Institute for Pure & Applied Mathematics (IPAM) Courses

Correlation Inequalities for Schur Functions and Young Tableaux

Explore correlation inequalities in mathematics, focusing on Schur functions and Young tableaux. Discover connections to probability, statistical physics, and algebraic combinatorics in this advanced lecture.

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

Sums of GUE Matrices and Concentration of Hives from Correlation Decay of Eigengaps

Explore the concentration of augmented hives in sums of random Hermitian matrices, using GUE ensemble eigenvalues and analyzing asymptotic behavior as eigenvalue count increases.

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

Global Asymptotics of Jack-Deformed Random Young Diagrams via Lukasiewicz Paths

Explores discrete analogues of log-gas systems, examining universal formulas for global asymptotics in various temperature regimes, using weighted lattice paths and revealing phase transition phenomena.

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

Jack Characters as Generating Series of Bipartite Maps and Proof of Lassalle's Conjecture

Explores Jack polynomials' connection to non-orientable map enumeration, presenting a formula for power-sum expansion and proving Lassalle's conjecture on Jack characters in Stanley's coordinates.

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

Random Partitions, Hurwitz Numbers and Counting High Genus Surfaces

Explore connections between random partitions, Hurwitz numbers, and high genus surfaces. Discover asymptotic behavior of Plancherel-Hurwitz measures and their implications for counting complex mathematical structures.

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

Toric Promotion with Reflections and Refractions

Exploration of toric promotion with reflections and refractions in combinatorial billiards, generalizing dynamics and revealing orbit structures in various graph configurations.

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

Unifying Lattices Through Hourglass Plabic Graphs

Explore connections between web bases, quantum groups, and lattice models. Discover new combinatorial frameworks linking alternating sign matrices, plane partitions, and the Tamari lattice.

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

Symmetric Functions: Foundations and Applications in Combinatorics - Part 1

Explore symmetric functions in algebraic combinatorics, representation theory, and statistical mechanics. Learn formulas, combinatorial models, and key properties with applications and open problems.

• YouTube
• 1 hour 18 minutes
• Self-Paced
• Free Video

Dimer Models and Random Tilings - Part 1

Explore dimer models and random tilings with Cédric Boutillier. Learn about Kasteleyn's theory, combinatorial correspondences, and asymptotic methods for studying perfect matchings on lattices.

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

Gaussian Free Field and Schramm-Loewner Evolution - Part 1

Explore the Gaussian free field and Schramm-Loewner Evolution, two key concepts in random geometry. Learn their applications in statistical physics and connections to critical phenomena.

• YouTube
• 1 hour 18 minutes
• Self-Paced
• Free Video

Introduction to Cluster Algebras - Part 2

Explore the Laurent phenomenon in cluster algebras, focusing on octahedron recurrences. Gain insights into geometric and algebraic aspects of this advanced mathematical topic.

• YouTube
• 1 hour 11 minutes
• Self-Paced
• Free Video

Gaussian Free Field and Schramm-Loewner Evolution - Part 2

Explore Gaussian free field and Schramm-Loewner Evolution in random geometry. Discover connections between these canonical objects and their applications in statistical physics and conformal field theory.

• YouTube
• 1 hour 19 minutes
• Self-Paced
• Free Video

Introduction to Cluster Algebras - Part 1

Explore cluster algebras, quivers, and mutation through examples, with a focus on the Grassmannian. Gain insights into this fundamental algebraic structure and its applications.

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

Embeddings and Statistical Mechanics in Dimer Graphs - Part 2

Explore geometric embeddings of dimer graphs and their algebra-combinatorial properties in this advanced tutorial on statistical mechanics and integrability.

• YouTube
• 1 hour 20 minutes
• Self-Paced
• Free Video

Embeddings and Statistical Mechanics in Planar Ising Models - Part 1

Explore connections between criticality, exact solvability, and geometric embeddings in planar Ising models through this advanced statistical mechanics lecture at UCLA's IPAM.

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