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Ivan Mirkovi\'c

Office: LGRT 1235I, E-mail: mirkovic@math.umass.edu , Phone: (413) 545-6023.

COURSES in Fall 2008: 411.1 Algebra

• GEOMETRIC LANGLANDS/QUANTUM FIELD THEORY. .
  in 2006/2007 the QFT seminar is concentrating on Witten's approach to the Geometric Langlands Program.
  Seminar Notes
• Quantum Field Theory Seminar 04 These are notes on talks in preceding years.

• Algebraic Geometry
• Homological Algebra

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.

• 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 Finkelberg, 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,