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#Combinatorial Mathematics

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Insights into Mathematics

The Deep Structure of the Rational Numbers - Real Numbers and Limits Math Foundations

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Explores the deep structure of rational numbers, focusing on their layered nature within [0,1]. Covers key concepts like Farey sequences and Ford circles, emphasizing rationals' importance in modern mathematics.
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10 Lesons
36 minutes
On-Demand
Free-Video
Simons Institute

Real-Rooted Polynomials

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Explore real-rooted polynomials, their properties, and connections to combinatorics in this comprehensive lecture covering fundamental theorems, root interlacing, and applications to random spanning trees.
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12 Lesons
33 minutes
On-Demand
Free-Video
IMSA

A Categorical Interpretation of the GKZ D-Module

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Explore the categorical interpretation of GKZ D-modules in toric homological mirror symmetry, focusing on B-side categories and characteristic cycle strata.
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16 Lesons
1 hour 4 minutes
On-Demand
Free-Video
Applied Algebraic Topology Network

Kohei Tanaka - Sectional Category for Maps of Finite Spaces

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Explore combinatorial approaches to sectional category in finite T_0 spaces, examining McCord maps, weak homotopy equivalences, and Fadell-Neuwirth fibrations through computational examples.
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1 Lesons
47 minutes
On-Demand
Free-Video
Applied Algebraic Topology Network

Parametrized Topological Complexity of Hyperplane Arrangement Bundles

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Exploring parametrized motion planning in hyperplane arrangement bundles, focusing on topological complexity under supersolvability conditions. Joint work with Dan Cohen.
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1 Lesons
51 minutes
On-Demand
Free-Video
Hausdorff Center for Mathematics

On Circuit Imbalance Measures and Their Role in Circuit Augmentation Algorithms

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Explore new combinatorial condition numbers for linear and integer programs, their relation to existing measures, and their impact on circuit diameter bounds and simplex methods.
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1 Lesons
25 minutes
On-Demand
Free-Video
Institute for Pure & Applied Mathematics (IPAM)

Superport Networks: Generalizing Kirchhoff's Matrix-Tree Theorem

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Exploration of multiport networks, generalizing Kirchhoff's theorem with novel mathematical approaches. Insights into electrical engineering applications and superport network theory.
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1 Lesons
49 minutes
On-Demand
Free-Video
Institute for Advanced Study

Quasipolynomial Bounds for Some Problems in Extremal Combinatorics

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Explore quasipolynomial bounds in extremal combinatorics with Zander Kelley, examining key problems and recent advancements in this mathematical field.
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1 Lesons
17 minutes
On-Demand
Free-Video
Institute for Advanced Study

Combinatorial Inequalities and Combinatorial Interpretations - Part I

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Explore classical inequalities in enumerative and algebraic combinatorics, their combinatorial interpretations, and their impact on the field. Gain insights into complexity theoretic aspects.
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1 Lesons
1 hour 13 minutes
On-Demand
Free-Video
Kolmogorov-Seminar

Rectangles, Complexity and Games in Communication Theory - December 4, 2023

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Delve into communication complexity theory through rectangles, exploring inequality principles, combinatorial strategies, and their applications in computational game theory.
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1 Lesons
1 hour 58 minutes
On-Demand
Free-Video
Institute for Advanced Study

Geometry of Delta-Matroids

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Explore advanced geometric constructions in delta-matroids, examining their relationship to matroids and proving ultra log-concavity of independent sets in mathematical structures.
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1 Lesons
1 hour 3 minutes
On-Demand
Free-Video
MIT OpenCourseWare

Crossing Number Inequality in Graph Theory and Combinatorics

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Explore the probabilistic method in combinatorics and its application to graph theory, focusing on proving the crossing number inequality in graph drawings.
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1 Lesons
18 minutes
On-Demand
Free-Video