Graph Theory Courses

Topos Institute

As If Category Theory Were a Foundation - A Methodological Approach to Mathematical Foundations

Explore the philosophical intersection of mathematics and methodology, examining how 'as-if' interpretations can bridge mathematical practice with theoretical foundations in category theory.

• YouTube
• 1 hour 20 minutes
• Self-Paced
• Free Video

Topos Institute

Categories as Ideas - A Dynamic Theory of Platonic Ontology

Explore the philosophical intersection of category theory and Platonism, examining how mathematical structures can illuminate our understanding of abstract ideas and modern ontology.

• YouTube
• 1 hour 1 minute
• Self-Paced
• Free Video

Topos Institute

Structured and Decorated Cospans from Double Category Theory

Delve into advanced category theory concepts, exploring structured and decorated cospans through the lens of double categories, with applications to open systems modeling.

• YouTube
• 32 minutes
• Self-Paced
• Free Video

Topos Institute

Metric Spaces, Entropic Spaces and Convexity in Category Theory

Delve into advanced mathematical concepts exploring metric spaces, entropic spaces, and convexity monads, connecting thermodynamics with category theory and optimal transport.

• YouTube
• 59 minutes
• Self-Paced
• Free Video

Topos Institute

Dual Algebraic Structures and Enrichment: From Sweedler Theory to Operadic Structures

Delve into advanced algebraic concepts including Sweedler theory, enriched categories, and operadic structures through detailed mathematical explorations and theoretical frameworks.

• YouTube
• 51 minutes
• Self-Paced
• Free Video

Topos Institute

Philosophical Perspectives on Category Theory and Its Applications

Explore the philosophical implications of category theory across mathematics, physics, probability, and modern applications like machine learning and natural language processing.

• YouTube
• 1 hour 2 minutes
• Self-Paced
• Free Video

Topos Institute

Metagames and Imprecise Probability - Game Theory and Agent Behavior

Explore the intersection of game theory and probability through recursive agent modeling, combining imprecise probability with domain theory to understand complex agent interactions and beliefs.

• YouTube
• 1 hour 6 minutes
• Self-Paced
• Free Video

Topos Institute

Co- and Contra-categories: Theory of Decomposition and Directed Obstructions

Delve into the mathematical foundations of contra-categories, exploring directed obstructions, apartness spaces, and their relationships with ultrafilters and Lawvere metric spaces.

• YouTube
• 1 hour 1 minute
• Self-Paced
• Free Video

Topos Institute

Fuzzy Type Theory - From Martin-Löf to Fuzzy Sets

Delve into the mathematical foundations of fuzzy type theory and its relationship to Martin-Löf type theory, exploring how it models opinions with parameterized evidence and categorical connections.

• YouTube
• 1 hour 16 minutes
• Self-Paced
• Free Video

IAS | PCMI Park City Mathematics Institute

Mathematics and Physics in Creative Crafts - From Curvature to Knot Theory

Explore the fascinating intersection of mathematics and crafting, discovering how physics, geometry, and knot theory connect with crochet, quilting, and textile manufacturing patterns.

• YouTube
• 50 minutes
• Self-Paced
• Free Video

IAS | PCMI Park City Mathematics Institute

Arithmetic Properties of Local Systems in Motivic Homotopy Theory

Delve into fundamental group theory and local systems in arithmetic geometry, exploring classical conjectures and recent developments in motivic representations and their arithmetic properties.

• YouTube
• 58 minutes
• Self-Paced
• Free Video

IAS | PCMI Park City Mathematics Institute

Characteristic Classes in Stable Motivic Homotopy Theory - Part 4

Delve into advanced concepts of characteristic classes in stable motivic homotopy theory, exploring Quillen's work extensions, Panin-Walter orientation theories, and applications in quadratic enumerative geometry.

• YouTube
• 1 hour 3 minutes
• Self-Paced
• Free Video

IAS | PCMI Park City Mathematics Institute

Characteristic Classes in Stable Motivic Homotopy Theory - Part 3

Delve into advanced concepts of characteristic classes in stable motivic homotopy theory, exploring Quillen's work extensions, Panin-Walter orientation theories, and applications to quadratic enumerative geometry.

• YouTube
• 1 hour 3 minutes
• Self-Paced
• Free Video

IAS | PCMI Park City Mathematics Institute

Characteristic Classes in Stable Motivic Homotopy Theory - Part 2

Delve into advanced concepts of characteristic classes in stable motivic homotopy theory, exploring Quillen's work extensions and modern developments in quadratic enumerative geometry.

• YouTube
• 1 hour 4 minutes
• Self-Paced
• Free Video

IAS | PCMI Park City Mathematics Institute

Contractibility and Spheres: A Motivic View in Homotopy Theory

Explore algebraic geometry through the lens of spheres and contractibility in topology, using motivic homotopy theory to bridge classical and modern mathematical concepts.

• YouTube
• 1 hour 2 minutes
• Self-Paced
• Free Video