Related papers: A software package for Mori dream spaces

Real toric manifolds are the real loci of nonsingular complete toric varieties. In this paper, we calculate the integral cohomology groups of real toric manifolds in terms of the combinatorial data contained in the underlying simplicial…

In this article we describe applications of the numerical method of discrete differential forms in computational GR. In particular we consider the initial value problem for vacuum space-times that admit plane gravitational waves. As…

If two conical symplectic resolutions $X\to X_0$ and $X^!\to X_0^!$ are symplectic dual, the cohomology ring $H^*(X)$ and the coordinate ring of $\mathbb{C}^*$-fixed points in $X_0^!$ are expected to be isomorphic as graded algebras. This…

Moduli spaces of complete skew-forms are compactifications of spaces of skew-symmetric linear maps of maximal rank on a fixed vector space, where the added boundary divisor is simple normal crossing. In this paper we compute their…

In this paper, we propose a new way to approach qudit systems using toric geometry and related topics including the local mirror symmetry used in the string theory compactification. We refer to such systems as (n,d) quantum systems where…

A dormant oper is a specific type of principal bundle with a flat connection, defined on an algebraic curve in positive characteristic. The moduli spaces of dormant opers and their variants, known as dormant Miura opers, have been studied…

We consider a variational convex relaxation of a class of optimal partitioning and multiclass labeling problems, which has recently proven quite successful and can be seen as a continuous analogue of Linear Programming (LP) relaxation…

We discuss the application of random projections to conic programming: notably linear, second-order and semidefinite programs. We prove general approximation results on feasibility and optimality using the framework of formally real Jordan…

Motivated by recent work on the use of topological methods to study collections of rings between an integral domain and its quotient field, we examine spaces of subrings of a commutative ring, where these spaces are endowed with the Zariski…

We complete Mori's program for Kontsevich's moduli space of degree 2 stable maps to Grassmannian of lines. We describe all birational models in terms of moduli spaces (of curves and sheaves), incidence varieties, and Kirwan's partial…

We study sum of squares (SOS) relaxations to optimize polynomial functions over a set $V\cap R^n$, where $V$ is a complex algebraic variety. We propose a new methodology that, rather than relying on some algebraic description, represents…

Let $R:= \Bbbk[x_1,\ldots,x_{n}]$ be a polynomial ring over a field $\Bbbk$, $I \subset R$ be a homogeneous ideal with respect to a weight vector $\omega = (\omega_1,\ldots,\omega_n) \in (\mathbb{Z}^+)^n$, and denote by $d$ the Krull…

Numerical algebraic geometry is the field of computational mathematics concerning the numerical solution of polynomial systems of equations. Bertini, a popular software package for computational applications of this field, includes…

In the first part of the paper we construct a ring structure on the rational cobordism classes of Morin maps (i. e. smooth generic maps of corank 1). We show that associating to a Morin map its singular strata defines a ring homomorphism to…

We have developed in the past several algorithms with intrinsic complexity bounds for the problem of point finding in real algebraic varieties. Our aim here is to give a comprehensive presentation of the geometrical tools which are…

We compute the Chow-Witt rings of the classifying spaces for the symplectic and special linear groups. In the structural description we give, contributions from real and complex realization are clearly visible. In particular, the…

QMCPACK is an open source quantum Monte Carlo package for ab-initio electronic structure calculations. It supports calculations of metallic and insulating solids, molecules, atoms, and some model Hamiltonians. Implemented real space quantum…

This paper is concerned with the combinatorial description of the graded minimal free resolution of certain monomial algebras which includes toric rings. Concretely, we explicitly describe how the graded minimal free resolution of those…

We introduce the notion of chiral symplectic cores in a vertex Poisson variety, which can be viewed as analogs of symplectic leaves in Poisson varieties. As an application we show that any quasi-lisse vertex algebra is a quantization of the…

The CompModels package for R provides a suite of computer model test functions that can be used for computer model prediction/emulation, uncertainty quantification, and calibration, but in particular, the sequential optimization of computer…