Related papers: Pyramids and monomial blowing-ups

The classical matrix tree theorem relates the number of spanning trees of a connected graph with the product of the nonzero eigenvalues of its Laplacian matrix. The class of regular matroids generalizes that of graphical matroids, and a…

In a previous work, we proved that each minimal symplectic filling of any oriented lens space, viewed as the singularity link of some cyclic quotient singularity and equipped with its canonical contact structure, can be obtained from the…

We provide a procedure for resolving, in characteristic 0, singularities of a variety $X$ embedded in a smooth variety $Y$ by repeatedly blowing up the worst singularities, in the sense of stack-theoretic weighted blowings up. No history,…

The probability for two monic polynomials of a positive degree n with coefficients in the finite field F_q to be relatively prime turns out to be identical with the probability for an n x n Hankel matrix over F_q to be nonsingular.…

A representation of finite-dimensional probabilistic models in terms of formally real Jordan algebras is obtained, in a strikingly easy way, from simple assumptions. This provides a framework in which real, complex and quaternionic quantum…

We introduce a homological approach to exhibiting instances of Stembridge's q=-1 phenomenon. This approach is shown to explain two important instances of the phenomenon, namely that of partitions whose Ferrers diagrams fit in a rectangle of…

We initiate the study of factorization centers of birational maps, and complete it for surfaces over a perfect field in this article. We prove that for every birational automorphism $\phi : X \dashrightarrow X$ of a smooth projective…

Gromov introduced the notion of a pyramid as a generalization of a metric measure space, based on the idea of the concentration of measure phenomenon. In this paper, we introduce the concept of a direct sum of pyramids, which naturally…

A semialgebraic map $f:X\to Y$ between two real algebraic sets is called blow-Nash if it can be made Nash (i.e. semialgebraic and real analytic) by composing with finitely many blowings-up with non-singular centers. We prove that if a…

We study blow-ups around fixed points at Type I singularities of the Ricci flow on closed manifolds using Perelman's W-functional. First, we give an alternative proof of the result obtained by Naber and Enders-M\"{u}ller-Topping that…

A planar polygonal billiard $\P$ is said to have the finite blocking property if for every pair $(O,A)$ of points in $\P$ there exists a finite number of ``blocking'' points $B_1, ..., B_n$ such that every billiard trajectory from $O$ to…

By formulating N = 1, 2, 4, 8, D = 3, Yang-Mills with a single Lagrangian and single set of transformation rules, but with fields valued respectively in R,C,H,O, it was recently shown that tensoring left and right multiplets yields a…

The direct or algorithmic approach for the Jacobian problem, consisting of the direct construction of the inverse polynomials is proposed. The so called principle and derived Jacobi conditions are proposed and discussed. The algorithmic…

In these short notes, we will show the following. Let F_q be a finite field and let E/\F_q be an elliptic curve. Let S_r be the rth summation/Semaev polynomial for E. Under an assumption, we show that it is NP-complete to check if S_r…

We provide several examples of bounded Laurent monomials of minors of a totally positive matrix, which can not be factored into a product of so called primitive ratios, thus showing that the conjecture about factorization of bounded ratios…

We prove the log-Brunn-Minkowski conjecture for convex bodies with symmetries to $n$ independent hyperplanes, and discuss the equality case and the uniqueness of the solution of the related case of the logarithmic Minkowski problem. We also…

In a previous paper Cuntz and Deninger introduced the ring $C(R)$ for a perfect $\mathbb{F}_p$-algebra $R$. The ring $C(R)$ is canonically isomorphic to the $p$-typical Witt ring $W(R)$. In fact there exist canonical isomorphisms $\alpha_n…

Let I=(x^{v_1},...,x^{v_q} be a square-free monomial ideal of a polynomial ring K[x_1,...,x_n] over an arbitrary field K and let A be the incidence matrix with column vectors {v_1},...,{v_q}. We will establish some connections between…

We show that with high probability the number of real zeroes of a random polynomial is bounded by the number of vertices on its Newton-Hadamard polygon times the cube of the logarithm of the polynomial degree. A similar estimate holds for…

We provide a mirror symmetry theorem in a range of cases where the state-of-the-art techniques relying on concavity or convexity do not apply. More specifically, we work on a family of FJRW potentials named after Fan, Jarvis, Ruan, and…