Omer Bobrowski - Maximally Persistent Cycles in Random Geometric Complexes

Explore the fascinating world of random geometric complexes and maximally persistent cycles in this hour-long lecture by Omer Bobrowski. Delve into the main tools and concepts, including check complexes, restricted complexes, and Poisson processes. Examine key results, drawing connections to random graph theory and discussing convergence and order of magnitude. Gain insights into the two main ideas and key steps involved in the research. Observe simulations and learn about the properties of inclusions. Conclude with a summary of findings and potential future work in this field. Engage with the speaker during the audience question session to deepen your understanding of this complex topic in applied algebraic topology.

Introduction
Main tool
Check complex
Restrict complex
Poisson process
Features
Results
Random graph theory
Convergence
Order of magnitude
Two ideas
Key steps
Simulation
Properties of inclusions
Summary
Future work
Audience questions