Hausdorff Center for Mathematics Courses

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
• On-Demand
• 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
• On-Demand
• 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
• On-Demand
• 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
• On-Demand
• 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
• On-Demand
• 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
• On-Demand
• 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
• On-Demand
• 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
• On-Demand
• 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
• On-Demand
• Free Video

Ulrich Kohlenbach: Extraction of Information from Proofs

Explore proof mining techniques and their applications in mathematics, focusing on extracting computational content from nonconstructive proofs in analysis and ergodic theory.

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

Ulrich Kohlenbach - Extraction of Information from Proofs

Explore proof theory and its applications in mathematics, focusing on extracting computational content from nonconstructive proofs for practical problem-solving.

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

Thierry Coquand- Constructive Algebra

Explore constructive algebra with Thierry Coquand, delving into foundational concepts and innovative approaches within the Types, Sets and Constructions program.

• YouTube
• 1 hour 2 minutes
• On-Demand
• Free Video

Modular Forms, Elliptic Polylogarithms and Feynman Integrals

Explores advanced mathematical concepts in Feynman integrals, focusing on epsilon-form solutions, modular forms, and elliptic polylogarithms, with applications in number theory and physics.

• YouTube
• 1 hour 17 minutes
• On-Demand
• Free Video

Christian Bogner: The Analytic Continuation of the Kite and the Sunrise Integral

Explores advanced Feynman integrals using elliptic generalizations of polylogarithms, discussing properties through periods of elliptic curves and the Picard-Lefschetz theorem.

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

Johannes Brödel- From Elliptic Multiple Zeta Values to Modular Graph Functions

Explore the connection between elliptic multiple zeta values and modular graph functions in this advanced mathematics lecture by Johannes Brödel.

• YouTube
• 1 hour 14 minutes
• On-Demand
• Free Video