Leonardo Ignacio Martínez Sandoval

- Mathematical Researcher
- Python Coder
- Advocate of Problem-Solving

Geometric Transversal Theory

Introduction

Helly's theorem on intersecting convex sets gave birth to a very fruitful area of discrete and computational geometry called Geometric Transversal Theory. This area has rich interactions with algortihms, combinatorics and topology. Although the progress throughout the years has been substantial, there are still many interesting and deep open questions to solve that keep the research in the area quite alive.

This mini-course is a selected research-oriented introduction to the topic. It is based on the diagram below. We will overview some interrelated theorems and give a sketch of their proofs. A wide variety of open problems will be presented.

Colorful Helly
Geometric Transversal Theory Map