Topos Institute Courses

Topological Quantum Gates in Homotopy Type Theory

Dive into advanced concepts of topological quantum gates and their relationship with homotopy type theory through expert analysis and theoretical frameworks.

• YouTube
• 1 hour 4 minutes
• On-Demand
• Free Video

Emergent Selves and Unconventional Intelligences in Biological Systems

Explore groundbreaking research on cellular intelligence, problem-solving behaviors across biological scales, and their applications in regenerative medicine, birth defects, and cancer treatment.

• YouTube
• 1 hour 27 minutes
• On-Demand
• Free Video

Generalized Algebraic Theory and Dependent Type Theory Semantics

Explore the relationship between Generalized Algebraic Theories and dependent type theory semantics, focusing on Cartmell's work and its modern applications in categories with families.

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

Lean 4 - Empowering the Formal Mathematics Revolution and Beyond

Discover how Lean 4 proof assistant revolutionizes formal mathematics, enabling mathematicians to formalize complex theories while serving as a functional programming language for seamless mathematical-computational integration.

• YouTube
• 1 hour 18 minutes
• On-Demand
• Free Video

Abstraction Engineering with the Prototype Verification System (PVS) - Introduction to Interactive Theorem Proving

Explore the Prototype Verification System (PVS) for mathematical abstraction and theorem proving, covering its expressive logic, automated reasoning tools, and practical applications in formal verification.

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

Effective Quantum Certification via Linear Homotopy Types

Delve into quantum computing certification through Linear Homotopy Type theory, exploring classical control, topological error protection, and practical implementation of quantum algorithms.

• YouTube
• 1 hour 8 minutes
• On-Demand
• Free Video

Unit Systems and Physical Quantities: A Category Theory Approach to Software Architecture

Explore the complex challenges of implementing unit systems and physical quantities in software, examining edge cases through category theory and their implications for programming languages.

• YouTube
• 1 hour 3 minutes
• On-Demand
• Free Video

Approximate Vector Bundles

Explore topological data analysis through approximate vector bundles, examining innovative mathematical approaches for analyzing complex datasets and geometric structures.

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

Linear Logic as a Language for Structured Data

Explore how linear logic provides a powerful framework for expressing complex data structures like HTML, HTTP, and databases through graph-based interpretations and practical applications.

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

Compositional System Dynamics Modeling for Public Health Applications

Delve into advanced System Dynamics modeling for public health, exploring compositional frameworks, diagram types, and innovative tools like StockFlow.jl and ModelCollab for enhanced interdisciplinary collaboration.

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

Applying Categorical Thinking to Practical Domains - From Probabilistic Modeling to Robotics

Explore categorical thinking applications across probabilistic modeling, clustering, and robotics, focusing on hybrid systems and sequential composition in legged robot controllers.

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

Categorical Causality and Systems Theory - From Structural Models to Dynamical Systems

Delve into categorical systems theory and causality, exploring their relationship, limitations in AI modeling, and implications for understanding complex system behaviors.

• YouTube
• 1 hour 6 minutes
• On-Demand
• Free Video

Abstraction in Programming Language Theory - Howe's Method

Delve into advanced programming language theory, exploring Howe's method for proving applicative bisimilarity and its abstract congruence theorem through category theory applications.

• YouTube
• 1 hour 3 minutes
• On-Demand
• Free Video

Algebraic Theories and Computer Algebra

Explore how category theory illuminates mathematical structures like monoids and groups, and discover its practical applications in computer algebra implementation and algebraic theories.

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

Scientific and Software Engineering Applications of Category Theory

Explore how category theory enhances scientific programming by providing robust abstractions for data modeling, simulations, and workflows, leading to more maintainable and scalable solutions.

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