Betti Numbers Courses and Certifications

Applied Algebraic Topology Network

Statistical Invariance of Betti Numbers in the Thermodynamic Regime

Explore statistical invariance of Betti numbers in random topology, examining conditions for topological inference through parametric statistics lens. Investigates asymptotic behavior and group invariance concepts.

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

Insights into Mathematics

Delta Complexes, Betti Numbers, and Torsion in Algebraic Topology

Explore homology groups of torus and projective plane using delta-complexes. Learn about Betti numbers and torsion in algebraic topology, with practical computations and insights into fundamental concepts.

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

ICTP Mathematics

What Are the Betti Numbers of a Manifold? - Don Zagier - 2017

Explore the concept of Betti numbers in manifolds with renowned mathematician Don Zagier, delving into their significance and applications in topology and geometry.

• YouTube
• 1 hour 19 minutes
• On-Demand
• Free Video

Applied Algebraic Topology Network

The Asymptotics of Betti Numbers in Preferential Attachment Clique Complexes

Explore the higher-order connectivity of preferential attachment networks through Betti numbers, examining growth rates and asymptotic behavior in this advanced mathematical analysis.

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

Applied Algebraic Topology Network

A Limit Theorem for Betti Numbers of Random Simplicial Complexes

Explore asymptotic behavior of Betti numbers in homogeneous and spatially independent random simplicial complexes, extending previous work on Linial-Meshulam complexes using local weak convergence.

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

BIMSA

Complex Algebraic Surfaces with Minimal Betti Numbers

Explore complex algebraic surfaces with minimal Betti numbers through advanced mathematical analysis and geometric insights.

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

International Centre for Theoretical Sciences

Lower Dimensional Betti Numbers of Homogeneous Spaces of Lie Groups

Exploration of lower dimensional Betti numbers in homogeneous spaces of Lie groups, discussing mathematical techniques and applications in algebraic topology and differential geometry.

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

INI Seminar Room 2

Group Theoretic Dehn Fillings and Their L²-Betti Numbers

Explore group theoretic Dehn fillings and their L²-Betti numbers in this advanced mathematical seminar by Prof. Nansen Petrosyan from the University of Southampton.

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

Applied Algebraic Topology Network

The Generalized Persistence Diagram Encodes the Bigraded Betti Numbers

Explore how generalized persistence diagrams encode bigraded Betti numbers in 2-parameter persistence modules, with implications for RIVET software and interval decomposable modules.

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

Centre de recherches mathématiques - CRM

Orbit Equivalence Theory, Cost, Ergodic Dimension and L2 Betti Numbers - Lecture 3

Explore orbit equivalence theory, cost, ergodic dimension, and L2 Betti numbers in measured group theory. Gain insights into foundational concepts and invariants through examples and exercises.

• YouTube
• 1 hour 7 minutes
• On-Demand
• Free Video

Centre de recherches mathématiques - CRM

Orbit Equivalence Theory, Cost, Ergodic Dimension and L2 Betti Numbers - Lecture 2

Explore orbit equivalence theory, cost, ergodic dimension, and L2 Betti numbers in measured group theory. Delve into advanced mathematical concepts with examples and exercises.

• YouTube
• 1 hour 7 minutes
• On-Demand
• Free Video

Centre de recherches mathématiques - CRM

Orbit Equivalence Theory: Cost, Ergodic Dimension, and L2 Betti Numbers - Part I

Explore orbit equivalence theory, cost, ergodic dimension, and L2 Betti numbers in measured group theory. Gain insights into foundational concepts and invariants through examples and exercises.

• YouTube
• 1 hour 3 minutes
• On-Demand
• Free Video

Fields Institute

Graded Betti Numbers of Jacobian Ideals of Hyperplane Arrangements

Explore the mathematical theory of graded Betti numbers in Jacobian ideals of hyperplane arrangements with Uwe Nagel from University of Kentucky.

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

Mathemaniac

The More General Euler Characteristic Formula - Understanding Surface Topology

Explore the deeper implications of Euler's characteristic formula as an inequality, examining its relationship with genus, Morse functions, and topological surfaces through intuitive explanations.

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

Applied Algebraic Topology Network

Applied Algebraic Topology Methods, Computation, and Science - ATMCS/AATRN 2020

Explore cutting-edge research in applied algebraic topology through expert presentations on persistence diagrams, homology, and computational methods for data analysis.

• YouTube
• 17 hours 43 minutes
• On-Demand
• Free Video