Related papers: Boardman's whole-plane obstruction group for Carta…

Every multiplier algebra of an irreducible complete Pick kernel arises as the restriction algebra $\mv = \{f\big|_V : f \in \cM_d\}$, where $d$ is some integer or $\infty$, $\cM_d$ is the multiplier algebra of the Drury-Arveson space…

We define the notion of torically hyperbolic varieties and we construct pair-of-pants decompositions for these in terms of angle sets of essential projective hyperplane complements. This construction generalizes the classical pair-of-pants…

We show that the vector bundle on the moduli stack $M_\mathrm{ell}$ of elliptic curves associated to the $2$-cell complex $C\nu$ is isomorphic to the de Rham cohomology sheaf $\mathrm{H}^1_\mathrm{dR}(\mathcal{E}/M_\mathrm{ell})$ of the…

For a complex Lie group $G$ with a real form $G_0\subset G$, we prove that any Hamiltionian automorphism $\phi$ of a coadjoint orbit $\mathcal O_0$ of $G_0$ whose connected components are simply connected, may be approximated by holomorphic…

Given a zero-dimensional scheme Z, the higher-rank interpolation problem asks for the classification of slopes of vector bundles cohomologically orthogonal to the ideal sheaf of Z. In this paper, we solve this problem for all…

We introduce a new class of two(multi)-matrix models of positive Hermitean matrices coupled in a chain; the coupling is related to the Cauchy kernel and differs from the exponential coupling more commonly used in similar models. The…

It is shown by Barchini, Kable, and Zierau that conformally invariant systems of differential operators yield explicit homomorphisms between certain generalized Verma modules. In this paper we determine whether or not the homomorphisms…

Let $A$ denote the alternation limit algebra, studied by Hopenwasser and Power, and by Poon, which is the closed direct limit of upper triangular matrix algebras determined by refinement embeddings of multiplicity $r_k$ and standard…

We give a geometric method for determining the cohomology groups and the product structure of a polyhedral product, under suitable freeness conditions or with coefficients taken in a field. This is done by considering first a special class…

For every fake projective plane $X$ with automorphism group of order 21, we prove that $H^i(X, 2L)=0$ for all $i$ and for every ample line bundle $L$ with $L^2=1$. For every fake projective plane with automorphism group of order 9, we prove…

A chiral 4-fermion or 4-unit charge Coulomb structure for perturbed atom H implies that an intra-atomic H-Hbar transition must obey the same quantitative criteria as a classical intra-molecular Walden inversion. In a trigonal pyramid model…

In order to obtain a reasonable phase diagram involving hole-pair condensation for hole-doped cuprate systems, we propose a modified t-J Hamiltonian in which a Coulomb repulsion term between nearest neighbor holes is considered. We show…

We construct a polarized Hodge structure on the primitive part of Chen and Ruan's orbifold cohomology $H_{orb}^k(X)$ for projective $SL$-orbifolds $X$ satisfying a ``Hard Lefschetz Condition''. Furthermore, the total cohomology…

In this work, we introduce a variant of the Grothendieck-Teichm{\"u}ller group, defined in terms of complements of hyperplane arrangements and pro-$\ell$ two-step nilpotent fundamental groups, and prove that it is isomorphic to the absolute…

We obtain the full hamiltonian structure for a parametric coupled KdV system. The coupled system arises from four different real basic lagrangians. The associated hamiltonian functionals and the corresponding Poisson structures follow from…

In the previous paper, we defined a new category which categorifies the Hecke algebra. This is a generalization of the theory of Soergel bimodules. To prove theorems, the existences of certain homomorphisms between Bott-Samelson bimodules…

Dual-unitary circuits are being vigorously studied as models of many-body quantum chaos that can be solved exactly for correlation functions and time evolution of states. Here we define their classical counterparts as dual-canonical…

We find lower bounds on the number of intersection points between two relatively exact Hamiltonian isotopic Lagrangians. The bounds are given in terms of the cuplength of the Lagrangian in various multiplicative generalised cohomology…

Using Hamiltonian methods, we find six relativistic theories of nonlinear electrodynamics for which plane wave perturbations about a constant uniform background are not birefringent. All have the same conformal strong-field limit to…

Building on [1], we examine a holographic model in which a U(1) symmetry and translational invariance are broken spontaneously at the same time. The symmetry breaking is realized through the St\"{u}ckelberg mechanism, and leads to a scalar…