Topos Institute Courses

Amortized Analysis via Coalgebra

Explore coalgebraic perspectives on amortized analysis, examining how this mathematical framework enhances understanding of data structure operations and computational costs.

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

Classical and Constructive Logics Together: Ecumenical Systems

Explore Ecumenical Logic systems that combine classical and intuitionistic logic, examining their proof theoretical properties and potential for enhancing interoperability between proof assistants.

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

Neural Certificates for Model Checking

Explore how neural networks can represent correctness certificates for formal verification, combining machine learning with symbolic reasoning to ensure system safety and trustworthiness.

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

Language, Technology, and Care

Explore "care" as a missing dimension in tech discussions, using LLMs and AI alignment as case studies. Examine how abstraction and optimization reshape our relationship with reality and the challenge of pursuing progress within a context of care.

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

Does It Matter Whether There Are Infinite Sets?

Explore the philosophical and mathematical foundations of set theory, examining the axiom of infinity and its implications for modern mathematics, programming, and handling "big" objects.

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

Open Translations in Mathematics

Explore community-driven approaches to mathematical translation, addressing challenges and opportunities for non-English speakers while preserving linguistic diversity in academia.

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

Geometric Principles of Data Visualization

Explore geometric and topological principles behind data visualization algorithms like UMAP, including mathematical foundations from Riemannian geometry and category theory that lead to the improved IsUMap algorithm.

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

The Path-Complete Formalism for Switched Systems: Stability and Beyond

Explore the path-complete Lyapunov framework for analyzing switched systems, covering stability analysis, constrained switching, stabilization techniques, and safety through barrier functions.

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

V-graded Categories for Enrichment and Actions of Monoidal Categories

Explore V-graded categories as a unifying framework for enriched categories and V-actegories, understanding how they accommodate arbitrary monoidal categories through parameterized morphisms.

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

Distillation Systems as Models of Homotopy Colimits

Delve into the mathematical concept of distillation systems and their relationship to homotopy colimits in category theory, exploring how these structures govern properties needed for functor calculus.

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

ZX Calculus and Fault-Tolerant Quantum Computing

Explore ZX calculus applications in fault-tolerant quantum computing, covering error correction techniques and compositional approaches to quantum computation challenges.

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

2-Classifiers for 2-Algebras

Explore advanced category theory concepts through 2-classifiers for 2-algebras, examining discrete opfibration classifiers and their lifting properties in algebraic contexts.

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

Categories of Systems - DOTS Lectures 1

Explore the foundational concepts of system categories through David Jaz Myers' introduction to Double Operadic Theory of Systems (DOTS) mathematical framework.

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

Abstractions for Real People

Explore how mathematical abstractions in computing can better serve society through accessible, responsive approaches that address AI risks and societal needs.

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

Composing Moore Machines - DOTS Lectures 4

Explore advanced mathematical frameworks for composing Moore machines using double operadic theory in systems modeling and categorical approaches.

• YouTube
• 1 hour 14 minutes
• Self-Paced
• Free Video