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THE PUZZLE CONJECTURE FOR THE COHOMOLOGY OF TWO-STEP FLAG MANIFOLDS
PUZZLE CONJECTURE TWO-STEP FLAG MANIFOLDS
2015/12/17
We prove a conjecture of Knutson asserting that the Schubert
structure constants of the cohomology ring of a two-step flag variety are equal
to the number of puzzles with specified borde...
QUANTUM COHOMOLOGY OF THE LAGRANGIAN GRASSMANNIAN
LAGRANGIAN GRASSMANNIAN QUANTUM COHOMOLOGY
2015/12/17
Let V be a symplectic vector space and LG be the Lagrangian
Grassmannian which parametrizes maximal isotropic subspaces in V . We give
a presentation for the (small) quantum cohomology ring QH¤(LG) ...
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...
GROMOV-WITTEN INVARIANTS AND QUANTUM COHOMOLOGY OF GRASSMANNIANS
GROMOV-WITTEN INVARIANTS QUANTUM COHOMOLOGY
2015/12/17
This is the written version of my ˉve lectures at the Banach Center
mini-school on `Schubert Varieties', in Warsaw, Poland, May 18{22, 2003.
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...
COHOMOLOGY OF SL(2, C) CHARACTER VARIETIES OF SURFACE GROUPS AND THE ACTION OF THE TORELLI GROUP
SL(2, C) CHARACTER VARIETIES SURFACE GROUPS TORELLI GROUP
2015/12/17
We determine the action of the Torelli group on the equivariant cohomology of the space of flat SL(2, C) connections on a closed Riemann surface. We show that the trivial part of the action contains t...
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...
COHOMOLOGY OF U(2,1) REPRESENTATION VARIETIES OF SURFACE GROUPS
U(2,1) REPRESENTATION VARIETIES SURFACE GROUPS
2015/12/17
In this paper we use the Morse theory of the Yang-Mills-Higgs functional on the singular space of Higgs bundles on Riemann surfaces to compute the equivariant cohomology of the space of semistable U(2...
The p-cohomology of algebraic varieties and special values of zeta functions
zeta functions algebraic varieties
2015/12/10
The p-cohomology of an algebraic variety in characteristic p lies naturally in the
category Db
c
.R/ of coherent complexes of graded modules over the Raynaud ring
(Ekedahl-Illusie-Raynaud). We stu...
BOUNDARY BEHAVIOR OF SPECIAL COHOMOLOGY CLASSES ARISING FROM THE WEIL REPRESENTATION
BOUNDARY BEHAVIOR SPECIAL COHOMOLOGY CLASSES ARISING WEIL REPRESENTATION
2015/10/14
In our previous paper [9], we established a correspondence between vector-valued holomorphic Siegel modular forms and cohomology with local coefficients for local symmetric spaces X attached to real o...
COHOMOLOGY OPERATIONS AND INVERTING THE MOTIVIC BOTT ELEMENT
COHOMOLOGY OPERATIONS AND INVERTING BOTT ELEMENT
2015/9/29
In this note we explore the relationships between the motivic cohomology operations and the (classical)
cohomology operations defined on mod-l ′etale cohomology. More precisely we show that the...
Orbit equivalence,flow equivalence and ordered cohomology
Orbit equivalence flow equivalence ordered cohomology
2015/9/29
We study self-homeomorphisms of zero dimensional metrizable compact Hausdorff spaces by means of the ordered first cohomology group, particularly in the light of the recent work of Giordano, Putnam, a...
It is well known that the real cohomology of a compact Riemannian manifold
M is isomorphic to the algebra of its harmonic forms. When M is a fiat
Riemannian manifold, i.e. a Euclidean manifold, a ...
Geometric positivity in the cohomology of homogeneous spaces and generalized Schubert calculus
homogeneous spaces generalized Schubert calculus
2015/7/14
We describe recent work on positive descriptions of the structure constants of the cohomology of homogeneous spaces such as the Grassmannian, by degenerations and related methods. We
give various ext...
Equivariant cohomology and localization for Lie algebroids and applications
Equivariant cohomology localization Lie algebroids applications
2015/3/19
Equivariant cohomology and localization for Lie algebroids and applications.