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#Cluster Algebras

Showing: 46 courses
BIMSA

Tilting Theory Revisited - Developments in Real Grothendieck Groups

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Explore recent developments in tilting theory, focusing on real Grothendieck groups and 2-term silting complexes. Gain insights into g-fans, representation theory, and connections with canonical decompositions.
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1 Lesons
52 minutes
On-Demand
Free-Video
International Centre for Theoretical Sciences

New Signed Bijections Pertaining to Alternating Sign Matrices and Gelfand-Tsetlin Patterns

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Delve into advanced mathematical concepts exploring signed bijections, alternating sign matrices, and Gelfand-Tsetlin patterns through rigorous theoretical analysis and problem-solving approaches.
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1 Lesons
1 hour 30 minutes
On-Demand
Free-Video
International Mathematical Union

The Positive Grassmannian, the Amplituhedron, and Cluster Algebras

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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.
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15 Lesons
47 minutes
On-Demand
Free-Video
International Centre for Theoretical Sciences

Representations of Acyclic Quivers and Auslander-Reiten Sequences - Lecture 1

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Explore representations of acyclic quivers, Auslander-Reiten sequences, and the Caldero-Chapoton formula in this advanced mathematics lecture on cluster algebras and quiver representations.
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14 Lesons
1 hour 13 minutes
On-Demand
Free-Video
Fields Institute

Shadow Sequences of Integers

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Explore integer shadow sequences, cluster algebras, and supergeometry in this advanced mathematics talk, delving into coordinate transformations and hypergraphs.
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13 Lesons
39 minutes
On-Demand
Free-Video
Fields Institute

Cluster Algebra Structures from Decorated Super-Teichmüller Spaces

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Explore cluster algebra structures derived from decorated super-Teichmüller spaces, examining dimer models and labels in the context of supergeometry and bracket structures.
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7 Lesons
26 minutes
On-Demand
Free-Video
IMSA

Deformation Theory for Finite Cluster Complexes

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Explore geometric relationships between cluster varieties and complexes, focusing on finite cluster types with universal coefficients and their connection to Hilbert schemes via torus actions.
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1 Lesons
59 minutes
On-Demand
Free-Video
ICTP Mathematics

Cluster Algebras and Mirror Symmetry - Lecture 2

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Explore connections between cluster algebras and mirror symmetry in algebraic geometry, delving into advanced mathematical concepts and their applications.
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1 Lesons
57 minutes
On-Demand
Free-Video
ICTP Mathematics

Cluster Algebras and Mirror Symmetry - Lecture 1

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Explore the intricate connection between cluster algebras and mirror symmetry in mathematics, delving into advanced concepts and their applications in algebraic geometry.
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1 Lesons
1 hour 2 minutes
On-Demand
Free-Video
Hausdorff Center for Mathematics

A Geometric Model for the Bounded Derived Category of a Gentle Algebra - Sibylle Schroll Lecture 3

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Explore geometric models for bounded derived categories of gentle algebras, their role in cluster algebras and homological mirror symmetry, and connections to partially wrapped Fukaya categories.
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1 Lesons
1 hour 8 minutes
On-Demand
Free-Video
Hausdorff Center for Mathematics

A Geometric Model for the Bounded Derived Category of a Gentle Algebra - Sibylle Schroll

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Explore geometric models for gentle algebras' derived categories, connecting algebra to surface topology and line fields. Gain insights into representation theory and homological mirror symmetry.
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1 Lesons
1 hour 6 minutes
On-Demand
Free-Video
Institute for Pure & Applied Mathematics (IPAM)

Introduction to Cluster Algebras - Part 1

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Explore cluster algebras, quivers, and mutation through examples, with a focus on the Grassmannian. Gain insights into this fundamental algebraic structure and its applications.
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1 Lesons
1 hour 6 minutes
On-Demand
Free-Video
Fields Institute

Clusters and Weaves in Mathematical Structures

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Explore mathematical connections between cluster algebras and weaves, delving into their structures and applications in algebraic geometry and representation theory.
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1 Lesons
57 minutes
On-Demand
Free-Video
Fields Institute

Cluster Algebras and Monotone Lagrangian Tori

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Explore the connection between cluster algebras and monotone Lagrangian tori in this advanced mathematics talk, delving into complex geometric structures and algebraic relationships.
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1 Lesons
44 minutes
On-Demand
Free-Video
Western Hemisphere Virtual Symplectic Seminar

Introduction to Lagrangian Fillings of Legendrian Links - Part 1

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Explore Lagrangian fillings of Legendrian links, their construction, and techniques to distinguish Hamiltonian isotopy classes. Delve into the connection with cluster algebras and key proof elements.
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3 Lesons
1 hour 11 minutes
On-Demand
Free-Video
Western Hemisphere Virtual Symplectic Seminar

Applications of the Relation Between Cluster Algebras and Symplectic Topology - Part 2

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Explore applications of cluster algebras in symplectic topology, including detection of Lagrangian fillings and holomorphic symplectic structures. Examine implications for Richardson varieties and quasi-cluster structures.
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4 Lesons
1 hour 10 minutes
On-Demand
Free-Video
Western Hemisphere Virtual Symplectic Seminar

Cluster Algebras Associated to Bott-Samelson Braids

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Explore cluster algebras associated with Bott-Samelson braids, focusing on Legendrian links and their connection to algebraic varieties and Lagrangian fillings. Discover weaves and their computational applications.
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2 Lesons
1 hour 6 minutes
On-Demand
Free-Video
Western Hemisphere Virtual Symplectic Seminar

Cluster Algebras for General Braid Varieties

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Explore cluster algebras on braid varieties using weaves, Lusztig cycles, and symplectic topology. Gain insights into localization processes and A=U proof through Lie-theoretic and combinatorial perspectives.
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1 Lesons
1 hour 1 minute
On-Demand
Free-Video
Centre International de Rencontres Mathématiques

A∞-Categories

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Explore A∞-categories in mathematics with Rafael Bocklandt's comprehensive lecture, delving into advanced concepts in representation theory and algebra.
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1 Lesons
57 minutes
On-Demand
Free-Video
Centre International de Rencontres Mathématiques

Cluster Algebras and the Amplituhedron - Definition - Lecture 1

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Explore cluster algebras and the amplituhedron definition with Lauren K. Williams in this advanced mathematics conference talk from CIRM's Audiovisual Mathematics Library.
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1 Lesons
1 hour 1 minute
On-Demand
Free-Video
Centre International de Rencontres Mathématiques

Cluster Algebras with Coefficients and Relative Calabi-Yau Structures

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Explore cluster algebras with coefficients and relative Calabi-Yau structures in this advanced mathematics lecture by Bernhard Keller at CIRM's thematic meeting.
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1 Lesons
1 hour 4 minutes
On-Demand
Free-Video
Isaac Newton Institute for Mathematical Sciences

Cluster Algebras and Related Notions - Kirk Lecture

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Explore cluster algebras and related mathematical concepts through a single illustrative picture, connecting various fields and interpretations in this comprehensive lecture.
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1 Lesons
1 hour 2 minutes
On-Demand
Free-Video
Isaac Newton Institute for Mathematical Sciences

Cluster Algebras and Representation Theory - Rothschild Lecture

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Explore cluster algebras' definition, impact on representation theory, and ongoing research. Gain insights into this influential mathematical concept and its wide-ranging applications.
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1 Lesons
1 hour 16 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
Institut des Hautes Etudes Scientifiques (IHES)

Reddening Sequences for Cluster Algebras

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Explore reddening sequences in cluster algebras, their implications, and known cases, delving into finite dimensionality, invariants, and canonical bases.
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12 Lesons
44 minutes
On-Demand
Free-Video
Centre de recherches mathématiques - CRM

Cluster Algebras and Hyperbolic Geometry

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Explore the application of cluster algebra to 2D and 3D hyperbolic geometry, examining ideal triangulations, Teichmuller spaces, and knot volumes through mutations and cluster variables.
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1 Lesons
1 hour 1 minute
On-Demand
Free-Video
Centre de recherches mathématiques - CRM

Higher Order KR-Modules, Imaginary Modules and Monoidal Categorification

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Explore connections between cluster algebras, quantum affine algebras, imaginary modules, and representation theory of general linear groups over non-archimedean fields.
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1 Lesons
44 minutes
On-Demand
Free-Video
Centre de recherches mathématiques - CRM

The Deep Locus of Cluster Varieties

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Explore the deep locus of cluster varieties, focusing on finite types with full rank and specific infinite types. Gain insights into applications for homological mirror symmetry of Grassmannians.
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1 Lesons
38 minutes
On-Demand
Free-Video
BIMSA

Total Positivity: Combinatorics, Geometry and Representation Theory

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Explore total positivity theory in matrices, its applications, and recent developments in combinatorics, geometry, and representation theory.
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1 Lesons
1 hour 4 minutes
On-Demand
Free-Video
International Centre for Theoretical Sciences

Stationary Measures for Integrable Probabilistic Systems

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Explore advanced mathematical concepts in integrable probabilistic systems, focusing on stationary measures, discrete models, and their applications in theoretical physics and mathematics.
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1 Lesons
1 hour 28 minutes
On-Demand
Free-Video
International Centre for Theoretical Sciences

Colored Vertex Models, Orthogonal Functions and Probability - Lecture 2

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Delve into advanced concepts of colored vertex models, exploring their connections to orthogonal functions and probability theory through expert mathematical analysis and demonstrations.
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1 Lesons
1 hour 32 minutes
On-Demand
Free-Video
International Centre for Theoretical Sciences

Branes and Quivers in String Theory - Lecture 1

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Explore connections between string theory, branes, and quivers. Learn about spatial dimensions, brain setups, Coulomb branches, and moduli spaces in this advanced theoretical physics lecture.
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16 Lesons
1 hour 17 minutes
On-Demand
Free-Video
International Centre for Theoretical Sciences

Scattering Amplitudes and Positive Grassmannian by Jaroslav Trnka

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Explore connections between scattering amplitudes and positive Grassmannians, covering on-shell diagrams, permutations, and cluster algebras. Gain insights into particle physics and mathematical structures.
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65 Lesons
1 hour 57 minutes
On-Demand
Free-Video
Galileo Galilei Institute

Exactly Solvable Five-Dimensional BPS Spectra and Discrete Integrable Systems

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Explore five-dimensional BPS spectra and their connection to discrete integrable systems in this advanced physics lecture by Fabrizio Del Monte.
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1 Lesons
1 hour 15 minutes
On-Demand
Free-Video
M-Seminar, Kansas State University

Cluster Nature of Quantum Groups

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Explore quantum groups through a rigid cluster model, discovering natural Hopf algebra isomorphisms and a cluster canonical basis with unique invariance properties.
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1 Lesons
1 hour 10 minutes
On-Demand
Free-Video
Institut des Hautes Etudes Scientifiques (IHES)

Combinatorics and Geometry of the Amplituhedron

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Explore the amplituhedron's geometric properties, connections to various mathematical fields, and recent progress on key conjectures in this advanced mathematical lecture.
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1 Lesons
54 minutes
On-Demand
Free-Video
International Centre for Theoretical Sciences

Extensions of Discrete Toda Lattices and their Applications - Lecture 3

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Delve into advanced mathematical concepts of discrete Toda lattices, exploring integrable systems, difference equations, and their applications in theoretical physics and mathematics.
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1 Lesons
1 hour 34 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

Cluster Structures on Kinematic Spaces

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Delve into advanced mathematical concepts exploring cluster structures and their applications in kinematic spaces, focusing on combinatorial approaches in fundamental physics.
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1 Lesons
58 minutes
On-Demand
Free-Video
International Centre for Theoretical Sciences

Total Positivity, Directed Networks and Integrable Cluster Dynamics - Lecture 1

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Explore advanced mathematical concepts in discrete integrable systems, focusing on difference equations, cluster algebras, and their connections to theoretical physics and probability theory.
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1 Lesons
1 hour 4 minutes
On-Demand
Free-Video
International Centre for Theoretical Sciences

Extensions of Discrete Toda Lattices and their Applications - Lecture 2

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Delve into advanced mathematical concepts of discrete Toda lattices, exploring integrable systems, difference equations, and their applications in theoretical physics and mathematics.
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1 Lesons
1 hour 3 minutes
On-Demand
Free-Video
International Centre for Theoretical Sciences

Total Positivity, Directed Networks and Integrable Cluster Dynamics - Lecture 3

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Delve into advanced mathematical concepts of total positivity, directed networks, and integrable cluster dynamics through rigorous theoretical exploration and problem-solving approaches.
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1 Lesons
1 hour 11 minutes
On-Demand
Free-Video
International Centre for Theoretical Sciences

Quadratic Differentials and Degenerate Eigenvalues

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Explore the relationship between quadratic differentials and degenerate eigenvalues in discrete integrable systems through advanced mathematical concepts and theoretical physics applications.
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1 Lesons
26 minutes
On-Demand
Free-Video
International Centre for Theoretical Sciences

Ruijsenaars and Toda Integrable Systems

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Explore advanced mathematical concepts in discrete integrable systems, focusing on difference equations, cluster algebras, and their applications in theoretical physics and probability theory.
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1 Lesons
57 minutes
On-Demand
Free-Video
International Centre for Theoretical Sciences

The Boundary-driven q-Hahn Process

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Delve into discrete integrable systems, exploring difference equations, cluster algebras, and probabilistic models through advanced mathematical physics and theoretical applications.
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1 Lesons
57 minutes
On-Demand
Free-Video
International Centre for Theoretical Sciences

Integrable Difference Equations and Orthogonal Polynomials with respect to a Discrete Measure

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Explore advanced mathematical concepts in discrete integrable systems, focusing on difference equations, cluster algebras, and probabilistic models through expert-led mini-courses and workshops.
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1 Lesons
58 minutes
On-Demand
Free-Video