Related papers: Monotone Lagrangians in flag varieties

We show that for every complex simple Lie algebra, the equations of Schubert divisors on the flag variety give a complete integrable system of the minimal nilpotent orbit. The approach is motivated by the integrable system on Coulomb…

We propose a combinatorial model for the Schubert structure constants of the complete flag manifold when one of the factors is Grassmannian.

We present in this article a family of new combinatorial identities via purely differential/complex geometry methods, which include as a speical case a unified and explicit formula for Chern numbers of all complex flag manifolds. Our…

In this paper, we study the Gelfand--Cetlin systems and polytopes of the co-adjoint $\mathrm{SO}(n)$-orbits. We describe the face structure of Gelfand--Cetlin polytopes and iterated bundle structure of Gelfand--Cetlin fibers in terms of…

We give Chern-Weil definitions of the Maslov indices of bundle pairs over a Riemann surface \Sigma with boundary, which consists of symplectic vector bundle on \Sigma and a Lagrangian subbundle on \partial{\Sigma} as well as its…

Marked chain-order polytopes are convex polytopes constructed from a marked poset, which give a discrete family relating a marked order polytope with a marked chain polytope. In this paper, we consider the Gelfand-Tsetlin poset of type A,…

Systems with a first integral (i.e., constant of motion) or a Lyapunov function can be written as ``linear-gradient systems'' $\dot x= L(x)\nabla V(x)$ for an appropriate matrix function $L$, with a generalization to several integrals or…

We prove that the count of Maslov index 2 $J$-holomorphic discs passing through a generic point of a real Lagrangian submanifold in a closed spherically monotone symplectic manifold must be even. As a corollary, we exhibit a genuine real…

In this paper we detect new restrictions on the Maslov class of displaceable Lagrangian submanifolds of symplectic manifolds which are symplectically aspherical. These restrictions are established using action selectors for Hamiltonian…

We show that for Sturm-Liouville Systems on the half-line $[0,\infty)$, the Morse index can be expressed in terms of the Maslov index and an additional term associated with the boundary conditions at $x = 0$. Relations are given both for…

We prove an extension of the Index Theorem for Morse-Sturm systems of the form $-V''+RV=0$, where R is symmetric with respect to a (non positive) symmetric bilinear form, and thus the corresponding differential operator is not self-adjoint.…

A Maslov cycle is a singular variety in the lagrangian grassmannian L(V) of a symplectic vector space V consisting of all lagrangian subspaces having nonzero intersection with a fixed one. Givental has shown that a Maslov cycle is a…

Solitons are non-dispersing localized waves that occur in diverse physical settings. A variety of optical solitons have been observed, but versions that involve both spatial and temporal degrees of freedom are rare. Optical fibers designed…

In this paper, we consider the flag manifold of $p$ orthogonal subspaces of equal dimension which carries an action of the cyclic group of order $p$. We provide a complete calculation of the associated Fadell-Husseini index. This may be…

Maslov indices are integers that appear in semiclassical wave functions and quantization conditions. They are often notoriously difficult to compute. We present methods of computing the Maslov index that rely only on typically elementary…

We build homogeneous quasi-morphisms on the universal cover of the contactomorphism group for certain prequantizations of monotone symplectic toric manifolds. This is done using Givental's nonlinear Maslov index and a contact reduction…

A Schubert variety in the complete flag manifold $GL_n/B$ is Levi-spherical if the action of a Borel subgroup in a Levi subgroup of a standard parabolic has a dense orbit. We give a combinatorial classification of these Schubert varieties.…

For any flag simplicial complex $K$, we describe the multigraded Poincare series, the minimal number of relations and the degrees of these relations in the Pontryagin algebra of the corresponding moment-angle complex $Z_K$. We compute the…

In this paper, we study how global index formulas arise in the theory of one-dimensional holomorphic foliation from the microlocal point of view. We give short proofs and generalizations to a few exisiting index formulas concerning…

We examine the noncommutative index theory associated to the dynamics of a Delone set and the corresponding transversal groupoid. Our main motivation comes from the application to topological phases of aperiodic lattices and materials, and…