Differential Topology Courses and Certifications

ICTP Mathematics

Topology - Lecture 12

Explore advanced concepts in topology, including complex geometric structures and their properties, in this comprehensive lecture by mathematician Bruno Zimmerman.

• YouTube
• 1 hour 40 minutes
• On-Demand
• Free Video

Institut des Hautes Etudes Scientifiques (IHES)

Stable Homotopy Groups, Higher Algebra, and the Telescope Conjecture

Explore stable homotopy groups, spectra, and their applications in topology and geometry. Gain insights into fundamental concepts shaping modern algebraic topology and related fields.

• YouTube
• 1 hour 12 minutes
• On-Demand
• Free Video

Institut des Hautes Etudes Scientifiques (IHES)

The Geometric Ideas of René Thom Related to Manifolds with Singularities

Explore René Thom's groundbreaking papers on transversality, cobordism, and manifolds with singularities, revealing their geometric insights and impact on mathematical understanding.

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

Fields Institute

Bordism of Manifolds - Lecture 1

Explore the concept of bordism in manifolds with Stanford's Mohammed Abouzaid, delving into advanced mathematical theories and their applications in topology and geometry.

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

Harvard CMSA

Fibered Ribbon Knots vs. Major 4D Conjectures - Part 1

Delve into advanced mathematical concepts exploring fibered ribbon knots, their relationship to smooth 4D Poincaré conjecture, and criteria for extending fibrations in topological studies.

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

IAS | PCMI Park City Mathematics Institute

Heegaard Floer Homology

Dive into Heegaard Floer homology through comprehensive lectures covering fundamental concepts and advanced applications in low-dimensional topology and knot theory.

• YouTube
• 3 hours 53 minutes
• On-Demand
• Free Video

Applied Algebraic Topology Network

Generalized Morse Theory of Distance Functions to Surfaces for Persistent Homology

Unifying distance fields, persistent homology, and Morse theory to quantify complex shape textures, with applications in characterizing vascular structures in leukemia samples.

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

IMSA

Milnor Spheres - 60 Years Later

Explore Milnor Spheres through a category theory lens, examining recent findings and insights in this seminar on classical differential topology by Ludmil Katzarkov.

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

Galileo Galilei Institute

On the Fukaya-Morse A-infinity Category

Explore the intricacies of Fukaya-Morse A-infinity category with Pavel Mnev, delving into advanced mathematical concepts and their applications in topology and geometry.

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

Fields Institute

TQFTs and the Renaissance of the Algebraic Topology of Manifolds

Explore the resurgence of algebraic topology in manifold studies, focusing on Topological Quantum Field Theories and their impact on modern mathematical research.

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

Fields Institute

Bordism of Derived Orbifolds - Lecture 3

Explore advanced mathematical concepts in bordism theory and derived orbifolds with Stanford University expert Mohammed Abouzaid in this Fields Institute lecture.

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

Centre International de Rencontres Mathématiques

Brazil-France School on Foliation Theory - Lecture

Explore advanced concepts in foliation theory with renowned mathematician Carolina Araujo in this Brazil-France School lecture.

• YouTube
• 1 hour 10 minutes
• On-Demand
• Free Video

NCCR SwissMAP

Poincare Duality and TQFT Structures for Loop Spaces

Explore Poincaré duality and TQFT structures in loop spaces, delving into advanced algebraic topology concepts with K. Cieliebak from Augsburg.

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

NCCR SwissMAP

Applied Cobordism Hypothesis in Quantum Field Theory

Explore the Applied Cobordism Hypothesis and its implications in quantum field theory with expert insights from D. Jordan of the University of Edinburgh.

• YouTube
• 2 hours 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