Fiber Bundles Courses and Certifications

Richard Behiel

Introduction to Fiber Bundles and the Hopf Fibration

Explore the fascinating world of fiber bundles and Hopf fibration, discovering their mathematical beauty and applications in quantum mechanics and theoretical physics.

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

HyperComplex Seminar

GRACYASK: Graphs, Cycles, and Skyrmions in Discrete Trivial Fiber Bundles

Explore topological structures in higher dimensions, focusing on Skyrmions and Hopons. Gain insights into their potential applications in material science and biological processes, bridging theoretical physics with practical advancements.

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

ICTP Mathematics

Algebraic Topology

Master algebraic topology fundamentals through comprehensive lectures covering topological spaces, homotopy theory, and homological methods in this ICTP diploma program.

• YouTube
• 15 hours 42 minutes
• On-Demand
• Free Video

IAS | PCMI Park City Mathematics Institute

Advanced Topics in Mathematical Gauge Theory - Higgs Bundles

Delve into advanced mathematical gauge theory and Higgs bundles through expert lectures covering sophisticated theoretical frameworks and their geometric applications.

• YouTube
• 4 hours 11 minutes
• On-Demand
• Free Video

IAS | PCMI Park City Mathematics Institute

Introduction to Gauge Theory

Dive into gauge theory fundamentals through comprehensive mathematical lectures covering connections, curvature, and applications in modern geometry and physics.

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

Wolfram

Using Graph Rewriting to Study Discrete Lattice Systems - Wolfram Student Podcast Episode 3

Explore graph rewriting techniques for studying topological invariants in finite lattice systems and their applications to physical phenomena.

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

Applied Algebraic Topology Network

Topological Complexity of Pure Graph Braid Groups

Explore topological complexity in graph braid groups, focusing on Farber's conjecture about ordered configuration spaces and its implications for topological robotics.

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

Applied Algebraic Topology Network

Parametrized Topological Complexity of Hyperplane Arrangement Bundles

Exploring parametrized motion planning in hyperplane arrangement bundles, focusing on topological complexity under supersolvability conditions. Joint work with Dan Cohen.

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

Applied Algebraic Topology Network

A Fiber Bundle Theory for Shapes

Explore fiber bundle applications in probabilistic modeling for shapes and surfaces, focusing on regression, variable selection, and Gaussian processes in evolutionary biology and biomedicine.

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

BIMSA

From Quadratic Forms to Motivic Cohomologies

Explore the journey from quadratic forms to motivic cohomologies, delving into advanced mathematical concepts and their applications in algebraic geometry.

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

Institut des Hautes Etudes Scientifiques (IHES)

Geometric Structures Associated to Anosov Representations

Explore geometric structures linked to Anosov representations, focusing on domains of discontinuity and their quotients as smooth fiber bundles over closed hyperbolic manifolds.

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

NCCR SwissMAP

Quillen Metrics and Applications - Part 2

Explorez les métriques de Quillen et leurs applications dans cette conférence approfondie sur les cartes jaugées, les vortex et leurs moduli.

• YouTube
• 1 hour 9 minutes
• On-Demand
• Free Video

Simons Semester on Dynamics

Structural Stability for Fibrewise Anosov Diffeomorphisms on Principal Torus Bundles

Explore structural stability for fibrewise Anosov diffeomorphisms on principal torus bundles, focusing on topological conjugacy and linear fiber mappings.

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

ICTP Mathematics

Lefschetz Fibrations and Closed Exotic 4-Manifolds - Lecture 1

Explore the mathematical concepts of Lefschetz fibrations and their applications in understanding closed exotic 4-manifolds in this advanced mathematics lecture.

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

ICTP Mathematics

Lefschetz Fibrations and Closed Exotic 4-Manifolds

Explore advanced techniques in 4-dimensional topology through Lefschetz fibrations and their role in constructing exotic smooth structures on closed 4-manifolds.

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