Higher Category Theory Courses and Certifications

Schmid College, Chapman University

Foundational Aspects of Size and Dimension in Higher Categorical Structures

Explore foundational aspects of size and dimension in higher categorical structures, examining universes, smallness notions, and truncation hierarchies in HoTT.

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

BIMSA

Higher Hilbert Spaces and Their Operator Algebras

Explore higher category theory through 3-Hilbert spaces that categorify 2-Hilbert spaces, featuring unitary constructions and operator algebra condensation techniques.

• YouTube
• 1 hour 24 minutes
• On-Demand
• Free Video

Topos Institute

Higher Category Theory in Cat-Sharp

Delve into advanced categorical theory through polynomial comonads, exploring applications in database theory, effects handlers, and dynamical systems with focus on Cat^# structures.

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

Topos Institute

Simplicial Delta Versus Fat Delta in Higher Category Theory

Delve into advanced category theory concepts, exploring the relationship between simplicial delta and fat delta, weak 2-categories, and their structural implications for higher-dimensional mathematics.

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

BIMSA

Instanton and Chern-Simons in Lattice Yang-Mills Theory from Higher Category Theory

Delve into higher category theory's application to lattice Yang-Mills theory, exploring innovative approaches to define instantons and Chern-Simons terms through multiplicative bundle gerbes.

• YouTube
• 2 hours 4 minutes
• On-Demand
• Free Video

Kavli Institute for Theoretical Physics

Instanton Density Operator in Lattice QCD from Higher Category Theory

Explore the application of higher category theory to instanton density operators in lattice QCD, examining connections between lattice gauge theory and continuum approaches to quantum field theory.

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

BunG Seminar

Higher Category Theory: DG Categories and Homological Algebra Applications - Talk 13

Dive into higher category theory fundamentals, exploring DG categories and their applications in homological algebra through expert insights and practical examples.

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

Schmid College, Chapman University

Universes and Higher Algebra in Synthetic ∞-Category Theory

Explore advanced mathematical structures where function composition is defined up to homotopy, covering ∞-groupoids, synthetic ∞-categories, and applications to higher algebra.

• YouTube
• 1 hour 47 minutes
• On-Demand
• Free Video

Hausdorff Center for Mathematics

Thomas Nikolaus- K-Theory of Z-P^n and Relative Prismatic Cohomology

Explore K-theory computation for Z/p^n rings using prisms and prismatic cohomology. Learn about generalized prisms and their universal property in this advanced mathematical discussion.

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

Isaac Newton Institute for Mathematical Sciences

Higher Algebra and Arithmetic - Rothschild Lecture

Explore higher algebra's impact on arithmetic, examining how counting processes influence number theory and cohomology, with applications in geometry and zeta functions.

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

PCS Institute for Basic Science

Finding the Missed Topological Operators in Lattice Models

Explore the profound connection between higher category theory and lattice models, uncovering solutions to long-standing topological operator challenges in quantum field theory.

• YouTube
• 1 hour 25 minutes
• On-Demand
• Free Video

Prague Mathematical Physics Seminar

Higher Differential Cohomology and Atiyah Connections - Part 2

Explore connections for principal bundles in higher categories, their relation to higher parallel transport, and generalised Atiyah sequence splittings.

• YouTube
• 1 hour 30 minutes
• On-Demand
• Free Video

Centre International de Rencontres Mathématiques

Exact ∞-Categories

Explore exact ∞-categories with Gustavo Jasso in this advanced mathematical lecture, delving into current trends in representation theory and cluster algebras.

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

NCCR SwissMAP

Applied Cobordism Hypothesis in Quantum Field Theory

Explore categorical symmetries in quantum field theory through applied cobordism hypothesis, enhancing understanding of advanced mathematical concepts.

• YouTube
• 3 hours 20 minutes
• On-Demand
• Free Video

Topos Institute

Cartesian Polynomial Monads in Homotopy Type Theory

Explore how polynomial monads in homotopy type theory solve infinite coherence challenges in higher category theory, focusing on Finster, Allioux, and Sozeau's innovative approach.

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