Homotopy Theory Courses and Certifications

International Mathematical Union

Motivic Cohomology - Past, Present and Future

Explore motivic cohomology's evolution, recent developments, and future prospects in algebraic geometry, including cycles with modulus and Chow-Witt theory.

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

International Centre for Theoretical Sciences

Topological Strings, Knots, and Quivers - Lecture 1

Explore topological strings, knots, and quivers in this lecture covering knot invariants, Chern-Simons theory, A-polynomials, volume conjectures, and knot homology, with exercises and examples.

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

International Mathematical Union

Georges Gonthier - Computer Proofs - Teaching Computers Mathematics, and Conversely

Explore computer-assisted mathematical proofs, from the four-color puzzle to homotopy type theory. Learn how computer science methods enhance mathematical language, leading to new insights and advancements in formal proofs.

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

Hausdorff Center for Mathematics

Introduction to Fukaya Categories - James Pascaleff

Explore symplectic geometry fundamentals for Fukaya categories, covering symplectic manifolds, Lagrangian submanifolds, exactness conditions, and more in this comprehensive lecture.

• YouTube
• 1 hour 17 minutes
• Self-Paced
• Free Video

ICTP Mathematics

Topology - Lecture 13

Explore advanced concepts in topology, including complex geometric structures and their properties, in this comprehensive lecture by mathematician Bruno Zimmerman.

• YouTube
• 1 hour 33 minutes
• Self-Paced
• Free Video

ICTP Mathematics

Topology - Lecture 20

Explore advanced concepts in topology, including complex mathematical structures and their properties, in this comprehensive lecture by Bruno Zimmerman.

• YouTube
• 1 hour 38 minutes
• Self-Paced
• Free Video

ICTP Mathematics

Topology - Lecture 10

Explore advanced concepts in topology, including complex geometric structures and their properties, in this comprehensive lecture by mathematician Bruno Zimmerman.

• YouTube
• 1 hour 29 minutes
• Self-Paced
• Free Video

ICTP Mathematics

Topology - Lecture 4

Explore fundamental concepts of topology, including continuous functions, homeomorphisms, and topological properties, in this advanced mathematics lecture.

• YouTube
• 1 hour 40 minutes
• Self-Paced
• Free Video

ICTP Mathematics

Topology - Lecture 6

Explore fundamental concepts and advanced techniques in topological spaces, including continuity, compactness, and connectedness, with expert guidance from Bruno Zimmerman.

• YouTube
• 1 hour 37 minutes
• Self-Paced
• Free Video

ICTP Mathematics

Topology - Lecture 12

Explore advanced concepts in topology, including complex geometric structures and their properties, in this comprehensive lecture by mathematician Bruno Zimmerman.

• YouTube
• 1 hour 40 minutes
• Self-Paced
• Free Video

ICTP Mathematics

Topology - Lecture 16

Explore advanced concepts in topology, including complex geometric structures and their properties, in this comprehensive lecture by mathematician Bruno Zimmerman.

• YouTube
• 1 hour 35 minutes
• Self-Paced
• Free Video

ICTP Mathematics

Topology - Lecture 14

Explore advanced concepts in topology with Bruno Zimmerman, delving into complex mathematical structures and their properties in this comprehensive lecture.

• YouTube
• 1 hour 34 minutes
• Self-Paced
• Free Video

ICTP Mathematics

Topology - Lecture 8

Explore fundamental concepts and advanced techniques in topological spaces, manifolds, and algebraic topology with expert guidance from Bruno Zimmerman.

• YouTube
• 1 hour 36 minutes
• Self-Paced
• Free Video

Fields Institute

Bordism of Manifolds - Lecture 1

Explore the concept of bordism in manifolds with Stanford's Mohammed Abouzaid, delving into advanced mathematical theories and their applications in topology and geometry.

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

Institut des Hautes Etudes Scientifiques (IHES)

Prismatic Cohomology of Commutative Ring Spectra

Explore motivic filtrations on trace invariants of commutative ring spectra and their extension to prismatic cohomology, as presented by Arpon Raksit from MIT.

• YouTube
• 1 hour 9 minutes
• Self-Paced
• Free Video