The many faces of modern combinatorics

TL;DR

This survey explores recent advances in combinatorics, highlighting its diverse interactions with various mathematical disciplines like algebra, geometry, topology, probability, and computer science, providing a comprehensive overview.

Contribution

It offers a broad overview of modern combinatorics and its interdisciplinary connections, emphasizing recent developments and the field's expanding scope.

Findings

Highlights combinatorics' connections with other math areas

Summarizes recent key developments in the field

Provides a comprehensive interdisciplinary perspective

Abstract

This is a survey of recent developments in combinatorics. The goal is to give a big picture of its many interactions with other areas of mathematics, such as: group theory, representation theory, commutative algebra, geometry (including algebraic geometry), topology, probability theory, and theoretical computer science.