IAS | PCMI Park City Mathematics Institute Courses

Mathematics and Physics in Creative Crafts - From Curvature to Knot Theory

Explore the fascinating intersection of mathematics and crafting, discovering how physics, geometry, and knot theory connect with crochet, quilting, and textile manufacturing patterns.

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

Mathematical Maturity - Story vs Craft - Why I Like to Lecture

Explore the philosophical debate between storytelling and craftsmanship in mathematics education through an engaging lecture that challenges traditional teaching perspectives.

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

Arithmetic Properties of Local Systems in Motivic Homotopy Theory

Delve into fundamental group theory and local systems in arithmetic geometry, exploring classical conjectures and recent developments in motivic representations and their arithmetic properties.

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

Motivic Explorations in Enumerative Geometry - Part 4

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

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

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
• On-Demand
• 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
• On-Demand
• 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
• On-Demand
• 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
• On-Demand
• 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
• On-Demand
• 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
• On-Demand
• 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
• On-Demand
• 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
• On-Demand
• 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
• On-Demand
• 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
• On-Demand
• 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
• On-Demand
• Free Video