Tverberg's theorem is 50 years old: a survey

TL;DR

This survey reviews the recent two decades of research on Tverberg's theorem, highlighting developments in topological, linear-algebraic, and combinatorial aspects, along with open problems and conjectures.

Contribution

It provides a comprehensive overview of recent advances and open problems related to Tverberg's theorem over the past 20 years.

Findings

Significant progress in topological and combinatorial aspects

Identification of key open problems and conjectures

Applications across various mathematical fields

Abstract

This survey presents an overview of the advances around Tverberg's theorem, focusing on the last two decades. We discuss the topological, linear-algebraic, and combinatorial aspects of Tverberg's theorem and its applications. The survey contains several open problems and conjectures.