Related papers: Some Open Problems in Topological Algebra

Several open questions are discussed. The topics include cohomology of current and related Lie algebras, algebras represented as the sum of subalgebras, structures and phenomena peculiar to characteristic $2$, and variations on themes of…

Open problems in information geometry are collected and discussed in the conference ``Further Developments of Information Geometry (FDIG) 2025'' held at the University of Tokyo, Japan, from March 18 to 21, 2025.

A compendium of thirty previously published open problems in computational geometry is presented.

This document presents a series of open questions arising in matrix computations, i.e., the numerical solution of linear algebra problems. It is a result of working groups at the workshop Linear Systems and Eigenvalue Problems, which was…

This survey article on Hilbert's first and second problems is adapted from a one-hour colloquium lecture given at the University of Auckland in May, 2000, just three months before the 100th anniversary of Hilbert's lecture. It includes an…

This is a list of some problems and conjectures related to various types of algebras, that is to algebraic operads. Some comments and hints are included.

We present updates to the problems on Hirzebruch's 1954 problem list focussing on open problems, and on those where substantial progress has been made in recent years. We discuss some purely topological problems, as well as geometric…

We investigate the rectifiable spaces, the Mal'cev algebras, the almost quasivarieties of topological algebraic systems and their free systems and others. It specifies and corrects the roughest mistakes, incorrect statements and nonsense of…

We present a number of questions in commutative algebra posed on the problem solving seminar in algebra at Stockholm University during the period Fall 2014 - Spring 2017.

Fifteen years after their discovery, ample fields now stand at the center of research in contemporary Galois theory and attract more and more attention also from other areas of mathematics. This survey gives an introduction to the theory of…

We discuss selected topics on the topology of moduli spaces of curves and maps, emphasizing their relation with Gromov--Witten theory and integrable systems.

We discuss some mistakes and curiosities concerned with the celebrated First International Topological Conference in Moscow, 1935.

An algebraic deformation theory of algebras over the Landweber-Novikov algebra is obtained.

The paper gives a collection of open problems on abstract polytopes that were either presented at the Polytopes Day in Calgary or motivated by discussions at the preceding Workshop on Convex and Abstract Polytopes at the Banff International…

The paper consists of lecture notes for a mini-course given by the authors at the G\"okova Geometry \& Topology conference in May 2014. We start the exposition with tropical curves in the plane and their applications to problems in…

These notes are an expanded version of an introductory lecture on contact geometry given at the 2001 Georgia Topology Conference. They are intended to present some of the "topological" aspects of three dimensional contact geometry.

This is an expository introduction to tropical algebraic geometry based on my lectures at the Workshop on Tropical Geometry and Integrable Systems in Glasgow, July 4-8, 2011, and at the ELGA 2011 school on Algebraic Geometry and…

This list of 10 problems and their subsequent discussion by prominent scholars at the workshop in Geneva Observatory, 1993, were published in Lecture Notes in Physics, 1994, not too reachable now. The problems cover Theory, Computer…

A short survey on applications of algebraic geometry in topological data analysis.

Enumeration of tilings is the mathematical study concerning the total number of coverings of regions by similar pieces without gaps or overlaps. Enumeration of tilings has become a vibrant subfield of combinatorics with connections and…