Related papers: Euler obstructions for the Lagrangian Grassmannian

Schemes based on anticommuting scalar coordinates, corresponding to properties, lead to generations of particles naturally. The application of Grassmannian duality cuts down the number of states substantially and is vital for constructing…

We prove that all lattice path matroids are Ehrhart positive. This unifies and generalizes numerous results on the Ehrhart positivity of matroids developed over the last two decades. We rely on our previous work on the positivity of order…

The covariant phase space of a Lagrangian field theory is the solution space of the associated Euler-Lagrange equations. It is, in principle, a nice environment for covariant quantization of a Lagrangian field theory. Indeed, it is…

Vakil studied the intersection theory of Schubert varieties in the Grassmannian in a very direct way: he degenerated the intersection of a Schubert variety X_mu and opposite Schubert variety X^nu to a union {X^lambda}, with repetition. This…

This paper studies, for a positive integer $m$, the subalgebra of the cohomology ring of the complex Grassmannians generated by the elements of degree at most $m$. We build in two ways upon a conjecture for the Hilbert series of this…

We study a generalization of Lian-Liu-Yau's notion of Euler data in genus zero and show that certain sequences of multiplicative equivariant characteristic classes on Kontsevich's stable map moduli with markings induce data satisfying the…

Each point $x$ in Gr$(r,n)$ corresponds to an $r \times n$ matrix $A_x$ which gives rise to a matroid $M_x$ on its columns. Gel'fand, Goresky, MacPherson, and Serganova showed that the sets $\{y \in \mathrm{Gr}(r,n) | M_y = M_x\}$ form a…

We resolve a conjecture about a class of binomial initial ideals of $I_{2,n}$, the ideal of the Grassmannian, Gr$(2,\mathbb{C}^n$), which are associated to phylogenetic trees. For a weight vector $\omega$ in the tropical Grassmannian,…

We prove that the prime torsion in the local integral intersection cohomology of Schubert varieties in the flag variety of the general linear group grows exponentially in the rank. The idea of the proof is to find a highly singular point in…

M.-P. Sch\"utzenberger asked to determine the support of the free Lie algebra ${\mathcal L}_{{\mathbb Z}_{m}}(A)$ on a finite alphabet $A$ over the ring ${\mathbb Z}_{m}$ of integers $\bmod m$ and all the corresponding pairs of twin and…

The space of positive Lagrangians in an almost Calabi-Yau manifold is an open set in the space of all Lagrangian submanifolds. A Hamiltonian isotopy class of positive Lagrangians admits a natural Riemannian metric $\Upsilon$, which gives…

Consider a Maslov zero Lagrangian submanifold diffeomorphic to a Lie group on which an anti-symplectic involution acts by the inverse map of the group. We show that the Fukaya $A_\infty$ endomorphism algebra of such a Lagrangian is…

Let $G$ and $\tilde G$ be reductive groups over a local field $F$. Let $\eta : \tilde G \to G$ be a $F$-homomorphism with commutative kernel and commutative cokernel. We investigate the pullbacks of irreducible admissible…

In this paper we prove the Gromov--Milman conjecture (the Dvoretzky type theorem) for homogeneous polynomials on $\mathbb R^n$, and improve bounds on the number $n(d,k)$ in the analogous conjecture for odd degrees $d$ (this case is known as…

We study the $l$-adic cohomology of unramified Rapoport-Zink spaces of EL-type. These spaces were used in Harris and Taylor's proof of the local Langlands correspondence for $\mathrm{GL_n}$ and to show local-global compatibilities of the…

It is well known that many geometric properties of Schubert varieties of type $A$ can be interpreted combinatorially. Given two permutations $w,x\in S_n$ we give a combinatorial consequence of the property that the smooth locus of the…

We record an observation about the Witten indices in two families of gauged linear sigma models: the U(2) model for linear sections of Grassmannians, and the U(1) model for quadric complete intersections. We describe how the Witten indices…

We prove the existence, uniqueness, and sharp bilateral pointwise estimates for positive bounded solutions to the Lane--Emden type problem \[ \begin{cases} L u = \sum\limits_{i=1}^{m}\sigma_{i} u^{q_{i}}+\sigma_0, \quad u\geq0 & \text{in }…

Let $\ell, n$ be positive integers such that $\ell\geq n$. Let $\mathbb{G}_{n,\ell}$ be the Grassmannian which consists of the set of $n$-dimensional subspaces of $\mathbb{C}^{\ell}$. There is a $\mathbb{Z}$-graded algebra isomorphism…

We show that 4D gauge theories with Green-Schwarz anomaly cancellation and possible generalized Chern-Simons terms admit a formulation that is manifestly covariant with respect to electric/magnetic duality transformations. This generalizes…