Hausdorff Center for Mathematics Courses

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

Arithmetic Predicates and Decidability of Logical Theories

Explore recent breakthroughs in arithmetic predicates and logical theory decidability, covering undecidable theories with Ramanujan tau functions and decidable fragments.

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

Analytic, Difference, and Differential Structures

Explore advanced model theory of valued fields, covering AKE principles from classical henselian fields to tame extensions with difference and differential structures.

• YouTube
• 1 hour 5 minutes
• Self-Paced
• Free Video

The Grunwald Problem for Solvable Groups

Explore the Grunwald problem for solvable groups, examining closure of H^1(K,G) images and proving the Brauer-Manin obstruction is the only barrier using new fibration techniques.

• YouTube
• 1 hour 5 minutes
• Self-Paced
• Free Video

Updates on the Exponential-Algebraic Closedness

Explore Zilber's exponential-algebraic closedness conjecture and its implications for complex exponentiation, including recent results on the j-function and non-trivial zeroes.

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

Nonstandard Methods in Almost Mathematics

Discover nonstandard approaches to almost mathematics using ultraproducts, transforming "almost" properties into genuine ones with applications in p-adic geometry.

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

On Certain Definable Coarsenings of Valuation Rings and Their Applications

Explore definable coarsenings of valuation rings in Artin-Schreier and Kummer extensions, focusing on independent defect cases and applications to Kähler differentials.

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

Rank Stability in Quadratic Extensions and Hilbert's 10th Problem

Explore recent proof showing rank stability in quadratic extensions of number fields, connecting abelian varieties to Hilbert's 10th problem with negative solutions.

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

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

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

Fields with the Absolute Galois Group of ℚ

Explore how fields with absolute Galois groups isomorphic to ℚ share arithmetic properties, impacting Birational Section Conjecture and Hilbert's Tenth Problem approaches.

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