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.
Articles
Linear Koszul duality (with S Riche), Composito Mathematica (2010)
In this paper we construct, for F1 and F2 subbundles of a vector bundle E,...
Geometric Langlands duality and representations of algebraic groups over commutative rings (with K Vilonen), Annals Mathematics (2007)
Singular localization and intertwining functors for reductive Lie algebras in prime characteristic (with R Bezrukavnikov and D Rumynin), Nagoya Mathematical Journal (2006)
In [BMR] we observed that, on the level of derived categories, representations of the Lie...
Equivariant homology and K-theory of affine Grassmannians and Toda lattices (with R Bezrukavnikov and M Finkelberg), Composito Mathematica (2005)
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...
Some results about geometric Whittaker model (with R Bezrukavnikov and A Braverman), Advances in Mathematics (2004)
Let G be an algebraic reductive group over a field of positive characteristic. Choose a...
Other
Representations of semi-simple lie algebras in prime characteristics and noncommutative springer resolution (with R Bezrukavnikov), Mathematics and Statistics Department Faculty Publication Series (2011)
Linear koszul duality and Affine Hecke algebras (with S Richie), Mathematics and Statistics Department Faculty Publication Series (2009)
n this paper we prove that the linear Koszul duality equivalence constructed in a previous...
Quiver varieties and beilinson-Drinfeld grassmannians of type A (with M Vybornov), Mathematics and Statistics Department Faculty Publication Series (2008)
Semiinfinite flags. II. local and global intersection cohomology of quasimaps’ spaces (with B Feigin, M Finkelberg, and A Kuznetsov), Mathematics and Statistics Department Faculty Publication Series (2008)
Modules over the small quantum group and semi-infinite flag manifold (with S Arkhipov, R Bezrukavnikov, A Braverman, and D Gaitsgory), Mathematics and Statistics Department Faculty Publication Series (2005)
We develop a theory of perverse sheaves on the semi-infinite flag manifold G((t))/N((t)) · T[[t]],...