Related papers: New polytope decompositions and Euler-Maclaurin fo…

We describe a technique to obtain linear descriptions for polytopes from extended formulations. The simple idea is to first define a suitable lifting function and then to find linear constraints that are valid for the polytope and guarantee…

Any finite simplicial complex K and a partition of the vertex set of K determines a canonical quotient space of the moment-angle complex of K. We prove that the cohomology groups of such a space can be computed via some Hochster's type…

There has been increasing interest in studying the Richardson model from which one can derive the exact solution for certain pairing Hamiltonians. However, it is still a numerical challenge to solve the nonlinear equations involved. In this…

In this paper, we study parabolic equations in divergence form with coefficients that are singular degenerate as some Muckenhoupt weight functions in one spatial variable. Under certain conditions, weighted reverse H\"{o}lder's inequalities…

We derive a sharp decomposition formula for the state polytope of the Hilbert point and the Hilbert-Mumford index of reducible varieties by using the decomposition of characters and basic convex geometry. This proof captures the essence of…

Following ideas of Lurie, we give in this article a general construction of equivariant elliptic cohomology without restriction to characteristic zero. Specializing to the universal elliptic curve we obtain in particular equivariant spectra…

We study superpositions and direct integrals of quadratic and Dirichlet forms. We show that each quasi-regular Dirichlet space over a probability space admits a unique representation as a direct integral of irreducible Dirichlet spaces,…

We construct a cocycle model for complex analytic equivariant elliptic cohomology that refines Grojnowski's theory when the group is connected and Devoto's when the group is finite. We then construct Mathai--Quillen type cocycles for…

We study character varieties arising as moduli of representations of an orientable surface group into a reductive group $G$. We first show that if $G/Z$ acts freely on the representation variety, then both the representation variety and the…

A shape of a combinatorial polytope is a convex embedding into Euclidean space. We provide necessary and sufficient conditions for a piecewise linear map between two shapes of the same polytope to be a compression (respectively a weak…

First three sections of this overview paper cover classical topics of deformation theory of associative algebras and necessary background material. We then analyze algebraic structures of the Hochschild cohomology and describe the relation…

We consider the spectral decomposition of singularities of integrals and their integrands. Our results apply to any integral of Euler-Mellin type, and thus especially to every scalar Feynman integral. Specifically we provide for both the…

We investigate the value distribution of holomorphic maps defined on one class of K\"ahler manifolds. With the very natural settings, we establish a Second Main Theorem which is of the similar form as ones of the classical Second Main…

We employ the gravitational decoupling approach for static and spherically symmetric systems to develop a simple and powerful method in order to a) continuously isotropize any anisotropic solution of the Einstein field equations, and b)…

The aim of this paper is to describe how to obtain residue-type formulas for push-forwards in equivariant cohomology, using the Jeffrey-Kirwan nonabelian localization theorem and the related result of Guillemin and Kalkman. This paper…

For every compact Kaehler manifold we give a canonical extension of Griffith's period map to generalized deformations, intended as solutions of Maurer-Cartan equation in the algebra of polyvector fields. Our construction involves the notion…

We use localization method to understand the rational equivariant cohomology rings of real Grassmannians and oriented Grassmannians, then relate this to the Leray-Borel description which says the ring generators are equivariant Pontryagin…

Both the additional non-linear term in the Schr\"odinger equation and the additional non-Hamiltonian term in the von Neumann equation, proposed to ensure localisation and decoherence of macro-objects, resp., contain the same Newtonian…

We shall present an elementary approach to extremal decompositions of (quantum) covariance matrices determined by densities. We give a new proof on former results and provide a sharp estimate of the ranks of the densities that appear in the…

We review localization techniques for functional integrals which have recently been used to perform calculations in and gain insight into the structure of certain topological field theories and low-dimensional gauge theories. These are the…