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#Matroids

Showing: 24 courses
Institute for Advanced Study

From Matroids to Moduli Spaces

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Explore the mathematical foundations of matroids and their applications in OSCAR software, focusing on hyperplane arrangements, particle physics, and algebraic geometry applications.
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1 Lesons
56 minutes
On-Demand
Free-Video
Institute for Advanced Study

Tropical Vector Bundles and Matroids

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Delve into advanced geometric concepts exploring toric vector bundles, matroids, and their tropical counterparts through classification, equivariant K-theory, and characteristic classes.
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1 Lesons
1 hour 3 minutes
On-Demand
Free-Video
Institute for Advanced Study

Paths to Matroid Representations

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Delve into advanced matroid theory, exploring representation theorems, connectivity statements, and orthogonal matroids through historical developments and modern algebraic approaches.
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1 Lesons
1 hour 5 minutes
On-Demand
Free-Video
Institute for Advanced Study

Multimatroids and Rational Curves with Cyclic Action

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Explore the intersection of multimatroids and rational curves, discovering how these mathematical structures connect through combinatorial formulas and independence polytopal complexes in topological graph theory.
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1 Lesons
50 minutes
On-Demand
Free-Video
Institute for Advanced Study

The External Activity Complex of a Pair of Matroids

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Delve into advanced matroid theory, exploring external activity complexes and their relationship to Schubert varieties, with applications to tautological classes and Speyer's matroid invariant.
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1 Lesons
1 hour 8 minutes
On-Demand
Free-Video
Hausdorff Center for Mathematics

Cynthia Vinzant - Log Concave Polynomials and Matroids

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Explore strong log concavity in polynomials, its applications to matroids, and connections to combinatorics and geometry. Learn about recent developments and their implications.
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8 Lesons
58 minutes
On-Demand
Free-Video
IMSA

Kazhdan-Lusztig Theory and Singular Hodge Theory for Matroids I

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Explore the fascinating parallel between Coxeter groups and matroids in combinatorial cohomology, featuring recent research on singular Hodge theory for combinatorial geometries.
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1 Lesons
1 hour 3 minutes
On-Demand
Free-Video
IMSA

Kazhdan-Lusztig Theory and Singular Hodge Theory for Matroids II

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Explore the parallel between Coxeter groups and matroids in combinatorial cohomology, with insights on singular Hodge theory for combinatorial geometries from recent collaborative research.
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1 Lesons
1 hour 9 minutes
On-Demand
Free-Video
Applied Algebraic Topology Network

Greg Henselman - Matroids & Canonical Forms Theory and Applications

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Explore matroids and canonical forms, their theoretical foundations, and practical applications in algebraic topology and related fields.
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1 Lesons
1 hour 8 minutes
On-Demand
Free-Video
QuantumTopology

Matroids, Delta Matroids, and Knot Invariants

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Explore matroids, delta matroids, and their applications in knot theory with Sergei Lando. Gain insights into these mathematical structures and their role in understanding knot invariants.
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1 Lesons
56 minutes
On-Demand
Free-Video
Fields Institute

Vector-valued Laurent Polynomial Equations, Toric Vector Bundles and Matroids

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Explore connections between Laurent polynomials, toric vector bundles, and matroids in algebraic geometry and topology with expert Kiumars Kaveh.
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1 Lesons
48 minutes
On-Demand
Free-Video
Institute for Advanced Study

Chow Polynomials of Matroids

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Explore the intriguing world of Chow polynomials in matroid theory with Luis Ferroni's concise presentation on this advanced mathematical concept.
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1 Lesons
15 minutes
On-Demand
Free-Video
Institut des Hautes Etudes Scientifiques (IHES)

Combinatorics of the Amplituhedron

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Explore the amplituhedron's connections to cluster algebras, matroids, and combinatorics in this gentle introduction by Lauren Williams from Harvard University.
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1 Lesons
49 minutes
On-Demand
Free-Video
Institute for Advanced Study

Derived Categories of Permutahedral Varieties Through Matroids

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Explore derived categories of permutahedral varieties using matroid theory, uncovering connections between algebraic geometry and combinatorics.
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1 Lesons
21 minutes
On-Demand
Free-Video
Institute for Advanced Study

K-rings of Wonderful Varieties and Matroids

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Explore K-rings of wonderful varieties and matroids with Shiyue Li, delving into advanced mathematical concepts and their applications in algebraic geometry.
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1 Lesons
21 minutes
On-Demand
Free-Video
Simons Institute

Quotient Sparsification for Submodular Functions

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Explores sparsification of matroids and submodular functions, unifying graph and hypergraph cut sparsifiers with applications to set systems and algorithmic efficiency.
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1 Lesons
29 minutes
On-Demand
Free-Video
Institute for Advanced Study

Complexity of Log-concave Inequalities in Matroids

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Delve into the mathematical complexity of log-concave inequalities in matroids, exploring combinatorics, complexity theory, and geometric approaches to understanding Mason's conjecture and related mathematical concepts.
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1 Lesons
1 hour 6 minutes
On-Demand
Free-Video
Institute for Advanced Study

Valuated Delta Matroids and Principal Minors

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Delve into advanced mathematical concepts of valuated Delta matroids, their relationship with principal minors of Hermitian matrices, and their applications in combinatorial structures.
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1 Lesons
1 hour 10 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
Institute for Advanced Study

The Moduli Space of Matroids - Lecture 1

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Delve into advanced mathematical concepts exploring matroid theory, F1-geometry, and tropical schemes, focusing on Baker-Bowler's theory and its applications to Grassmannians and representation theory.
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1 Lesons
1 hour 14 minutes
On-Demand
Free-Video
Institute for Advanced Study

Matroids and Amplitudes: From Linear Independence to Scattering Theory

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Delve into the mathematical theory of matroids, exploring their relationship with scattering amplitudes, intersection theory, and positive geometry through advanced theoretical physics concepts.
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1 Lesons
1 hour 10 minutes
On-Demand
Free-Video
Institute for Advanced Study

Foundations of Matroids - Lecture 2

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Delve into advanced matroid theory, exploring foundations, structure theorems, and applications in representation theory, realization spaces, and Lorentzian polynomials with expert Oliver Lorscheid.
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1 Lesons
1 hour 55 minutes
On-Demand
Free-Video
Institute for Advanced Study

The Schubert Variety of a Pair of Linear Spaces

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Delve into advanced mathematical concepts exploring Schubert varieties, Kempf collapsing, and matroid theory through the lens of linear spaces and their geometric relationships.
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1 Lesons
1 hour 7 minutes
On-Demand
Free-Video
Institute for Advanced Study

Twisted (Co)homology of Matroids and Hyperplane Arrangement Complements

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Delve into advanced mathematical concepts exploring twisted (co)homology, hyperplane arrangements, and matroidal pairings, with applications to scattering amplitudes in physics.
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1 Lesons
1 hour 51 minutes
On-Demand
Free-Video