YoVDO

Higher-Dimensional Expansion of Random Geometric Complexes

Offered By: Simons Institute via YouTube

Tags

Simplicial Complexes Courses Graph Theory Courses Hypergraphs Courses

Course Description

Overview

Save Big on Coursera Plus. 7,000+ courses at $160 off. Limited Time Only!
Explore the concept of higher-dimensional expansion in random geometric complexes through this lecture by Tselil Schramm from Stanford University. Delve into the generalization of graph expansion to hypergraphs and simplicial complexes, focusing on 2-dimensional spectral expansion. Examine how local expansion of vertex links and neighborhoods can indicate global expansion. Investigate the open question of whether sparse 2-dimensional expanders are abundant or rare in nature. Learn about new evidence supporting their abundance, including findings on triangles in random geometric graphs on high-dimensional spheres forming expanding simplicial complexes. Gain insights into this collaborative research with Siqi Liu, Sidhanth Mohanty, and Elizabeth Yang, which contributes to the field of structural results in geometric complexes.

Syllabus

Higher-dimensional Expansion of Random Geometric Complexes


Taught by

Simons Institute

Related Courses

Aplicaciones de la teoría de grafos a la vida real
Miríadax
Aplicaciones de la Teoría de Grafos a la vida real
Universitat Politècnica de València via UPV [X]
Introduction to Computational Thinking and Data Science
Massachusetts Institute of Technology via edX
Genome Sequencing (Bioinformatics II)
University of California, San Diego via Coursera
Algorithmic Information Dynamics: From Networks to Cells
Santa Fe Institute via Complexity Explorer