IAS | PCMI Park City Mathematics Institute Courses

Characteristic Classes in Stable Motivic Homotopy Theory - Part 2

Delve into advanced concepts of characteristic classes in stable motivic homotopy theory, exploring Quillen's work extensions and modern developments in quadratic enumerative geometry.

• YouTube
• 1 hour 4 minutes
• Self-Paced
• Free Video

Contractibility and Spheres: A Motivic View in Homotopy Theory

Explore algebraic geometry through the lens of spheres and contractibility in topology, using motivic homotopy theory to bridge classical and modern mathematical concepts.

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

Field Arithmetic and the Complexity of Galois Cohomology - Part 1

Delve into fundamental concepts of Galois cohomology, exploring its role in field arithmetic, algebraic structures, and geometric obstructions through expert analysis of definitions, interpretations, and open problems.

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

Characteristic Classes in Stable Motivic Homotopy Theory - Part 1

Delve into the foundations of characteristic classes in stable motivic homotopy theory, exploring Quillen's work extensions and modern developments in algebraic geometry and schemes.

• YouTube
• 1 hour 4 minutes
• Self-Paced
• Free Video

A¹-Homotopy and A¹-Algebraic Topology - Part 2

Delve into advanced concepts of A^1-homotopy theory and algebraic topology with expert Fabien Morel, exploring motivic homotopy theory's applications in algebra and algebraic geometry.

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

Representation Categories and Motives - Part 1

Delve into advanced mathematical concepts of representation categories and mixed motives, exploring Tannakian categories and derived representation theories of various algebraic groups.

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

Motivic Adams Conjecture in Algebraic Geometry

Delve into the algebraic-geometric interpretation of Adams conjecture, exploring vector bundles on smooth algebraic varieties and their implications for stable homotopy groups of spheres.

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

A^1-Algebraic Topology and Unstable Motivic Homotopy Theory - Part 4

Delve into unstable motivic homotopy theory, exploring Morel-Voevodsky spaces, homotopy sheaves, and fundamental theorems through expert guidance in advanced algebraic topology and geometry.

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

A1-Homotopy Theory and the Weil Conjectures - Part 4

Delve into advanced A1-homotopy theory concepts, exploring cellular homology and Weil conjectures through expert lectures, problem sets, and comprehensive mathematical analysis at the graduate level.

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

Torsors Over Affine Curves - Part 4

Delve into advanced algebraic geometry concepts focusing on G-torsors and G-bundles, exploring their behavior over affine smooth curves and Dedekind rings, with applications to étale cohomology and patching techniques.

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

A^1-Algebraic Topology and Unstable Motivic Homotopy Theory - Part 3

Delve into unstable motivic homotopy theory, exploring Morel-Voevodsky spaces, homotopy sheaves, and fundamental theorems. Perfect for those with algebraic geometry and topology foundations.

• YouTube
• 1 hour 6 minutes
• Self-Paced
• Free Video

A1-Homotopy Theory and the Weil Conjectures - Part 3

Delve into A1-homotopy theory, exploring cellular homology and Weil conjectures through advanced mathematical concepts. Learn from expert insights on derived categories and discover new developments in algebraic topology.

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

Torsors Over Affine Curves - Part 3

Delve into advanced algebraic geometry concepts focusing on G-torsors and G-bundles, exploring their behavior over affine curves, Dedekind rings, and affine surfaces with emphasis on étale cohomology.

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

A^1-Algebraic Topology and Unstable Motivic Homotopy Theory - Part 2

Delve into unstable motivic homotopy theory, exploring Morel-Voevodsky spaces, homotopy sheaves, and fundamental theorems through expert guidance in advanced algebraic topology and geometry.

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

A1-Homotopy Theory and the Weil Conjectures - Part 2

Delve into advanced A1-homotopy theory, exploring cellular homology construction and Weil conjectures analogues through expert-led lectures on derived categories and modern algebraic topology concepts.

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