edu ,
Phone: (413) 545-6023.
COURSES:
523 Fundamental Ideas of Analysis
Graduate Program Director Office Hours:
Tue 2-3 and Th 1-2 in 1523G.
SEMINARS:
COURSE NOTES:
RESEARCH INTERESTS:
The motivating dream is to
understand the geometry that underlies the Langlands
conjectures and the related phenomena such as
string dualities.
Towards
this goal
I
study geometric objects that contain represantation theoretic-information,
such as flag varieties and loop Grassmannians.
PUBLICATIONS
-
S. Arkhipov, R. Bezrukavnikov, A. Braverman, D. Gaitsgory, I. Mirkovi\'c,
Modules over the small quantum group and semi-infinite flag manifold.
Source
PDF
(math.AG/0505280).
-
I. Mirkovic.
Character Sheaves on Reductive Lie Algebras.
Source
PDF,
Mosc. Math. J. 4 (2004), no. 4, 897--910, 981.
(math.RT/0411532).
-
I. Mirkovic, K. Vilonen.
Geometric Langlands duality and representations of algebraic groups over
commutative rings.
Source
PDF,
To appear in Annals of Math. (math.RT/0401222).
-
Roman Bezrukavnikov, Michael Finkelberg, Ivan Mirkovi\'c. 26 pages.
Equivariant ($K$-)homology of affine Grassmannian and Toda lattuce.
Source
PDF,
Compos. Math. 141 (2005), no. 3, 746--768. (math.AG/0306413).
-
A. Beilinson, R. Bezrukavnikov, I. Mirkovic.
Tilting exercises.
Source
PDF,
Mosc. Math. J. 4 (2004), no. 3, 547--557, 782. (math.RT/0301098).
-
Roman Bezrukavnikov, Alexander Braverman, Ivan Mirkovi\'c,
Some results about the geometric Whittaker model
Source
PDF,
Adv. Math. 186 (2004), no. 1, 143--152.
(math.AG/0210250).
-
Ivan Mirkovi\'c, Maxim Vybornov,
On quiver varieties and affine Grassmannians of type A
Source
PDF,
C. R. Math. Acad. Sci. Paris 336 (2003), no. 3, 207--212.
(math.AG/0206084).
-
Roman Bezrukavnikov, Ivan Mirkovi\'c, Dmitriy Rumynin,
Localization of modules for a semisimple Lie algebra in prime characteristic
Source
PDF,
To appear in Annals of Math. (math.RT/0205144).
- Alexander Braverman, Dennis Gaitsgory,
Michael Fnkelberg,
Ivan Mirkovi\'c,
Intersection cohomology of Drinfeld's compactifications.
Source
PDF,
Selecta Math. (N.S.) 8 (2002), no. 3, 381--418.
and erratum in Selecta Math. (N.S.) 10 (2004), no. 3, 429--430.
(math.AG/0012129).
-
Ivan Mirkovi\'c, Kari Vilonen,
Perverse Sheaves on affine Grassmannians and Langlands Duality
Source
PDF
(math.AG/9911050).
-
Ivan Mirkovi\'c, Dmitriy Rumynin,
Geometric Representation Theory of Restricted Lie Algebras of Classical Type
Source
PDF,
Math. Res. Lett. 7 (2000), no. 1, 13--24.
(math.RT/9909058).
-
Michael Finkelberg, Alexander Kuznetsov, Nikita Markarian, Ivan Mirkovi\'c,
A note on the symplectic structure on the space of G-monopoles
Source
PDF,
Comm. Math. Phys. 201 (1999), no. 2, 411--421.
(math.AG/9803124 ).
-
Boris Feigin, Michael Finkelberg, Alexander Kuznetsov, Ivan Mirkovi\'c,
Semiinfinite Flags. II. Local and Global Intersection Cohomology of Quasimaps' Spaces
Source
PDF,
Differential topology, infinite-dimensional Lie algebras, and applications, 113--148, Amer. Math. Soc. Transl. Ser. 2, 194, Amer. Math. Soc., Providence, RI, 1999.
(alg-geom/9711009).
-
Michael Finkelberg, Ivan Mirkovi\'c,
Semiinfinite Flags. I. Case of a global curve P^1
Source
PDF,
Differential topology, infinite-dimensional Lie algebras, and applications, 81--112, Amer. Math. Soc. Transl. Ser. 2, 194, Amer. Math. Soc., Providence, RI, 1999.
(alg-geom/9707010).
-
Michael Finkelberg, Alexander Kuznetsov, Ivan Mirkovi\'c,
The Singular Supports of IC sheaves on Quasimaps' Spaces are Irreducible
Source
PDF,
Topics in quantum groups and finite-type invariants, 85--93, Amer. Math. Soc. Transl. Ser. 2, 185, Amer. Math. Soc., Providence, RI, 1998.
(alg-geom/9705003).
-
Sam Evans, Ivan Mirkovi\'c,
Characteristic Cycles for the Loop Grassmannians and Nilpotent Orbits,
Duke Math J.
- Sam Evans, Ivan Mirkovi\'c,
Iwahori-Matsumoto involution and Fourier Transform,
Duke Math J. 86, (1997) 453-418.
- Ivan Mirkovi\'c, Tohru Uzawa, Kari Vilonen,
Matsuki correspondence for sheaves,
Inventiones Math. 109 (1992).
-
Ivan Mirkovi\'c, Kari Vilonen,
Characteristic varieties of character sheaves,
Inventiones Math. 93 (1988), 405-418,
EDUCATION: