Institute for Pure & Applied Mathematics (IPAM) Courses

The Polytope of All Matroids - A Framework for Matroid Theory Conjectures

Delve into advanced matroid theory through an exploration of polytope construction, valuative invariants, and their role in proving or disproving key conjectures in combinatorial mathematics.

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

Interactions Between Commutative Algebra and Graph Coloring Theory

Explore the fascinating intersection of commutative algebra and graph coloring theory, examining stable set ideals and Kempe equivalence through innovative algebraic methods.

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

Algebra, Geometry and Combinatorics of Cosmological Polytopes

Delve into advanced mathematical concepts exploring cosmological polytopes, their algebraic structures, and connections to physics through Feynman diagrams and wave functions in this theoretical mathematics lecture.

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

Vertex Order Shellings in Simplicial Complexes

Delve into the mathematical exploration of vertex order shellings in simplicial complexes, examining their topological properties and relationship with matroid independence complexes through Björner's theorem.

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

Symmetric Edge Polytopes - Clustering, Degree Sequences, and Graphs with Few Edges

Delve into advanced geometric combinatorics through an exploration of symmetric edge polytopes, focusing on graph clustering metrics, degree sequences, and empirical sampling from random graph models.

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

Symmetries of Rings from Hyperplane Arrangements

Delve into advanced mathematical concepts exploring hyperplane arrangements, cohomology rings, and G-representations, with insights on computational methods and challenges in algebraic geometry.

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

Tropical Ideals and Their Properties in Computational Algebra

Delve into tropical ideals and their combinatorial properties, exploring matroid structures, polynomial ring relationships, and computational challenges in algebraic geometry and discrete mathematics.

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

The cd-index of a Semi-Eulerian Complex

Delve into advanced algebraic topology concepts exploring the cd-index generalization for semi-Eulerian posets, with focus on connected simplicial Buchsbaum posets and dimensional manifolds.

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

Cellular Resolutions for Normalizations of Toric Ideals

Delve into advanced algebraic geometry concepts, exploring cellular resolutions, toric ideals, and their normalizations through combinatorial chain complexes and lattice stratification techniques.

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

Presburger Modules: Quasipolynomial and Tameness

Delve into advanced mathematical concepts exploring Presburger modules, examining their quasipolynomial behavior and tameness through local cohomology and persistent homology applications.

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

Interval Complexes, Linear Resolutions, and Spaces of Digraph Maps

Delve into advanced mathematical concepts exploring interval complexes, ideals, and cellular resolutions through the lens of directed graph homomorphisms and their applications in combinatorial algebra.

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

Minkowski Bases of Type Cones in Deformation Theory

Delve into advanced geometric concepts exploring deformation cones, polytope decomposition, and barycentric subdivisions of simplicial fans, with applications to braid fans and normal fan products.

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

Yoshinaga Criterion and Topology of Complexified Complement of Real Arrangement

Delve into advanced topology concepts exploring Yoshinaga's criterion, homotopy groups, and complexified real arrangements through computational and combinatorial approaches in algebraic geometry.

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

Logical Quantum Processor with Neutral Atom Arrays - Part 1

Dive into quantum computing fundamentals as Harvard's Misha Lukin explores logical quantum processing using neutral atom arrays, focusing on error suppression and mitigation techniques.

• YouTube
• 1 hour 29 minutes
• Self-Paced
• Free Video

Logical Quantum Processor with Neutral Atom Arrays - Part 2

Delve into advanced quantum computing concepts focusing on neutral atom arrays and logical quantum processing through Harvard researcher Misha Lukin's detailed technical presentation.

• YouTube
• 1 hour 32 minutes
• Self-Paced
• Free Video