Related papers: Positive Pl\"ucker tree certificates for non-reali…

In this paper we construct Ricci-positive metrics on the connected sum of products of arbitrarily many spheres provided the dimensions of all but one sphere in each summand are at least 3. There are two new technical theorems required to…

Infinitely many large Schur sigma-groups G with non-elementary bicyclic commutator quotient G/G' = C(3^e) x C(3), e >= 2, are constructed as periodic sequences of vertices in descendant trees of finite 3-groups. A single root gives rise to…

We prove that the moment-angle complex $\mathcal Z_K$ corresponding to a 3-dimensional simplicial sphere $K$ has the cohomology ring isomorphic to the cohomology ring of a connected sum of products of spheres if and only if either (a) $K$…

Let M be an archimedean quadratic module of real t-by-t matrix polynomials in n variables, and let S be the set of all real n-tuples where each element of M is positive semidefinite. Our key finding is a natural bijection between the set of…

This note is about the interplay between the almost-hermitian and Riemannian geometries of a manifold. These geometries can be seen to interact through curvature. The main result is an obstruction equation to the integrability of…

Here we present certificates for 5 classes of 6-edged multigraphs whose symmetrized graph monomials may be represented as sum of squares, but not as linear combinations of partition square graphs. This is a complement to the results…

The problem of deciding if a given triangulation of a sphere can be realized as the boundary sphere of a simplicial, convex polytope is known as the "Simplicial Steinitz problem". It is known by an indirect and non-constructive argument…

In this paper we produce families of Riemannian metrics with positive constant $\sigma_k$-curvature equal to $2^{-k} {n \choose k}$ by performing the connected sum of two given compact {\em non degenerate} $n$--dimensional solutions…

Let $S \subseteq \mathbb{R}^n$ be a compact semialgebraic set and let $f$ be a polynomial nonnegative on $S$. Schm\"udgen's Positivstellensatz then states that for any $\eta > 0$, the nonnegativity of $f + \eta$ on $S$ can be certified by…

This paper introduces and develops the algebraic framework of moment polynomials, which are polynomial expressions in commuting variables and their formal mixed moments. Their positivity and optimization over probability measures supported…

We prove that many simply connected symplectic four-manifolds dissolve after connected sum with only one copy of $S^{2}\times S^{2}$. For any finite group G that acts freely on the three-sphere we construct closed smooth four-manifolds with…

We show that the Skolem Problem is decidable in finitely generated commutative rings of positive characteristic. More precisely, we show that there exists an algorithm which, given a finite presentation of a (unitary) commutative ring…

We focus on computing certified upper bounds for the positive maximal singular value (PMSV) of a given matrix. The PMSV problem boils down to maximizing a quadratic polynomial on the intersection of the unit sphere and the nonnegative…

Let $\Omega$ be a planar Jordan domain. We consider double-dome-like surfaces $\Sigma$ defined by graphs of functions of $dist( \cdot ,\partial \Omega)$ over $\Omega$. The goal is to find the right conditions on the geometry of the base…

We give some new explicit examples of putatively optimal projective spherical designs. i.e., ones for which there is numerical evidence that they are of minimal size. These form continuous families, and so have little apparent symmetry in…

Associated with a symmetric Clifford system $\{P_0, P_1,\cdots, P_{m}\}$ on $\mathbb{R}^{2l}$, there is a canonical vector bundle $\eta$ over $S^{l-1}$. For $m=4$ and $8$, we construct explicitly its characteristic map, and determine…

Properties of Hermitian forms are used to investigate several natural questions from CR Geometry. To each Hermitian symmetric polynomial we assign a Hermitian form. We study how the signature pairs of two Hermitian forms behave under the…

We give a general procedure for gluing together possibly noncompact manifolds of constant scalar curvature which satisfy an extra nondegeneracy hypothesis. Our aim is to provide a simple paradigm for making `analytic' connected sums. In…

In this work we consider periodic spherically symmetric metrics of constant positive scalar curvature on the n-dimensional cylinder called pseudo-cylindric metrics. These metrics belong to the conformal class $[g_0]$ of the Riemannian…

We prove the regularity of weak 1/2-harmonic maps from the real line into a sphere. The key point in our result is first a formulation of the 1/2-harmonic map equation in the form of a non-local linear Schr\"odinger type equation with a…