Institute for Pure & Applied Mathematics (IPAM) Courses

Inhomogeneous Multispecies t-PushTASEP and Macdonald Polynomials

Explore connections between inhomogeneous multispecies t-PushTASEP's stationary distribution and Macdonald polynomials at q=1 in this advanced mathematics lecture by Harvard's Lauren Williams.

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

The Inhomogeneous Multispecies PushTASEP

Explore multispecies PushTASEP variants, stationary distributions, and symmetry properties. Discover explicit formulas for correlations using Schur functions in this advanced mathematical presentation.

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

Compact Formula for Symmetric Macdonald Polynomials via ASEP and TAZRP

Explore connections between particle models and Macdonald polynomials, unveiling a new compact tableau formula with applications in probability and integrable systems.

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

Limit Shapes for Random Young Tableaux via Determinantal Point Processes

Explore limit shapes for random Young tableaux using determinantal point processes. Discover new insights on limiting surfaces for multirectangular shapes, including potential discontinuities.

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

The Symplectic Schur Process - Integrability and Algebraic Combinatorics

Explore the Symplectic Schur Process, a new probability ensemble with desirable properties. Discover its connections to symmetric functions, combinatorial identities, and applications in algebraic combinatorics.

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

The Squish Map and the SL_2 Double-Dimer Model

Explore measure-preserving maps between dimer models on hexagon lattices, connecting single and double-dimer models for insights into partition functions and plane partition enumeration.

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

Hypergeometric Matrix Models and their Duals

Explore hypergeometric functions of complex matrices, their connections to algebraic combinatorics, and a novel approach to approximating these functions using Hurwitz theory concepts.

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

The MacNeille Completion of the Type B Bruhat Poset

Explore MacNeille completion of Weyl groups, focusing on type B Bruhat poset. Discover connections to Alternating Sign Matrices and gain insights into algebraic combinatorics.

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

Schubert to Grothendieck via Ice

Explore formulas for transitioning between Schubert and Grothendieck polynomials using pipe dreams and bumpless pipe dreams in this advanced algebraic combinatorics lecture.

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

Move-Reduced Graphs on a Torus vs Positroid Catalan Numbers

Explore combinatorial dynamics in affine symmetric groups, connecting torus graph classification and positroid Catalan numbers. Applications to geometry, knot theory, and Grassmannian varieties discussed.

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

Sums of Weighted Lattice Points of Polytopes

Explore connections between polytopes and algebraic combinatorics, focusing on sums of weighted lattice points and their computational implications in estimating maximal weighted lattice points.

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

The Andrews-Gordon Partition Identities and Commutative Algebra

Explore partition identities, focusing on Andrews-Gordon identities and their connections to commutative algebra. Learn about new combinatorial techniques and q-series identities in number theory.

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

Rotation-Invariant Web Bases from Hourglass Plabic Graphs and Symmetrized Six-Vertex Configurations

Explore symmetrized six-vertex model, hourglass plabic graphs, and their applications in statistical mechanics and combinatorics. Discover connections to tableaux, alternating sign matrices, and plane partitions.

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

Log-Concave Polynomials, Lattice Point Counting, and Traveling Salesperson Problem

Explore log-concave polynomials and their applications in bounds, probability, and optimization, including recent advancements in lattice point counting and the Traveling Salesperson Problem.

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

Complexity of Log-Concave Poset Inequalities

Explore log-concave inequalities in mathematics, from elementary examples to complex cases like Stanley's inequality, and examine their intrinsic complexity using combinatorics, complexity theory, and geometry.

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