Topos Institute Courses

Everettian Quantum Mechanics and the Problem of Ontological Extravagance

Explore the philosophical challenges of Everettian quantum mechanics, focusing on the problem of ontological extravagance and examining alternative simplicity criteria to evaluate competing interpretations of quantum theory.

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

A Double Category Theorist's Perspective on Polynomials

Explore the universal property of polynomials in category theory, understanding their role beyond exponentiability constraints through Nathanael Arkor's journey and research with Bryce Clarke.

• YouTube
• 1 hour 6 minutes
• 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

Update Rules of Pearl and Jeffrey in Probabilistic Updating

Explore the differences between Pearl and Jeffrey's probabilistic updating rules, their applications in multiple data scenarios, and their role in machine learning algorithms like Expectation Maximization.

• YouTube
• 56 minutes
• 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

AI for Precision Oncology

Discover how artificial intelligence revolutionizes personalized cancer treatment through precision oncology approaches and cutting-edge computational methods.

• YouTube
• 1 hour 11 minutes
• Self-Paced
• Free Video

Developing Support for End-to-End Verification of Neural AI Agents

Explore Vehicle, a tool for writing, training, and formally verifying specifications for neural AI agents, with capabilities to export verified specifications to interactive theorem provers for environmental reasoning.

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

Combinatorial Foundation for Planar String Diagrams

Explore how diagrammatic sets provide a combinatorial foundation for 2D string diagrams, offering an alternative to Joyal and Street's topological approach with applications to (infty, n)-categories.

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

Advancing Human-Machine Interface Systems Through AI

Explore how AI can decode neural intent from non-invasive muscle signals to enhance human-machine interaction, with applications in prosthetics, rehabilitation, and assistive technologies.

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

Organization of the Information Flow in the Perception-Action Loop

Explore how Shannon information exchange in the perception-action loop reveals structural constraints and phenomena in agent-environment interactions.

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

Random Variables, Independence Structures and Dagger Categories of Relations

Explore the mathematical foundations of probability theory through sheaves over sample spaces, independence structures, and dagger categories of relations, examining how these concepts extend to nondeterminism and name generation.

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

Duality for Complete Atomic Partial Boolean Algebras

Explore the mathematical duality theory for complete atomic partial Boolean algebras, focusing on quantum propositions and exclusivity graphs as an alternative to classical Stone-type duality in quantum logic contexts.

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