Hausdorff Center for Mathematics Courses

Douglas Bridges - Ishihara’s Contributions to Constructive Analysis

Explore Ishihara's key contributions to constructive analysis, including tricks, principles, and theorems, with insights on their impact and applications in mathematical reasoning.

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

Every Metric Space Is Separable in Function Realizability

Explore function realizability topos, separable metric spaces, and countable objects with decidable equality. Delve into synthetic topology and its implications for intuitionistic logic.

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

Constructive Mathematics in Univalent Type Theory

Explore constructive mathematics within univalent type theory, delving into advanced concepts and their applications in modern mathematical foundations.

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

Derived Rules in Set Theory

Explore intuitionistic set theories and learn about a general machinery for demonstrating derived rules in this advanced mathematical lecture.

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

Triposes and Gödel's Dialectica Interpretation

Exploring semantic presentation of Gödel's Dialectica interpretation using triposes, addressing previous work and suggesting solutions to related questions in mathematical logic.

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

Two Observations on Intuitionistic Logic and Arithmetic

Explore intuitionistic logic and arithmetic through finite type formalisation and negative translations. Gain insights into extensional and intensional models, decidable atomic formulas, and equality at higher types.

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

Refinement Type Systems and Martin Lof Type Theory

Explores refinement type systems, their connection to Martin-Lof type theory, and various notions of comprehension. Discusses recent work on functors as type refinement systems and Isbell duality theorem.

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

An Introduction to Tensorial Logic and Dialogue Categories

An introduction to tensorial logic, exploring its relationship with dialogue games and categories. Refines linear logic and provides insights into dialogical interpretations of proofs and programs.

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

On B-adic Representation of Irrational Numbers

Explore b-adic representation of irrational numbers with Lars Kristiansen, delving into advanced mathematical concepts and their applications in number theory and analysis.

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

Erik Palmgren: A Constructive Examination of a Russell Style Ramified Type Theory

Exploration of ramified type theory in Martin-Löf type theory, examining functional reducibility and its applications in constructive mathematical analysis. Introduces an intuitionistic ramified type theory.

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

Proof Theory for Quantified Monotone Modal Logics

Explores proof-theoretic aspects of quantified non-normal modal logics, introducing labelled sequent calculi and examining their properties, completeness, and applications to neighborhood frames.

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

Cyclic Modal Proofs

Exploring cyclic proof theory for modal fixed point logic, its applications in deriving completeness results, and its advantages over traditional finite tree proofs in applied logic.

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

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

First Order Concatenation Theory vs First Order Number Theory

Comparative analysis of first-order concatenation theory and number theory, exploring similarities, differences, and extensions with bounded quantifiers in string-based structures.

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

Matthias Baaz - Fast Cut Elimination in Intuitionistic Logic

Explores elementary procedure for eliminating prenex cuts in intuitionistic logic, with implications for classical logic. Discusses surprising results in quantifier-based cut elimination.

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