Hausdorff Center for Mathematics Courses

Computability and Definability - Theory and Application - Lecture 3

Explore advanced mathematical definability theory, covering computability, Turing jumps, arithmetic hierarchies, and applications to normality and Hausdorff dimension.

• YouTube
• 1 hour 8 minutes
• Self-Paced
• Free Video

Computability and Definability - Theory and Application - 2

Explore mathematical definability theory, covering computability, Turing jumps, arithmetic hierarchies, and applications to topological complexity and real number analysis.

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

Computability and Definability - Theory and Application - 1

Explore mathematical definability theory, covering computability, Turing jumps, arithmetic hierarchies, and applications to topological complexity and real number analysis.

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

The Classical Ax-Kochen/Ershov Principles

Explore the foundational Ax-Kochen/Ershov principles for henselian valued fields, covering embedding lemmas, existential theories, and extensions to tame fields.

• YouTube
• 1 hour 7 minutes
• Self-Paced
• Free Video

Model Theory and Definability - Session 2

Explore model-theoretic methods in number theory, focusing on compactness, quantifier elimination, and definability of henselian valuations with practical applications.

• YouTube
• 1 hour 3 minutes
• Self-Paced
• Free Video

Model Theory and Definability - Session 1

Discover model-theoretic methods and their applications in number theory, covering first-order logic, compactness, quantifier elimination, and definability of henselian valuations.

• YouTube
• 1 hour 1 minute
• Self-Paced
• Free Video

Homogeneity and Categoricity of Linear Orderings

Explore sp-homogeneous linear orderings and their categorical properties, including Δ_4 and Δ_3 categoricity conditions with optimal classification results.

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

Definability of the Dimension of R-Analytic Groups

Explore the definability of dimension in R-analytic groups, extending beyond p-adic cases to general pro-p domains with recent mathematical breakthroughs and ongoing research insights.

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

The Power of Beth's Definability Theorem

Explore Beth's definability theorem and its applications to henselian valued fields and ordered abelian groups, revealing automatic definability characterizations.

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

Model Theory of Generic Vector Space Endomorphisms

Explore model-complete theories defining vector spaces and characterize existentially closed models with endomorphism expansions, including criteria for model companions.

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

Tame Topology in NTP2 Structures

Explore the connection between NTP2 theory and topological tameness, focusing on expansions of ordered real and p-adic fields that define finite Boolean combinations.

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

Bi-Colored Structures - Tameness and Definability

Explore bi-colored structures in model theory, examining how expanded structures inherit tameness properties like NIP and simplicity, plus definability of valuations in bi-colored fields.

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

Introduction to Anabelian Geometry

Discover anabelian geometry through étale fundamental groups, exploring key theorems and conjectures via analogies with surface bundles and mapping class groups.

• YouTube
• 1 hour 4 minutes
• Self-Paced
• Free Video

Anisotropic Quadratic Forms Over Global Fields Are Diophantine

Discover how anisotropic quadratic forms over global fields can be classified as Diophantine using class field theory and uniform descriptions across field completions.

• YouTube
• 1 hour 13 minutes
• Self-Paced
• Free Video

A Strong Version of Cobham's Theorem

Explore advanced mathematical logic through Cobham's theorem and its strengthening, examining k-recognizable sets and their computational complexity in Presburger arithmetic.

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