High Dimensional Expanders Courses and Certifications

Ryan O'Donnell

High-Dimensional Expanders - How I Learned to Stop Worrying and Love Group-Theoretic Constructions

Explore high-dimensional expanders, focusing on 2-dimensional cases, graphs of constant link, and group-theoretic constructions. Gain insights into advanced mathematical concepts and recent research developments.

• YouTube
• 47 minutes
• On-Demand
• Free Video

Institute for Advanced Study

Introduction to High Dimensional Expanders - Irit Dinur

Explore high dimensional expanders with Irit Dinur, covering random walks, spectral expansion, and hypergraphs. Gain insights into this advanced topic in discrete mathematics and computer science.

• YouTube
• 1 hour 51 minutes
• On-Demand
• Free Video

Simons Institute

High Dimensional Expanders - Introduction and Motivation

Explore high-dimensional expanders, their applications in error-correcting codes, and the motivations behind this emerging field of mathematics and computer science.

• YouTube
• 1 hour 35 minutes
• On-Demand
• Free Video

Simons Institute

Reverse Hypercontractivity and Improved Sampling in High Dimensional Expanders

Explore reverse hypercontractivity in high-dimensional expanders, its connection to mixing and sampling, and discover new Chernoff-like bounds in these mathematical structures.

• YouTube
• 58 minutes
• On-Demand
• Free Video

Hausdorff Center for Mathematics

High Dimensional Expanders

Explore high-dimensional expanders, their mathematical properties, and applications in theoretical computer science. Learn about coboundary and spectral expansion, and their implications for complex structures.

• YouTube
• 1 hour 15 minutes
• On-Demand
• Free Video

International Centre for Theoretical Sciences

High Dimensional Expanders - HDXs

Explore high-dimensional expanders, their mathematical foundations, and recent applications in computer science, including property testing, coding theory, and approximate counting.

• YouTube
• 1 hour 20 minutes
• On-Demand
• Free Video

MUNI Seminar Series

Expanders in Higher Dimensions: From Local to Global Properties and Applications

Explore high-dimensional expanders, their local-to-global properties, and applications in coding theory, networking, and computational complexity.

• YouTube
• 39 minutes
• On-Demand
• Free Video

Institute for Advanced Study

Local-to-Global Theorems on High Dimensional Expanders

Explore high dimensional expansion theory, from graph fundamentals to complex applications in error-correcting codes and PCPs, focusing on how local properties influence global behaviors in mathematical structures.

• YouTube
• 1 hour 2 minutes
• On-Demand
• Free Video

Simons Institute

Pseudorandomness

Explorations in pseudorandomness: SoS lower bounds, block rigidity, unbounded-width permutation branching programs, computational entropies, and random projections in circuit complexity.

• YouTube
• 1 hour 11 minutes
• On-Demand
• Free Video

International Centre for Theoretical Sciences

Stability, Non-approximate Groups and High Dimensional Expanders by Alex Lubotzky

Explore stability, non-approximate groups, and high-dimensional expanders in this advanced mathematics lecture. Gain insights into residually finite and sophic groups, with a focus on recent breakthroughs and proofs.

• YouTube
• 50 minutes
• On-Demand
• Free Video

Hausdorff Center for Mathematics

Cynthia Vinzant - Log Concave Polynomials and Matroids

Explore strong log concavity in polynomials, its applications to matroids, and connections to combinatorics and geometry. Learn about recent developments and their implications.

• YouTube
• 58 minutes
• On-Demand
• Free Video

IEEE

Spectral Independence in High-Dimensional Expanders and Applications to the Hardcore Model

Explore spectral independence in high-dimensional expanders and its application to the hardcore model, focusing on Glauber dynamics, complexity phase transitions, and future research directions.

• YouTube
• 26 minutes
• On-Demand
• Conference Talk

IEEE

Decodable Quantum LDPC Codes Beyond the Square Root Distance Barrier Using High Dimensional Expander

Explore quantum LDPC codes using high dimensional expanders, surpassing distance barriers. Learn about CSS codes, geometric complexes, and LSV constructions for improved quantum error correction.

• YouTube
• 29 minutes
• On-Demand
• Conference Talk

IEEE

Approximating Constraint Satisfaction Problems on High Dimensional Expanders

Explore high-dimensional expanders and their role in approximating constraint satisfaction problems, with insights on natural collections and general expanders.

• YouTube
• 18 minutes
• On-Demand
• Conference Talk

Institute for Pure & Applied Mathematics (IPAM)

High-Dimensional Sipser-Spielman Codes - IPAM at UCLA

Exploration of high-dimensional Sipser-Spielman codes, extending expander codes to cell complexes and cellular sheaves, with applications in quantum error correction and coding theory.

• YouTube
• 51 minutes
• On-Demand
• Free Video