IAS | PCMI Park City Mathematics Institute Courses

Lectures on Random Matrices

Dive into random matrix theory through expert lectures covering Wigner ensembles, free probability, KPZ equations, and applications in physics and statistics from leading researchers.

• YouTube
• 1 day 15 hours 42 minutes
• Self-Paced
• Free Video

Research Problems on Random Matrices

Explore cutting-edge research problems in random matrix theory through expert presentations covering eigenvalue densities, dynamical methods, and applications to physics and statistics.

• YouTube
• 12 hours 34 minutes
• Self-Paced
• Free Video

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
• 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

Massey Products in Galois Cohomology - Part 3

Delve into advanced Galois cohomology theory, focusing on Massey products, the Norm-Residue Theorem, and recent developments in the Massey Vanishing Conjecture for mod 2 fourfold products over arbitrary fields.

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

Massey Products in Galois Cohomology - Lecture 2

Delve into advanced Galois cohomology theory, exploring Massey products, the Norm-Residue Theorem, and recent developments in the Massey Vanishing Conjecture through expert-led mathematical discussions.

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

Motivic Homotopy Theory

Explore advanced mathematical concepts connecting algebraic geometry, topology, and arithmetic through motivic homotopy theory with leading experts in this specialized field.

• YouTube
• 1 day 23 hours 16 minutes
• Self-Paced
• Free Video

Quantum Computation - The 2023 IAS-PCMI Graduate Summer School

Dive into advanced quantum computing mathematics through expert-led minicourses covering quantum learning, error correction, complexity theory, and near-term quantum device analysis.

• YouTube
• 1 day 19 hours 46 minutes
• Self-Paced
• Free Video

An Introduction to Lattices, Lattice Reduction, and Lattice-Based Cryptography

Explore lattice theory and quantum-resistant cryptography through comprehensive lectures covering lattice problems, reduction algorithms, and practical cryptosystem construction.

• YouTube
• 4 hours 46 minutes
• Self-Paced
• Free Video

Quadratic Forms, Milnor K-Theory, and Arithmetic - 2021

Explore quadratic forms theory, Milnor K-theory, and arithmetic through the Hasse-Minkowski theorem, quadratic reciprocity law, and Siegel mass formula with experimental mathematics.

• YouTube
• 17 hours 6 minutes
• Self-Paced
• Free Video

Advanced Topics in Mathematical Gauge Theory - Higgs Bundles

Delve into advanced mathematical gauge theory and Higgs bundles through expert lectures covering sophisticated theoretical frameworks and their geometric applications.

• YouTube
• 4 hours 11 minutes
• Self-Paced
• Free Video

Wigner Random Matrices and the Semicircle Law

Explore Wigner's semicircle law through eigenvalues, graph theory, and Catalan numbers in random matrix theory with proofs and spectral analysis techniques.

• YouTube
• 3 hours 54 minutes
• Self-Paced
• Free Video

Extremal Graph Theory - Part 4

Explore extremal graph theory focusing on bipartite graphs and the maximum edges in H-free graphs with n vertices, covering recent progress in this challenging area.

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

How to Get from A to B - Configuration Transformation Problems in Mathematics

Explore transformation problems in mathematics, from the 14-15 puzzle to motion planning, examining how to move between configurations through specific moves and discussing open challenges.

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