Related papers: Integration Theory for Zero Sets of Polyfold Fredh…
We explain how to use computer experiments over finite fields to gain heuristic information about the solution set of polynomial equations in characteristic zero. These are notes of a tutorial I gave at the NATO Advanced Study Institute on…
We develop the theory of Gr\"obner bases for ideals in a polynomial ring with countably infinite variables over a field. As an application we reconstruct some of the one-one correspondences among various sets of partitions by using division…
In this paper we introduce and develop the concept of expansivity of a tuple whose entries are elements from the polynomial ring $\mathbb{C}[x]$. As an inverse problem, we examine how to recover a tuple from the expanded tuple at any given…
This paper develops a concept of 2-categorical algebraic quantum field theories (2AQFTs) that assign locally presentable linear categories to spacetimes. It is proven that ordinary AQFTs embed as a coreflective full 2-subcategory into the…
In this paper we present a new semilocal convergence theorem from data at one point for the Weierstrass iterative method for the simultaneous computation of polynomial zeros. The main result generalizes and improves all previous ones in…
In this paper we generalize the involutive methods and algorithms devised for polynomial ideals to differential ones generated by a finite set of linear differential polynomials in the differential polynomial ring over a zero characteristic…
This paper explains the recent developments on the symplectic theory of Hamiltonian completely integrable systems on symplectic 4-manifolds, compact or not. One fundamental ingredient of these developments has been the understanding of…
This article presents an overview of the theory of integrable systems with symmetries, focusing on toric systems, semitoric systems, and their classifications via decorated polygons. We discuss certain one-parameter families of integrable…
The chapter contains a detailed presentation of the surface integral theory for modelling light diffraction by surface-relief diffraction gratings having a one-dimensional periodicity. Several different approaches are presented, leading…
We study the non-invertible symmetries of class $\mathcal{S}$ theories obtained by compactifying the type $\mathfrak{a}_{p-1}$ 6d (2,0) theory on a genus $g$ Riemann surface with no punctures. After setting up the general framework, we…
In this letter, we continue the work we started at a previous paper and we propose new series of integrable models in quantum field theory. These models are obtained as perturbed models of the minimal conformal field theories on the…
This paper is concerned with the distribution of normalized zero-sets of random entire functions. The normalization of the zero-set is performed in the same way as that of the counting function for an entire function in Nevanlinna theory.…
We construct a multiplicative spectral sequence converging to the symplectic cohomology ring of any affine variety $X$, with first page built out of topological invariants associated to strata of any fixed normal crossings compactification…
The Shapley-Folkman theorem is a statement about the Minkowski sum of (non-convex) sets, expressing the closeness of the Minkowski sum to convexity in a quantitative manner. This paper establishes similar theorems for integrally convex…
The purpose of this note is to extend in a simple and unified way the known results on interlacing of zeros of paraorthogonal polynomials on the unit circle. These polynomials can be regarded as the characteristic polynomials of any matrix…
We survey results on the distribution of zeros of random polynomials and of random holomorphic sections of line bundles, especially for large classes of probability measures on the spaces of holomorphic sections. We provide furthermore some…
We prove a version of the fundamental theorems of Morse Theory in the setting of finite spaces or partially ordered sets. By using these results we extend Forman's discrete Morse theory to more general cell complexes and derive the…
Integral estimates for weak solutions to a class of Dirichlet problems for nonlinear, fully anisotropic, elliptic equations with a zero order term are obtained using symmetrization techniques.
The zero sets of harmonic polynomials play a crucial role in the study of the free boundary regularity problem for harmonic measure. In order to understand the fine structure of these free boundaries a detailed study of the singular points…
We construct a theory of distributions in the setting of analysis on post-critically finite self-similar fractals, and on fractafolds and products based on such fractals. The results include basic properties of test functions and…