IAS | PCMI Park City Mathematics Institute Courses

Field Arithmetic and the Complexity of Galois Cohomology - Part 4

Delve into advanced concepts of Galois cohomology, exploring field arithmetic, cohomological invariants, and their applications in algebraic geometry and arithmetic theory through expert-led mathematical discourse.

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

Field Arithmetic and the Complexity of Galois Cohomology - Part 3

Delve into advanced concepts of Galois cohomology, exploring field arithmetic, cohomological invariants, and their applications in algebraic geometry and arithmetic structures.

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

Characteristic Classes in Stable Motivic Homotopy Theory - Part 4

Delve into advanced concepts of characteristic classes in stable motivic homotopy theory, exploring Quillen's work extensions, Panin-Walter orientation theories, and applications in quadratic enumerative geometry.

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

Motivic Explorations in Enumerative Geometry - Part 3

Delve into advanced enumerative geometry concepts, exploring Bézout's theorem, cubic surface lines, and tropical geometry applications through motivic homotopy theory for solving complex mathematical problems.

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

Massey Products in Galois Cohomology - Part 1

Delve into advanced Galois cohomology concepts, focusing on Massey products, the Norm-Residue Theorem, and their applications in understanding absolute Galois groups of fields through expert mathematical analysis.

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

Massey Products in Galois Cohomology - Part 4

Delve into advanced Galois cohomology concepts, focusing on Massey products, the Norm-Residue Theorem, and recent developments in the Massey Vanishing Conjecture for absolute Galois groups of fields.

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

Characteristic Classes in Stable Motivic Homotopy Theory - Part 3

Delve into advanced concepts of characteristic classes in stable motivic homotopy theory, exploring Quillen's work extensions, Panin-Walter orientation theories, and applications to quadratic enumerative geometry.

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

Motivic Explorations in Enumerative Geometry - Part 2

Delve into advanced enumerative geometry concepts, exploring Bézout's theorem, cubic surface lines, and tropical geometry through motivic homotopy theory for solving problems over arbitrary fields.

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

Field Arithmetic and the Complexity of Galois Cohomology - Part 2

Delve into advanced concepts of Galois cohomology, exploring field arithmetic, cohomological invariants, and their applications in algebraic geometry and arithmetic structures.

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

Motivic Homotopy - Understanding Modern Approaches and Applications

Delve into the foundations and latest developments of Motivic Homotopy theory through an engaging exploration led by Harvard mathematician Michael Hopkins.

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

Motivic Explorations in Enumerative Geometry - Part 1

Explore motivic homotopy theory's application in enumerative geometry, focusing on Bézout's theorem and cubic surface line counting through A1 degree and tropical geometry concepts.

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

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