Type Theory Courses and Certifications

Hausdorff Center for Mathematics

Erik Palmgren: From Type Theory to Setoids and Back

Exploring setoids in constructive mathematics, their implementation in proof assistants, and their role in formalizing Bishop-style mathematics and Martin-Löf type theory models.

• YouTube
• 1 hour 6 minutes
• On-Demand
• Free Video

Hausdorff Center for Mathematics

The Extended Predicative Mahlo Universe and the Need for Partial Proofs

Explores the extended predicative Mahlo Universe in type theory, discussing the need for partial functions and proofs to achieve a more predicative justification of the Mahlo Universe.

• YouTube
• 41 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

Peter Dybjer - Intuitionistic Type Theory

Explore intuitionistic type theory, inductive definitions, and finite axiomatizations in this advanced lecture on mathematical foundations and type systems.

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

Institute for Advanced Study

Univalence from a Computer Science Point-of-View - Dan Licata

Explore univalence in computer science with Dan Licata, covering Martin-Löf type theory, computation, and applications in homotopy theory and group structures.

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

Institute for Advanced Study

Univalent Foundations and the Equivalence Principle - Benedikt Ahrens

Explore univalent foundations and the equivalence principle in mathematics, covering type theory, dependent types, and their applications to structures like monoids and categories.

• YouTube
• 1 hour 1 minute
• On-Demand
• Free Video

Hausdorff Center for Mathematics

Formalization of Nominal Equational Reasoning in PVS - Nominal Unification

Explore nominal equational reasoning and unification in PVS, focusing on formalizing techniques for handling bound variables in logical systems and programming languages.

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

Hausdorff Center for Mathematics

Lean4Lean - Formalizing the Type Theory of Lean

Explore the formalization of Lean's type theory with Mario Carneiro, delving into advanced concepts and techniques for theorem proving and mathematical reasoning.

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

Hausdorff Center for Mathematics

Structural Rules and Algebraic Properties of Intersection Types

Explore structural rules and algebraic properties of intersection types in lambda calculus, examining their impact on type assignment systems and programming language theory.

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

Hausdorff Center for Mathematics

A Type-Theoretic Framework for Certified Meta-programming

Explore a type-theoretic framework for certified meta-programming, delving into advanced concepts and techniques in programming language theory and formal verification.

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

Hausdorff Center for Mathematics

Inductive Definitions, Predicativity, and the Mahlo Universe

Explore inductive definitions, predicativity, and the Mahlo universe in type theory with Peter Dybjer. Gain insights into advanced mathematical concepts and their applications.

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

Code Sync

Gradualizing Languages with Set-Theoretic Types in Elixir

Explore practical implementations of gradual set-theoretic types in Elixir, focusing on disjoint unions, singleton types, and elegant solutions for type representation and checking.

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

Hausdorff Center for Mathematics

Condensed Type Theory - Axioms and Applications

Explore condensed sets' topos and internal type theory, examining axioms, predicates, and their interactions. Learn about compact Hausdorff and overt discrete types, with applications in category theory.

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

GOTO Conferences

What Are Types For, Or Are They Only Against? - Exploring Type Systems in Programming

Explore the purpose and benefits of types in programming, examining their role beyond just preventing errors, with insights into functional programming concepts and type theory.

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

Centre International de Rencontres Mathématiques

New Modal Operators for Constructive Mathematics

Explore new modal operators in constructive mathematics, focusing on preorders, wellfounded relations, and positive extensions. Gain insights into reformulating concepts and applying novel approaches.

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