University of North Carolina at Chapel Hill

Chapel Hill, NC 27599-3250, USA

Telephone: 919-962-9615, Telefax: 919-962-2568

e-mail: shrawan [at] email.unc.edu

Born in Ghazipur, U.P., INDIA.

- B.Sc. Gorakhpur University 1973
- M.Sc. Bombay University 1975
- Ph.D.(Maths.) Bombay University 1986

- 1975-76,Visiting Member, Tata Institute of Fundamental Research (Bombay)
- 1976-82, Research Assistant, Tata Institute of Fundamental Research
- 1982-85, Research Associate, Tata Institute of Fundamental Research
- Aug. 1983-July 84, Postdoctoral Research Fellow, Mathematical Sciences Research Institute (Berkeley)
- July 1984-Aug. 85, C.L.E. Moore Instructor, Massachusetts Institute of Technology (Cambridge)
- 1985-89, Fellow, Tata Institute of Fundamental Research
- Sept. 1988-May 89, Member, The Institute for Advanced Study (Princeton)
- 1989-92, Reader, Tata Institute of Fundamental Research
- 2006- , Adjunct Professor, Tata Institute of Fundamental Research
- 1991-2010, Professor, University of North Carolina at Chapel Hill
- 2010- , John R.
*and*Louise S. Parker Distinguished Professor, University of North Carolina at Chapel Hill

*Kac-Moody Groups, Their Flag Varieties and Representation Theory*,

Progress in Mathematics vol. 204, Birkhauser, Boston, 606 Pages (Aug. 2002). [Table of Contents]*Frobenius Splitting Methods in Geometry and Representation Theory*(with M. Brion),

Progress in Mathematics vol. 231, Birkhauser, Boston, 250 Pages (Dec. 2004). [Table of Contents]

A remark on universal connections

Math. Ann. 260, 453-462 (1982). [pdf]

A G-minimal model for principal G-bundles

Annales de L'Institut Fourier, Grenoble 32, 205-219 (1982). [pdf]

Geometry of Schubert cells and cohomology of Kac-Moody Lie algebras

J. Diff. Geometry 20, 389-431 (1984). [pdf]

Rational homotopy theory of flag varieties associated to Kac-Moody groups

In: "Infinite dimensional groups with applications" (ed. by V. Kac). MSRI (Springer-Verlag) publications Vol. 4, 233-273 (1985). [pdf]

Cohomology algebra of Schubert varieties associated to Kac-Moody groups

In: "Proceedings of the 1984 Vancouver Conference in Algebraic Geometry" (ed. by J. Carrell et. al.). CMS Conference Proceedings Vol. 6, 277-299 (1986). [pdf]

A generalization of the Conner conjecture and topology of Stein spaces dominated by C^n

Topology 25, 483-493 (1986). [pdf]

The nil Hecke ring and cohomology of G/P for a Kac-Moody group G (with B. Kostant)

Proc. Natl. Acad. Sci. USA 83, 1543-1545 (1986). [pdf]

A homology vanishing theorem for Kac-Moody algebras with coefficients in the category O

J. Algebra 102, 444-462 (1986). [pdf]

Non-representability of cohomology classes by bi-invariant forms (Gauge and Kac-Moody groups)

Commu. Math. Physics 106, 177-181 (1986). [pdf]

The nil Hecke ring and cohomology of G/P for a Kac-Moody group G (with B. Kostant)

Advances in Math. 62, 187-237 (1986). [pdf]

T-equivariant K-theory of generalized flag varieties (with B. Kostant)

Proc. Natl. Acad. Sci. USA 84, 4351-4354 (1987). [pdf]

Extension of the category O^g and a vanishing theorem for the Ext functor for Kac-Moody algebras

J. Algebra 108, 472-491 (1987). [pdf]

Demazure character formula in arbitrary Kac-Moody setting

Invent. Math. 89, 395-423 (1987). [pdf]

Proof of the Parthasarathy-Ranga Rao-Varadarajan conjecture

Invent. Math. 93, 117-130 (1988). [pdf]

Existence of certain components in the tensor product of two integrable highest weight modules for Kac-Moody algebras

In: "Infinite dimensional Lie algebras and groups" (ed. by V.G. Kac). Advanced series in Mathematical Physics Vol. 7, World Scientific, 25-38 (1989). [pdf]

A refinement of the PRV conjecture

Invent. Math. 97, 305-311 (1989). [pdf]

Bernstein-Gelfand-Gelfand resolution for arbitrary Kac-Moody algebras

Math. Annalen 286, 709-729 (1990). [pdf]

A new geometric invariant associated to the space of flat connections (with K. Guruprasad)

Compositio Math. 73, 199-222 (1990). [pdf]

T-equivariant K-theory of generalized flag varieties (with B. Kostant)

J. Diff. Geometry 32, 549-603 (1990). [pdf]

Proof of Wahl's conjecture on surjectivity of the Gaussian map for flag varieties

In: " Algebraic groups" (ed. by S. Ramanan). Proceedings of the Hyderabad conference. Manoj Prakashan, 275-278 (1991). [pdf]

A geometric realization of minimal rak k-type of Harish-Chandra modules for complex s.s. groups (with B. Kostant)

In: "Kazhdan-Lusztig theory and related topics" (ed. by V. Deodhar). Contemporary Mathematics vol. 139 published by AMS, 249-264 (1992). [pdf]

Proof of Wahl's conjecture on surjectivity of the Gaussian map for flag varieties

American J. of Math. 114, 1201-1220 (1992). [pdf]

Cohomology of quantum groups at roots of unity (with V. Ginzburg)

Duke Math. J. 69, 179-198 (1993). [pdf]

Finiteness of local fundamental groups for quotients of affine varieties under reductive groups

Comment. Math. Helvetici, 68, 209-215 (1993). [pdf]

Equivariant cohomology with generalized coefficients (with M. Vergne)

Ast\'erisque 215, 109-204 (1993). [pdf]

Toward proof of Lusztig's conjecture concerning negative level representations of affine Lie algebras

J. Algebra 164, 515-527 (1994). [pdf]

Symmetric and exterior powers of homogeneous vector bundles

Math. Annalen 299, 293-298 (1994). [pdf]

Representations of quantum groups at roots of unity

In: "Quantum topology" (ed. by D.N. Yetter). World Scientific, Singapore, 187-224 (1994). [pdf]

Infinite Grassmannians and moduli spaces of G-bundles (with M. S. Narasimhan and A. Ramanathan)

Math. Annalen 300, 41-75 (1994). [pdf]

The nil Hecke ring and singularity of Schubert varieties

In: "Lie theory and geometry (in honor of B. Kostant)" (ed. by J.-L. Brylinski et. al.). Progress in Math. vol. 123, Birkhauser, 497-507 (1994). [pdf]

The nil Hecke ring and singularity of Schubert varieties

Inventiones Math. 123, 471-506 (1996). [pdf]

Shapovalov determinant for restricted and quantized restricted enveloping algebras (with G. Letzter)

Pacific J. of Math. 179, 123-161 (1997). [pdf]

Infinite Grassmannians and moduli spaces of G-bundles

In: "Vector Bundles on Curves- New Directions," (ed. by M.S. Narasimhan). Springer Lecture Notes in Math. vol. 1649, 1-49 (1997). [pdf]

Picard group of the moduli spaces of G-bundles (with M.S. Narasimhan)

Math. Annalen 308, 155-173 (1997). [pdf]

Fusion product of positive level representations and Lie algebra homology

In: "Geometry and physics" (ed. by J.E. Andersen et. al.). Lecture Notes in Pure and Applied Mathematics vol. 184, Marcel Dekker, Inc., 253-259 (1997). [pdf]

Positivity of the cup product in cohomology of flag varieties associated to Kac-Moody groups (with M.V. Nori)

Inter. Math. Res. Not. 14, 757-763 (1998). [pdf]

Frobenius splitting of cotangent bundles of flag varieties (with N. Lauritzen and J. Thomsen)

Inventiones Math. 136, 603--621 (1999). [pdf]

Homology of certain truncated Lie algebras

In: "Recent Developments in Quantum Affine Algebras and Related Topics," (ed. by K.C. Misra et. al.). Contemporary Mathematics vol. 248, 309--325 (1999), published by AMS. [pdf]

Frobenius splitting in characteristic zero and the quantum Frobenius map (with P. Littelmann)

J. of Pure and applied Algebra 152, 201--216 (2000). [pdf]

Frobenius splitting of Hilbert schemes of points on surfaces (with J.F. Thomsen)

Math. Annalen 319, 797--808 (2001). [pdf]

Algebraization of Frobenius splitting via quantum groups (with P. Littelmann)

Annals of Mathematics 155, 491--551 (2002). [pdf]

A conjectural generalization of the n! result to arbitrary groups (with J.F. Thomsen)

Transformation Groups 8, 69--94 (2003). [pdf]

Equivariant analogue of Grothendieck's theorem for vector bundles on \Bbb P^1

In: "Perspectives in Geometry and Representation Theory (A tribute to C.S. Seshadri)," Hindustan Book Agency, 500--501 (2003). [pdf]

The generalized triangle inequalities for rank 3 symmetric spaces of noncompact type (with B. Leeb and J. Millson)

Contemporary Mathematics vol. 332, published by AMS, 171--195 (2003). [pdf]

A new realization of the cohomology of Springer fibers (with J.F. Thomsen)

In: "Proceedings of the International Conference on Algebraic Groups and Arithmetic" (Volume dedicated to M.S. Raghunathan on his sixtieth birthday), Narosa Publishing House, 119--125 (2004). [pdf]

Induction functor in noncommutative equivariant cohomology and Dirac cohomology

J. Algebra 291, 187--207 (2005). [pdf]

Explicit determination of the Picard group of moduli spaces of semi-stable G-bundles on curves (with A. Boysal)

Math. Annalen 332, 823--842 (2005). [pdf]

Extensions of algebraic groups (with K-H. Neeb)

In:"Studies in Lie Theory" (Volume dedicated to A. Joseph on his sixtieth birthday), Progress in Mathematics vol. 243, Birkhauser, 365--376 (2006). [pdf]

Eigenvalue problem and a new product in cohomology of flag varieties (with P. Belkale)

Inventiones Math. 166, 185--228 (2006). [pdf]

On Cachazo-Douglas-Seiberg-Witten conjecture for simple Lie algebras

J. of Am. Math. Soc., 21, 797--808 (2008). [pdf]

The eigencone and saturation for Spin(8) (with M. Kapovich and J. Millson)

Pure and Applied Math. Quarterly 5, 755--780 (2009). [pdf]

Descent of line bundles to GIT quotients of flag varieties by maximal torus

Transformation Groups 13, 757--771 (2008). [pdf]

Special isogenies and tensor product multiplicities (with J. Stembridge)

International Mathematics Research Notices, vol. 2007 (no. 20), 1--13 (2007). [pdf]

Eigencone, saturation and Horn problems for symplectic and odd othogonal groups (with P. Belkale)

J. Alg. Geom., 44 pages. [pdf]

Characters of simplylaced nonconnected groups versus characters of nonsimplylaced connected groups (with G. Lusztig and D. Prasad)

Contemporary Math. vol. 478, 99--101 (2009). [pdf]

On positivity in T-equivariant K-theory of flag varieties (with W. Graham)

International Mathematical Research Notices, vol. 2008, 1--43 (August, 2008). [pdf]

A conjectural presentation of fusion algebras (with A. Boysal)

In: "Algebraic Analysis and Around" (in honor of M. Kashiwara's sixtieth birthday). Advanced Studies in Pure Mathematics vol. 54, 95--107 (2009). [pdf]

A generalization of Cachazo-Douglas-Seiberg-Witten conjecture for symmetric spaces

Math. Annalen (2009), 18 pages. [pdf]

Finiteness of the number of compatibly split subvarieties (with V. Mehta)

International Mathematics Research Notices, vol. 2009 (no. 19), 3595--3597 (2009). [pdf]

Tensor Product Decomposition

In: Proceedings of the International Congress of Mathematicians, Hyderabad, India, 2010. [pdf]

A generalization of Fulton's conjecture for arbitrary groups (with P. Belkale and N. Ressayre)

Math. Annalen 354, 401-425 (2012). [pdf]

Geometry of orbits of permanents and determinants

Comment. Math. Helv. 88 (2013), pages 759-788. [pdf]

An algebro-geometric realization of equivariant cohomology of some Springer fibers (with C. Procesi)

J. Algebra 368, 70--74 (2012), 5 pages. [pdf]

An approach towards the Kollar-Peskine problem via the Instanton Moduli Space

Proceedings of Symposia in Pure Mathematics 86, 217-225 (2012), 9 pages. [pdf]

Richardson varieties have Kawamata log terminal singularities (with K. Schwede)

International Mathematics Research Notices, rns241, (2012), 23 pages [pdf]

Positivity in T-Equivariant K-Theory of flag varieties associated to Kac-Moody groups

Preprint (2012), 55 pages. [pdf]

A study of the representations supported by the orbit closure of the determinant

Compositio Math 151, 292-312 (2015), 21 pages. [pdf]

Dimension of zero weight space: an algebro-geometric approach (with D. Prasad)

J. Algebra 403, 324--344 (2014). 21 pages. [pdf]

A study of saturated tensor cone for symmetrizable Kac-Moody algebras (with M. Brown)

Math. Annalen 360, 901-936 (2014). 36 pages. [pdf]

A survey of the additive eigenvalue problem (with an appendix by M. Kapovich)

Transformation Groups 19, 1051-1148 (2014). 98 pages. [pdf]

Hitchin's conjecture for simply-laced Lie algebras implies that for any simple Lie algebra (with N. Bushek)

Differential Geometry and its Applications 35, 210--223 (2014), 14 pages. [pdf]

The multiplicative eigenvalue problem and deformed quantum cohomology (with P. Belkale)

Advances in Mathematics 288, 1309--1359 (2016), 51 pages. [pdf]

Connections between conjectures of Alon-Tarsi, Hadamard-Howe, and integrals over the special unitary group (with J.M. Landsberg)

Discrete Mathematics 338, 1232--1238 (2015), 7 pages. [pdf]

Additive Eigenvalue Problem

To appear in EMS Newsletter (2015), 8 pages. [pdf]

Components of V(ρ) ⊗ V(ρ) (with R. Chirivi and A. Maffei)

Transformation Groups, 6 pages (2016). [pdf]

Representation ring of Levi subgroups versus cohomology ring of flag varieties

Math. Annalen, 21 pages (2016). [pdf]

Positivity in T-equivariant K-theory of flag varieties associated to Kac-Moody groups II (with S. Baldwin)

Preprint (2016), 28 pages. [pdf]

A complete set of intertwiners for arbitrary tensor product representations via current algebras

Preprint (2016), 11 pages. [pdf]

Eigenvalue problem for Hermitian matrices and its generalization to arbitrary reductive groups

(Talk given at AMS Sectional meeting held at Davidson College, March 2007) [pdf]

Geometry of Schubert varieties and Demazure character formula

(Talks given at the Hausdorff Research Institute for Mathematics, Bonn, Germany, April 2011) [pdf]

Borel-Weil-Bott theorem and geometry of Schubert varieties

(Lectures given at the MRC Meeting, Snowbird, Utah, June 2012) [pdf]

Equivariant K-theory of flag varieties

(Talks given at Jacobs University, Bremen (Germany), August 2012) [pdf]