Related papers: Some conjectures regarding certain Schubert struct…
Motivated by a recent conjecture of R. P. Stanley we offer a lower bound for the sum of the coefficients of a Schubert polynomial in terms of $132$-pattern containment.
Let $X$ be a hyperk\"ahler variety, and let $G$ be a group of finite order non-symplectic automorphisms of $X$. Beauville's conjectural splitting property predicts that each Chow group of $X$ should split in a finite number of pieces. The…
In this paper we formulate a conjecture on the relationship between the equivariant \epsilon-constants (associated to a local p-adic representation V and a finite extension of local fields L/K) and local Galois cohomology groups of a Galois…
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 extensions of these rules, some new and…
We study an action of the skew divided difference operators on the Schubert polynomials and give an explicit formula for structural constants for the Schubert polynomials in terms of certain weighted paths in the Bruhat order on the…
We describe the torus-equivariant cohomology of weighted partial flag orbifolds ${\mathrm{w}}\Sigma$ of type $A$. We establish counterparts of several results known for the partial flag variety that collectively constitute what we refer to…
Chow rings of flag varieties have bases of Schubert cycles $\sigma_u$, indexed by permutations. A major problem of algebraic combinatorics is to give a positive combinatorial formula for the structure constants of this basis. The celebrated…
We calculate the stable pair theory of a projective surface $S$. For fixed curve class $\beta\in H^2(S)$ the results are entirely topological, depending on $\beta^2$, $\beta.c_1(S)$, $c_1(S)^2$, $c_2(S)$, $b_1(S)$ \emph{and} invariants of…
Motivated by the computation of the BPS-invariants on a local Calabi-Yau threefold suggested by S. Katz, we compute the Chow ring and the cohomology ring of the moduli space of stable sheaves of Hilbert polynomial $4m+1$ on the projective…
The construction of generators of the Clifford group and of stabilizer states from Chern-Simons theory is presented for the Kac-Moody algebras SU(2)1, U(N)N,N(K+N) with N = 2 and K = 1, and SU(N)1 extending results of Salton, et. al.
This paper proposes a conjectural picture for the structure of the Chow ring of a (projective) hyper-K\"ahler variety, and the construction of a Beauville decomposition, with emphasis on the Chow group of $0$-cycles, which is endowed with a…
We study the stability of topological structures in generalized models with a single real scalar field. We show that it is driven by a Sturm-Liouville equation and investigate the conditions that lead to the existence of explicit…
We give a generalization of Gabriel's Theorem on coherent sheaves to the case of coherent twisted sheaves on a smooth variety X over a field k. We show that the category Coh(X,\alpha) determines the scheme structure of X for \alpha in the…
We prove stability theorems in the Cuntz semigroup of a commutative C*-algebra which are analogues of classical stability theorems for topological vector bundles over compact Hausdorff spaces. Several applications to simple unital AH…
We provide a method for gluing (small) resolutions of singularities of Schubert varieties \(X_w\). An explicit isomorphism of \(X_w\) with an (iterated) bundle is constructed when \(w\) has an (iterated) BP decomposition. Combined with the…
We study the question for which commutative ring spectra $A$ the tensor of a simplicial set $X$ with $A$, $X \otimes A$, is a stable invariant in the sense that it depends only on the homotopy type of $\Sigma X$. We prove several structural…
We revisit the possibility of de Sitter vacua and slow-roll inflation in type II string theory at the level of the classical two-derivative supergravity approximation. Previous attempts at explicit constructions were plagued by ubiquitous…
Constant rank theorems are obtained for saddle solutions to the special Lagrangian equation and the quadratic Hessian equation. The argument also leads to Liouville type results for the special Lagrangian equation with subcritical phase,…
We consider the curvature of a family of warped products of two pseduo-Riemannian manifolds $(B,g_B)$ and $(F,g_F)$ furnished with metrics of the form $c^{2}g_B \oplus w^2 g_F$ and, in particular, of the type $w^{2 \mu}g_B \oplus w^2 g_F$,…
he analytic formulas for structure constants of $su(2S+1)$ algebra in terms of $3jm$ and $6j$ symbols of $su(2)$ have been derived for the decomplexification of the Liouville-von Neumann equation.