SelectedWorks - Ivan Mirkovic

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Selected Works of Ivan Mirkovic

Professor, Department of Mathematics and Statistics

The motivating dream is to understand the geometry that underlies Number Theory and QFT, for instance zeta functions, Langlands conjectures and string dualities. In this direction I study geometric objects that contain representation theoretic-information, such as flag varieties and loop Grassmannians.

Works
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About Ivan Mirkovic

The motivating dream is to understand the geometry that underlies Number Theory and QFT, for instance zeta functions, Langlands conjectures and string dualities. In this direction I study geometric objects that contain representation theoretic-information, such as flag varieties and loop Grassmannians.

Present	Professor, Department of Mathematics and Statistics, University of Massachusetts Amherst
Institution Organization Position Type Position Title Time Period to Options Current Position Affiliate my profile with this Institution

Algebraic Geometry

Personal Webpage

1235I Lederle Grad Research Tower
University of Massachusetts
Amherst MA, 01003
Tel:413-545-6023

Email:

Articles (13)

Linear Koszul duality

COMPOSITIO MATHEMATICA (2010)

I Mirkovic and S Riche

In this paper we construct, for F1 and F2 subbundles of a vector bundle E, a ‘Koszul duality’ equivalence between ...

Geometric Langlands duality and representations of algebraic groups over commutative ...

ANNALS OF MATHEMATICS (2007)

I Mirkovic and K Vilonen

Singular localization and intertwining functors for reductive Lie algebras in ...

NAGOYA MATHEMATICAL JOURNAL (2006)

R Bezrukavnikov, I Mirkovic and D Rumynin

In [BMR] we observed that, on the level of derived categories, representations of the Lie algebra of a semisimple algebraic ...

Equivariant homology and K-theory of affine Grassmannians and Toda lattices

COMPOSITIO MATHEMATICA (2005)

R Bezrukavnikov, M Finkelberg and I Mirkovic

For an almost simple complex algebraic group G with affine Grassmannian $\text{Gr}_G=G(\mathbb{C}(({\rm t})))/G(\mathbb{C}[[{\rm t}]])$, we consider the equivariant homology $H^{G(\mathbb{C}[[{\rm ...

Some results about geometric Whittaker model

ADVANCES IN MATHEMATICS (2004)

R Bezrukavnikov, A Braverman and I Mirkovic

Let G be an algebraic reductive group over a field of positive characteristic. Choose a parabolic subgroup P in G ...

On quiver varieties and affine Grassmanians of type A

COMPTES RENDUS MATHEMATIQUE (2003)

I Mirkovic and M Vybornov

We construct Nakajima's quiver varieties of type A in terms of affine Grassmannians of type A. This gives a compactification ...

Geometric representation theory of restricted lie algebras

TRANSFORMATION GROUPS (2001)

I Mirkovic and D Rumynin

We modify the Hochschild -map to construct central extensions of a restricted Lie algebra. Such central extension gives rise to ...

Perverse sheaves on affine Grassmannians and Langlands duality

MATHEMATICAL RESEARCH LETTERS (2000)

I Mirkovic and K Vilonen

A note on a symplectic structure on the space of ...

COMMUNICATIONS IN MATHEMATICAL PHYSICS (1999)

M Finkelberg, A Kuznetsov, N Markarian and I Mirkovic

Let G be a semisimple complex Lie group with a Borel subgroup B. Let X=G/B be the flag manifold of ...

Centers of reduced enveloping algebras

MATHEMATISCHE ZEITSCHRIFT (1999)

I Mirkovic and D Rumynin

We compute the inverse image of a functional in the Zassenhaus variety. We apply this computation to describe the category ...

Characteristic cycles for the loop Grassmannian and nilpotent orbits

DUKE MATHEMATICAL JOURNAL (1999)

S Evens and I Mirkovic

Fourier transform and the Iwahori-Matsumoto involution

DUKE MATHEMATICAL JOURNAL (1997)

S Evens and I Mirkovic

MATSUKI CORRESPONDENCE FOR SHEAVES

INVENTIONES MATHEMATICAE (1992)

I Mirkovic, T UZAWA and K VILONEN

REPRESENTATIONS OF SEMI-SIMPLE LIE ALGEBRAS IN PRIME CHARACTERISTIC AND NONCOMMUTATIVE ...

Mathematics and Statistics Department Faculty Publication Series (2011)

R Bezrukavnikov and I Mirkovic

LINEAR KOSZUL DUALITY AND AFFINE HECKE ALGEBRAS

Mathematics and Statistics Department Faculty Publication Series (2009)

I Mirkovic and S Richie

n this paper we prove that the linear Koszul duality equivalence constructed in a previous paper provides a geometric realization ...

QUIVER VARIETIES AND BEILINSON-DRINFELD GRASSMANNIANS OF TYPE A

Mathematics and Statistics Department Faculty Publication Series (2008)

I Mirkovic and M Vybornov

SEMIINFINITE FLAGS. II. LOCAL AND GLOBAL INTERSECTION COHOMOLOGY OF QUASIMAPS ...

Mathematics and Statistics Department Faculty Publication Series (2008)

B Feigin, M Finkelberg, A Kuznetsov and I Mirkovic

Modules over the small quantum group and semi-infinite flag manifold

Transformation Groups (2005)

S Arkhipov, R Bezrukavnikov, A Braverman, D Gaitsgory, et al.

We develop a theory of perverse sheaves on the semi-infinite flag manifold G((t))/N((t)) · T[[t]], and show that the subcategory ...

Character sheaves on reductive Lie algebras

MOSCOW MATHEMATICAL JOURNAL (2004)

The paper develops a linearized notion of Lusztig's character sheaves (on Lie algebras rather then on groups), which contains Lusztig's ...

Tilting exercises

MOSCOW MATHEMATICAL JOURNAL (2004)

A Beilinson, R Bezrukavnikov and I Mirkovic

We discuss tilting objects in categories of perverse sheaves smooth along some stratification. In case of the Schubert stratification we ...

Intersection cohomology of Drinfeld‚s compactifications

Selecta mathematica (2002)

A Braverman, M Finkelberg, D Gaitsgory and I Mirkovic

Let X be a smooth complete curve, G be a reductive group and a parabolic. Following Drinfeld, one defines a ...

SEMIINFINITE FLAGS. I. CASE OF GLOBAL CURVE P1.

Mathematics and Statistics Department Faculty Publication Series (1998)

M Finkelberg and I Mirkovic

PERVERSE SHEAVES ON LOOP GRASSMANNIANS AND LANGLANDS DUALITY

Mathematics and Statistics Department Faculty Publication Series (1997)

I Mirkovic and K Vilonen

THE SINGULAR SUPPORTS OF IC SHEAVES ON QUASIMAPS’ SPACES ARE ...

Mathematics and Statistics Department Faculty Publication Series (1997)

M Finkelberg, A Kuznetsov and I Mirkovic