Descriptive Set Theory Courses and Certifications

Centre International de Rencontres Mathématiques

Two Complexity Results in Descriptive Set Theory - Hyperfinite and Hyper-Hyperfinite Equivalence Relations

Explore connections between hyperfinite equivalence relations and Borel amenability in descriptive set theory through two major complexity results.

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

Erwin Schrödinger International Institute for Mathematics and Physics (ESI)

Computations, Countable Ranks and Complexity of Borel Codes

Explore infinite time algorithms, decision times, and countable ordinal ranks in Borel hierarchy complexity theory with applications to projective sets and computational analysis.

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

Erwin Schrödinger International Institute for Mathematics and Physics (ESI)

Strong Representation of Pi03 Sets and Dichotomies

Explore advanced mathematical concepts in Borel hierarchy, Pi03 sets representation, and dichotomy theorems through effective topological methods and collaborative research insights.

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

Erwin Schrödinger International Institute for Mathematics and Physics (ESI)

Generic Muchnik Reducibility

Explore generic Muchnik reducibility extending classical reducibility to uncountable structures, mixing descriptive set theory with forcing constructions in computable model theory.

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

Erwin Schrödinger International Institute for Mathematics and Physics (ESI)

Classical Versions of Effective Borel Uniformizations

Explore classical reformulations of effective descriptive set theory for Borel uniformization problems without requiring recursion-theoretic background knowledge.

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

Erwin Schrödinger International Institute for Mathematics and Physics (ESI)

On the Luzin-Novikov Theorem

Explore the Luzin-Novikov theorem through advanced mathematical analysis in this specialized workshop presentation on reverse mathematics and computability theory.

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

Centre International de Rencontres Mathématiques

Manifold Classification from the Descriptive Viewpoint

Explore manifold classification problems using descriptive set theory, examining Borel complexity for fundamental manifold classes and discrete subgroups of Lie groups.

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

Hausdorff Center for Mathematics

Scott Filtrations and Vaught Ordinals

Explore Scott filtrations connecting Scott rank and back-and-forth relations in computable structure theory, examining complexity of isomorphism relations up to Vaught ordinals.

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

Centre International de Rencontres Mathématiques

Descriptive Graph Combinatorics and Advanced Topics in Combinatorial Mathematics

Explore advanced mathematical topics through expert lectures on graph theory, random structures, algebraic combinatorics, and their applications in modern mathematics.

• YouTube
• 1 week 2 days 20 hours 33 minutes
• On-Demand
• Free Video

Fields Institute

Lindelöf Σ-Spaces in 2022

Explore recent developments in Lindelöf Σ-spaces, including their properties, applications, and connections to other areas of set theory and topology.

• YouTube
• 1 hour 35 minutes
• On-Demand
• Free Video

Fields Institute

Tame Control Theory

Explore tame geometry in control theory, covering basic definitions, motivation, logic, and vector fields. Gain insights into descriptive set theory and generic structures.

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

Banach Center

Geometric Set Theory - Part 3

Explore advanced concepts in geometric set theory, delving into complex mathematical principles and their applications in topology and analysis.

• YouTube
• 1 hour 1 minute
• On-Demand
• Free Video

Banach Center

Geometric Set Theory - Part 2

Explore advanced concepts in geometric set theory, focusing on complex mathematical structures and their applications in topology and analysis.

• YouTube
• 1 hour 5 minutes
• On-Demand
• Free Video

Centre de recherches mathématiques - CRM

Extremely Amenable Automorphism Groups of Countable Structures

Explore extreme amenability in topological groups, focusing on automorphism groups of countable structures. Discover the abundance of non-isomorphic extremely amenable Polish groups.

• YouTube
• 1 hour 15 minutes
• On-Demand
• Free Video

Centre de recherches mathématiques - CRM

Classification Using Sets of Sets of Reals as Invariants

Explore Borel equivalence relations and Friedman-Stanley jumps in classification problems. Analyze complexity, optimal invariants, and structural dichotomies in mathematical classifications.

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