Related papers: Lefschetz and Lower Bound theorems for Minkowski s…

For $1 \leq p < \infty$, Ludwig, Haberl and Parapatits classified $L_p$ Minkowski valuations intertwining the special linear group with additional conditions such as homogeneity and continuity. In this paper,a complete classification of…

We lift the Lefschetz number from an algebraic invariant of maps between spaces to an invariant of morphisms of data over the spaces.

Short and transparent proofs of central limit theorems for intrinsic volumes of random polytopes in smooth convex bodies are presented. They combine different tools such as estimates for floating bodies with Stein's method from probability…

In this short survey we want to present some of the impact of Minkowski's successive minima within Convex and Discrete Geometry. Originally related to the volume of an $o$-symmetric convex body, we point out relations of the successive…

In a seminal paper "Volumen und Oberfl\"ache" (1903), Minkowski introduced the basic notion of mixed volumes and the corresponding inequalities that lie at the heart of convex geometry. The fundamental importance of characterizing the…

In this paper we investigate some strong convergence theorems for partial sums with respect to Vilenkin system.

We study the regularity of the distance function to the boundary of a domain in $\mathbb{R}^n$, with respect to the Minkowski functional of a convex polytope. We obtain the regularity of the distance function in certain cases. We also…

For a collection of convex bodies $P_1,\dots,P_n \subset \mathbb{R}^d$ containing the origin, a Minkowski complex is given by those subsets whose Minkowski sum does not contain a fixed basepoint. Every simplicial complex can be realized as…

In this paper we investigate bounds for the zeros of a bicomplex polynomial using matrix method. In particular, we find analogue of Gershgorin disk theorem, Cauchy Theorem, theorem of Fujiwara, Walsh and other theorems concerning to zeros…

This short review is the result of a minicourse at the Sapienza University of Rome the author gave about the proof of the $g$-theorem. We review the hard Lefschetz theorem for simplicial spheres, as well as the theory at its core:…

In these proceedings, we summarize the Lefschetz thimble approach to the sign problem of Quantum Field Theories. In particular, we review its motivations, and we summarize the results of the application of two different algorithms to two…

The Lefschetz fixed point theorem and its converse have many generalizations. One of these generalizations is to endomorphisms of a space relative to a fixed subspace. In this paper we define relative Lefschetz numbers and Reidemeister…

This text is an appendix to our work "On the growth of Kronecker coefficients", arXiv:1607.02887. Here, we provide some complementary theorems, remarks, and calculations that for the sake of space are not going to appear into the final…

We present a new lower bound on the number of contingency tables, improving upon and extending previous lower bounds by Barvinok and Gurvits. As an application, we obtain new lower bounds on the volumes of flow and transportation polytopes.…

In this exposition of the equality and inequality of Minkowski for multiplicity of ideals, we provide simple algebraic and geometric proofs. Connections with mixed multiplicities of ideals are explained.

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…

To determine the relative position of any two surfaces in a system, one approach is to useoperations (Minkowski sum and intersection) on sets of constraints. These constraints aremade compliant with half-spaces of R^n where each set of…

Minkowski's First Theorem and Dirichlet's Approximation Theorem provide upper bounds on certain minima taken over lattice points contained in domains of Euclidean spaces. We study the distribution of such minima and show, under some…

Positive polynomials arising from Muirhead's inequality, from classical power mean and elementary symmetric mean inequalities and from Minkowski's inequality can be rewritten as sums of squares.

We give upper and lower bounds for weighted Chebyshev and residual polynomials on subsets of the real line. As an application, we prove a Szeg\H{o}-type theorem in the setting of Parreau--Widom sets.