O pätnástom Hilbertovom probléme
On a conjecture of Kottwitz and Rapoport
We prove a conjecture of Kottwitz and Rapoport which implies a converse to Mazur’s Inequality for all (connected) split and quasi-split unramified reductive groups. Our results are related to the non-emptiness of certain affine Deligne-Lusztig varieties.
On a theorem of Enriques - Swinnerton-Dyer
On base partitions and cover partitions of skew characters.
On congruences of lines in the projective space (Chapter 6 written in collaboration with M. Pedreira)
On Cycles in Flag Manifolds.
On elementary equivalence, isomorphism and isogeny
Motivated by recent work of Florian Pop, we study the connections between three notions of equivalence of function fields: isomorphism, elementary equivalence, and the condition that each of a pair of fields can be embedded in the other, which we call isogeny. Some of our results are purely geometric: we give an isogeny classification of Severi-Brauer varieties and quadric surfaces. These results are applied to deduce new instances of “elementary equivalence implies isomorphism”: for all genus zero...
On Fano 4-folds of index 1 and homogeneous vector bundles over Grassmannians.
On infinite-dimensional grassmannians and their quantum deformations
On multiplicities of points on Schubert varieties in Grassmannians.
On parabolic Whittaker functions II
We propose a Givental-type stationary phase integral representation for the restricted Grm,N-Whittaker function, which is expected to describe the (S 1×U N)-equivariant Gromov-Witten invariants of the Grassmann variety Grm,N. Our key tool is a generalization of the Whittaker model for principal series U(gl N)-modules, and its realization in the space of functions of totally positive unipotent matrices. In particular, our construction involves a representation theoretic derivation of the Batyrev-Ciocan-Fontanine-Kim-van...
On projective equivalence of univariate polynomial subspaces.
On real flag manifolds with cup-length equal to its dimension
We prove that for any positive integers there exists a real flag manifold with cup-length equal to its dimension. Additionally, we give a necessary condition that an arbitrary real flag manifold needs to satisfy in order to have cup-length equal to its dimension.
On Schubert Varieties in the Flag Manifold of SI (n, C).
On smooth surfaces in Gr(1, P3) with a fundamental curve.
On some geometric aspects of Bruhat orderings. I. A finer decomposition of Bruhat cells.
On tangent cones to Schubert varieties in type
We consider tangent cones to Schubert subvarieties of the flag variety , where is a Borel subgroup of a reductive complex algebraic group of type , or . We prove that if and form a good pair of involutions in the Weyl group of then the tangent cones and to the corresponding Schubert subvarieties of do not coincide as subschemes of the tangent space to at the neutral point.
On the Chow groups of quadratic Grassmannians.
On the cohomology of twistor flag spaces
On the degree of the Gauss mapping of a submanifold of an Abelian variety.