Cluster Algebras and Related Notions - Kirk Lecture
Explore cluster algebras and related mathematical concepts through a single illustrative picture, connecting various fields and interpretations in this comprehensive lecture.
Cluster Algebras and Representation Theory - Rothschild Lecture
Explore cluster algebras' definition, impact on representation theory, and ongoing research. Gain insights into this influential mathematical concept and its wide-ranging applications.
Combinatorics of the Amplituhedron
Explore the amplituhedron's connections to cluster algebras, matroids, and combinatorics in this gentle introduction by Lauren Williams from Harvard University.
Reddening Sequences for Cluster Algebras
Explore reddening sequences in cluster algebras, their implications, and known cases, delving into finite dimensionality, invariants, and canonical bases.
Cluster Algebras and Hyperbolic Geometry
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.
Higher Order KR-Modules, Imaginary Modules and Monoidal Categorification
Explore connections between cluster algebras, quantum affine algebras, imaginary modules, and representation theory of general linear groups over non-archimedean fields.
The Deep Locus of Cluster Varieties
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.
Total Positivity: Combinatorics, Geometry and Representation Theory
Explore total positivity theory in matrices, its applications, and recent developments in combinatorics, geometry, and representation theory.
Stationary Measures for Integrable Probabilistic Systems
Explore advanced mathematical concepts in integrable probabilistic systems, focusing on stationary measures, discrete models, and their applications in theoretical physics and mathematics.
Colored Vertex Models, Orthogonal Functions and Probability - Lecture 2
Delve into advanced concepts of colored vertex models, exploring their connections to orthogonal functions and probability theory through expert mathematical analysis and demonstrations.
Branes and Quivers in String Theory - Lecture 1
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.
Scattering Amplitudes and Positive Grassmannian by Jaroslav Trnka
Explore connections between scattering amplitudes and positive Grassmannians, covering on-shell diagrams, permutations, and cluster algebras. Gain insights into particle physics and mathematical structures.
Exactly Solvable Five-Dimensional BPS Spectra and Discrete Integrable Systems
Explore five-dimensional BPS spectra and their connection to discrete integrable systems in this advanced physics lecture by Fabrizio Del Monte.
Cluster Nature of Quantum Groups
Explore quantum groups through a rigid cluster model, discovering natural Hopf algebra isomorphisms and a cluster canonical basis with unique invariance properties.
Combinatorics and Geometry of the Amplituhedron
Explore the amplituhedron's geometric properties, connections to various mathematical fields, and recent progress on key conjectures in this advanced mathematical lecture.
Extensions of Discrete Toda Lattices and their Applications - Lecture 3
Delve into advanced mathematical concepts of discrete Toda lattices, exploring integrable systems, difference equations, and their applications in theoretical physics and mathematics.
The Moduli Space of Matroids - Lecture 1
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.
Cluster Structures on Kinematic Spaces
Delve into advanced mathematical concepts exploring cluster structures and their applications in kinematic spaces, focusing on combinatorial approaches in fundamental physics.
Total Positivity, Directed Networks and Integrable Cluster Dynamics - Lecture 1
Explore advanced mathematical concepts in discrete integrable systems, focusing on difference equations, cluster algebras, and their connections to theoretical physics and probability theory.
Extensions of Discrete Toda Lattices and their Applications - Lecture 2
Delve into advanced mathematical concepts of discrete Toda lattices, exploring integrable systems, difference equations, and their applications in theoretical physics and mathematics.
Total Positivity, Directed Networks and Integrable Cluster Dynamics - Lecture 3
Delve into advanced mathematical concepts of total positivity, directed networks, and integrable cluster dynamics through rigorous theoretical exploration and problem-solving approaches.