Homotopy Type Theory Courses and Certifications

Schmid College, Chapman University

From HoTT to HOTT - Exploring Homotopy Type Theory

Explore the evolution from Homotopy Type Theory (HoTT) to Higher-Order Type Theory (HOTT) in this insightful lecture by Michael Shulman, delving into advanced mathematical concepts and their philosophical implications.

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

Introduction to programming with dependent types in Scala

Explore type theory, dependent types, and theorem proving in Scala. Learn advanced concepts like type families, inductive types, and type-level programming for robust software development.

• Stepik
• On-Demand
• Free Online Course

International Mathematical Union

Georges Gonthier - Computer Proofs - Teaching Computers Mathematics, and Conversely

Explore computer-assisted mathematical proofs, from the four-color puzzle to homotopy type theory. Learn how computer science methods enhance mathematical language, leading to new insights and advancements in formal proofs.

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

Hausdorff Center for Mathematics

A Fibrational Framework for Modal Dependent Type Theories

Explore modal extensions of homotopy type theory, their frameworks, and applications in real-cohesive and differential-cohesive HoTT. Gain insights into fibrational frameworks for modal type theories.

• YouTube
• 1 hour 8 minutes
• On-Demand
• Free Video

Hausdorff Center for Mathematics

A Fibrational Framework for Modal Simple Type Theories

Explore modal extensions of homotopy type theory, focusing on fibrational frameworks for modal simple type theories and their applications in topology, geometry, and spectra.

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

Hausdorff Center for Mathematics

Discrete and Codiscrete Modalities in Cohesive HoTT

Explore discrete and codiscrete modalities in Cohesive Homotopy Type Theory, examining their applications in topology, differential geometry, and synthetic formalizations of mathematical concepts.

• YouTube
• 1 hour 4 minutes
• On-Demand
• Free Video

Hausdorff Center for Mathematics

Discrete and Codiscrete Modalities in Cohesive HoTT, II

Explore discrete and codiscrete modalities in Cohesive Homotopy Type Theory, advancing understanding of modal extensions and their applications in topology, geometry, and spectra.

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

Hausdorff Center for Mathematics

Formalization in Homotopy Type Theory - Equivalences, 3-for-2 and Definitional Equality

Explore practical techniques for proving map equivalence in Homotopy Type Theory, focusing on the 3-for-2 property and definitional equality.

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

Hausdorff Center for Mathematics

What is Homotopy Type Theory - HoTT

Explore Homotopy Type Theory (HoTT) with Steve Awodey, delving into its foundations, applications, and significance in modern mathematics and computer science.

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

Hausdorff Center for Mathematics

Automating Reasoning in Cubical Type Theory

Explore automated reasoning techniques in Cubical Type Theory, focusing on computational aspects and applications in formal verification and mathematics.

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

Hausdorff Center for Mathematics

HoTT in Lean4

Explore Homotopy Type Theory implementation in Lean4, focusing on advanced mathematical concepts and theorem proving techniques.

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

Hausdorff Center for Mathematics

Formalizing Cubical Interpretations of Homotopy Type Theory

Explore cubical interpretations of homotopy type theory with Evan Cavallo, delving into formalization techniques and advanced mathematical concepts.

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

Schmid College, Chapman University

Formalization of Infinity Category Theory

Explora la teoría de ∞-categorías, su formalización y aplicaciones en matemáticas, ciencias de la computación y física, incluyendo el Lema de Yoneda y el uso del asistente de pruebas Rzk.

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