Hausdorff Center for Mathematics Courses

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
• Self-Paced
• 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
• Self-Paced
• 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
• Self-Paced
• 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
• Self-Paced
• 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
• Self-Paced
• 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
• Self-Paced
• Free Video

Anton Freund- Bachmann Howard Fixed Points

Explores dilators, Bachmann-Howard fixed points, and their construction. Presents the equivalence between well-founded fixed points and ∏11-comprehension in mathematical logic.

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

The Absorption Law for Slow Provability

Explore the absorption law for slow provability, its simple proof, and application to Heyting Arithmetic's provability logic in this mathematical lecture by Albert Visser.

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

Reverse Mathematics of Caristi's Fixed Point Theorem and Ekeland's Variational Principle

Explore the mathematical strengths of Caristi's fixed point theorem and Ekeland's variational principle, examining their implications in complete separable metric spaces and their connections to various axiom systems.

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

An Overview Over Least Fixed Points in Weak Set Theories

Explore least fixed points in weak set theories, comparing standard constructions and their implications in Kripke Platek Set Theory extensions without the powerset axiom.

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

Hugo Herbelin- Investigations into Cubical Type Theory

Exploration of a variant of cubical type theory with type-based equality, direct coercion, and primitive composition, aiming for a parametricity translation to identity type theory.

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

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
• Self-Paced
• Free Video

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
• Self-Paced
• Free Video

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
• Self-Paced
• Free Video

Michael Rathjen - Opening and Introduction

Explore the foundations of mathematics in this lecture on types, sets, and constructions, delving into fundamental concepts that shape our understanding of mathematical structures.

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