Hausdorff Center for Mathematics Courses

Applications of O-Minimality to Computational Problems in Dynamical Systems Theory

Explore o-minimality applications to solve computational problems in dynamical systems, including the Skolem Problem and orbit verification for linear recurrence sequences.

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

Existentially Definable Henselian Valuations

Explore existential definability of henselian valuation rings within their fields of fractions, focusing on classification by residue field properties and key mathematical examples.

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

Generic Functions and Quasiminimality

Explore Zilber's theory of generic functions on fields, examining first-order axiomatization through Schanuel property and existential closedness, plus quasiminimality properties.

• YouTube
• 1 hour 7 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

Positive Residue Characteristic - Finite Ramification and Kaplansky's Hypothesis

Explore advanced model theory of henselian valued fields, focusing on AKE principles, finite ramification, and extensions to difference/differential field expansions.

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

Towards the Taming Theorem of Jahnke and Kartas Which Applies the AKE-Theory

Explore advanced model theory through AKE principles for henselian valued fields, from classical equal characteristic cases to tame fields and the groundbreaking Taming Theorem.

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

Tame Fields and Existential Theories in Equal Characteristic

Explore advanced model theory of henselian valued fields, covering AKE principles, embedding lemmas, and existential theories in equal characteristic zero settings.

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

Computability Questions About Infinite Galois Groups

Explore computability theory applied to infinite Galois groups through tree representations, examining decidability properties and complexity differences between finite fields and ℚ.

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

Cellular Automata and Algebraic Groups

Explore how additive cellular automata with vector states connect to algebraic group dynamics, revealing complex temporal behaviors and generalizations of Gauss's prime polynomial theorem.

• YouTube
• 1 hour 1 minute
• 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

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

Enlarge Your Spine - Augmentable Linear Orders and Ordered Abelian Groups

Discover how four mathematicians classify augmentable linear orders and transfer augmentability from spines to groups, revealing surprising consequences for ordered abelian groups.

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

Elliptic Curves and Definability Over Big Rings

Explore rank stability results and their implications for definability over big subrings of number fields through elliptic curve theory.

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

Convergence Rates for Graph-Based Learning Featuring Singular PDEs

Explore convergence rates in graph-based learning through singular partial differential equations with mathematical rigor and advanced theoretical insights.

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