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QUANTUM COHOMOLOGY OF ORTHOGONAL GRASSMANNIANS
ORTHOGONAL GRASSMANNIANS QUANTUM COHOMOLOGY
2015/12/17
Let V be a vector space with a nondegenerate symmetric form and
OG be the orthogonal Grassmannian which parametrizes maximal isotropic
subspaces in V . We give a presentation for the (small) quantum...
Fulton's universal Schubert polynomials [F3] represent degeneracy loci for morphisms of vector bundles with rank conditions coming from a
permutation.
We show that for arbitrary fixed conjugacy classes C1, . . . , Cl, l ≥ 3, of loxodromic isometries of the two-dimensional complex or quaternionic hyperbolic space there exist isometries g1, . . . , gl...
Let G be a classical Lie group and P a maximal parabolic subgroup. We describe a quantum Pieri rule which holds in the small quantum
cohomology ring of G=P. We also give a presentation of this ring i...
Let G be a semisimple complex algebraic group and P a parabolic subgroup of G.
The homogeneous space X = G=P is a projective complex manifold. My aim in
this lecture is to survey what is known about...
We study the Arakelov intersection ring of the arithmetic scheme
OG which parametrizes maximal isotropic subspaces in an even dimensional
vector space, equipped with the standard hyperbolic quadrati...
STABLE GROTHENDIECK POLYNOMIALS AND K-THEORETIC FACTOR SEQUENCES
STABLE GROTHENDIECK POLYNOMIALS K-THEORETIC FACTOR
2015/12/17
We formulate a nonrecursive combinatorial rule for the expansion
of the stable Grothendieck polynomials of [Fomin-Kirillov '94] in the basis of
stable Grothendieck polynomials for partitions. This g...
We study the three point genus zero Gromov-Witten invariants
on the Grassmannians which parametrize non-maximal isotropic subspaces in
a vector space equipped with a nondegenerate symmetric or skew-...
SCHUBERT POLYNOMIALS AND ARAKELOV THEORY OF SYMPLECTIC FLAG VARIETIES
SCHUBERT POLYNOMIALS ARAKELOV THEORY
2015/12/17
Let X = Sp2n/B the flag variety of the symplectic group. We
propose a theory of combinatorially explicit Schubert polynomials which represent the Schubert classes in the Borel presentation of t...
GIAMBELLI, PIERI, AND TABLEAU FORMULAS VIA RAISING OPERATORS
GIAMBELLI PIERI TABLEAU FORMULAS
2015/12/17
We give a direct proof of the equivalence between the Giambelli
and Pieri type formulas for Hall-Littlewood functions using Young’s raising operators, parallel to joint work with Buch and Kresch for ...
The Ptolemy coordinates for boundary-unipotent SL(n; C)-representations of a
3-manifold group were introduced in [7] inspired by the A-coordinates on higher Teichmuller
space due to Fock and Goncha...
We give an e
ient simpli
ial formula for the volume and ChernSimons invariant of a boundary-paraboli
PSL(2,C)representation of a tame
3manifold
THE EXTENDED BLOCH GROUP AND THE CHEEGER-CHERN-SIMONS CLASS
THE EXTENDED BLOCH GROUP CHEEGER-CHERN-SIMONS CLASS
2015/12/17
We present a formula for the full Cheeger-Chern-Simons class of the tautological flat
complex vector bundle of rank 2 over BSL(2, C
δ
). Our formula improves the formula in [DZ], where
the c...
OPTIMAL MULTILEVEL METHODS FOR GRADED BISECTION GRIDS
subspace correction method local mesh refi nement bisection method
2015/12/11
We design and analyze optimal additive and multiplicative multilevel methods for solving H1 problems on graded grids obtained by bisection. We deal with economical local smoothers: after a global smoo...
FIRST VARIATION OF THE GENERAL CURVATURE-DEPENDENT SURFACE ENERGY
Surface energy gradient fl ow mean curvature
2015/12/11
We consider general surface energies, which are weighted integrals
over a closed surface with a weight function depending on the position, the
unit normal and the total curvature of the surface. Ene...