Combinatorics Courses and Certifications

Hausdorff Center for Mathematics

Alexander Volberg - Poincaré Inequalities on Hamming Cube - Analysis, Combinatorics, Probability

Explore improved L^1-Poincaré inequality constants on Hamming cube, comparing with Gaussian space. Discuss proofs, estimates, and related mathematical concepts in analysis, combinatorics, and probability theory.

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

Hausdorff Center for Mathematics

Topology of Complexes Arising in Models for Distributed Computing

Explore simplicial models in distributed computing, focusing on chromatic subdivisions and their applications to problems like Weak Symmetry Breaking, leading to new mathematical questions.

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

ICTP Mathematics

The Rogers-Ramanujan Identities and the Icosahedron - Lecture 3

Explore the deep connections between Rogers-Ramanujan identities and the icosahedron, spanning number theory, modular forms, combinatorics, and more. Uncover the beauty and complexity of these mathematical gems.

• YouTube
• 1 hour 24 minutes
• On-Demand
• Free Video

ICTP Mathematics

The Rogers-Ramanujan Identities and the Icosahedron - Lecture 2

Explore connections between Rogers-Ramanujan identities and icosahedron, linking number theory, modular forms, combinatorics, and conformal field theory in an accessible survey for mathematicians.

• YouTube
• 1 hour 45 minutes
• On-Demand
• Free Video

ICTP Mathematics

The Rogers-Ramanujan Identities and the Icosahedron - Lecture 1

Explore the deep connections between the Rogers-Ramanujan identities and the icosahedron, spanning number theory, modular forms, combinatorics, and more in this accessible mathematical lecture.

• YouTube
• 1 hour 17 minutes
• On-Demand
• Free Video

ICTP Mathematics

Standard and Less Standard Asymptotic Methods - Lecture 6

Explore advanced asymptotic methods for evaluating infinite sums and recognizing sequence patterns, with practical examples and techniques for high-precision numerical computations.

• YouTube
• 1 hour 31 minutes
• On-Demand
• Free Video

ICTP Mathematics

Standard and Less Standard Asymptotic Methods - Lecture 5

Explore advanced asymptotic methods for evaluating infinite sums and sequences, including Euler-Maclaurin formula variants and less conventional techniques, with practical examples and applications.

• YouTube
• 1 hour 40 minutes
• On-Demand
• Free Video

Hausdorff Center for Mathematics

Alexander Volberg: The Probability of Buffon Needle to Land Near Cantor Set

Explore the probability of Buffon's needle landing near Cantor sets, delving into unexpected connections with various mathematical fields and theories.

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

Hausdorff Center for Mathematics

Cynthia Vinzant - Log Concave Polynomials and Matroids

Explore strong log concavity in polynomials, its applications to matroids, and connections to combinatorics and geometry. Learn about recent developments and their implications.

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

IMSA

Nonrational Toric Geometry III - Quasifolds, Foliations, Combinatorics and One-parameter Families

Explores nonrational toric geometry through quasifolds, foliations, and combinatorics, extending classical toric geometry to new contexts and examining one-parameter families of toric quasifolds.

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

International Mathematical Union

The Positive Grassmannian, the Amplituhedron, and Cluster Algebras

Explore the positive Grassmannian and amplituhedron, delving into their combinatorial structures and connections to physics, integrable systems, and scattering amplitudes using oriented matroids, tropical geometry, and cluster algebras.

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

Applied Algebraic Topology Network

Tropical Geometry of Phylogenetic Tree Spaces

Explore tropical geometry's application to phylogenetic tree spaces, examining BHV space, tropical Grassmannians, and their implications for computational biology and statistics.

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

International Mathematical Union

Julia Boettcher- Graph and Hypergraph Packing

Explore graph and hypergraph packing, Latin squares, and randomness in mathematics with Julia Boettcher's insightful lecture on combinatorial structures.

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

Applied Algebraic Topology Network

Pavle Blagojević - Bedlewo: Shadows of Cohen's Vanishing Theorem

Explore Cohen's Vanishing theorem and its applications in algebraic topology, geometry, and combinatorics. Discover its impact on configuration spaces and measure partition problems.

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

Applied Algebraic Topology Network

Henry Adams - Fair Division

Explore how Sperner's lemma and topology can solve fair rent division among roommates with differing preferences, based on research and a New York Times article.

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