Related papers: SPM Bulletin 33
We give a selection of major open problems involving selective properties, diagonalizations, and covering properties for sets of real numbers. This is a revision of the version published as a chapter in the book \textbf{Open Problems in…
The aim of this paper is to suggest a new viewpoint to study qualitative properties of solutions of semilinear elliptic PDE's defined outside a compact set. The relevant tools come from spectral theory and from a combination of stochastic…
We study the birational maps of $\mathbb{P}^3_\mathbb{C}$. More precisely we describe the irreducible components of the set of birational maps of bidegree $(3,3)$ (resp. $(3,4)$, resp. $(3,5)$).
We investigate algebraic and arithmetic properties of a class of sequences of sparse polynomials that have binomial coefficients both as exponents and as coefficients. In addition to divisibility and irreducibility results we also consider…
Cyclotomic polylogarithms are reviewed and new results concerning the special constants that occur are presented. This also allows some comments on previous literature results using PSLQ.
We present and discuss applications of the category of probabilistic morphisms, initially developed in \cite{Le2023}, as well as some geometric methods to several classes of problems in statistical, machine and manifold learning which shall…
We survey some recent applications of machine learning to problems in geometry and theoretical physics. Pure mathematical data has been compiled over the last few decades by the community and experiments in supervised, semi-supervised and…
The purpose of this manuscript is to gather together a large amount of source material pertaining to women in mathematics, from studies of girls in elementary school through data on females winning prizes for mathematical research. Along…
The typical processors used for scientific computing have fixed-width data-paths. This implies that mathematical libraries were specifically developed to target each of these fixed precisions (binary16, binary32, binary64). However, to…
Educational guide focused on the statistical treatment of measurement uncertainties. The conditions of application of current practices are detailed and precised: mean values, central limit theorem, linear regression. The last two chapters…
The field of computational statistics refers to statistical methods or tools that are computationally intensive. Due to the recent advances in computing power some of these methods have become prominent and central to modern data analysis.…
We review some selected recent results concerning selection principles in topology and their relations with several topological constructions.
The purpose of this bulletin board is to collect problems in higher dimensional complex analysis. We are interested both in basic research questions as well as interactive questions with other fields and sciences. We encourage everybody to…
Several recent SIGGRAPH papers on surface simplification are described.
The search for a point set configurations of the R^3 space which contains the smallest value of the Euclidean Steiner Ratio is almost finished. In the present work we introduce some analytical methods which aim to support a famous…
We derive properties and a characterization of discrete composition matrices which are useful in the field of numerical computation of shape correspondences.
Let $C$ be a smooth irreducible projective algebraic curve defined over the complex numbers. The notion of the Clifford index of $C$ was extended a few years ago to semistable bundles of any rank. Recent work has been focussed mainly on the…
This is a collection of teaching materials used in several Russian universities, schools, and mathematical circles. Most problems are chosen in such a way that in the course of the solution and discussion a reader learns important…
We aim to conduct a systematic mapping in the area of testing ML programs. We identify, analyze and classify the existing literature to provide an overview of the area. We followed well-established guidelines of systematic mapping to…
Contents 1. Algebraicity criterion: statement 2. Proof of the algebraicity criterion. 3. Pseudoeffectivity and movable classes. 4. Harder-Narasimhan filtrations and pseudo-effectivity. 5. Pseudo-effectivity of relative canonical bundles. 6.…