Knot Polynomials from Chern-Simons Field Theory and Their String Theoretic Implications by P. Ramadevi
Explore knot polynomials, Chern-Simons theory, and string theory connections. Learn about knot classification, invariants, homology, and gauge-string duality in topological strings. Discover M-theory descriptions and brane constructions.
The Geometric Langlands Conjecture and Non-Abelian Hodge Theory - Lecture 1
Explore the Geometric Langlands conjecture and non-abelian Hodge theory, examining connections between quantum fields, geometry, and representation theory in modern mathematics and theoretical physics.
Learning How to Break Symmetry With Symmetry-Preserving Neural Networks - IPAM at UCLA
Explore symmetry-preserving neural networks for data efficiency and generalization, learning symmetry-breaking information, and predicting structural distortions in crystalline materials.
Atsushi Ichino- Theta Lifting and Langlands Functoriality
Explore theta lifting, seesaw identities, and Langlands functoriality in number theory, focusing on modular forms and local Shimura-Waldspurger correspondence.
Character Estimates for Finite Simple Groups and Applications
Explore character estimates for finite simple groups and their applications in various mathematical problems, including mixing times, Waring's Problem, and conjectures by Ore and Thompson.
Allen Knutson- Schubert Calculus and Quiver Varieties
Explore Schubert calculus, quiver varieties, and their connections through puzzle rules, Yang-Baxter equations, and representation theory in this advanced mathematics lecture.
Cyclotomic KLR Algebras - Part 1 of 4
Exploring cyclotomic KLR algebras, their connection to quantum groups, and their role in categorifying highest weight representations, with a focus on type A and the Ariki–Brundan–Kleshchev theorem.
Drinfeld Center, Tube Algebra, and Representation Theory of Monoidal Categories
Explore connections between category theory, subfactor theory, and quantum groups. Learn about Drinfeld center, tube algebra, and representation theory of monoidal categories.
Representation Theory for Groups of Lie Type I
Explore representation theory for finite groups of Lie type, covering structural properties, Harish-Chandra theory, and Deligne-Lusztig theory for classifying irreducible complex representations.
Skew-Gentle Algebras and Surface Orbifolds, Claire Amiot
Explore skew-gentle algebras and their geometric models in derived categories, extending concepts from gentle algebras to skew-group algebras. Joint work with Thomas Brüstle.
Spectral Graph Theory - Lecture 1
Explore spectral graph theory, covering self-adjoint matrices, Rayleigh equalities, graph isomorphism, Cayley graphs, and automorphism groups. Gain insights into complex systems and network analysis.
Representations of Acyclic Quivers and Auslander-Reiten Sequences - Lecture 1
Explore representations of acyclic quivers, Auslander-Reiten sequences, and the Caldero-Chapoton formula in this advanced mathematics lecture on cluster algebras and quiver representations.
Foliations on Shimura Varieties
Explore foliations on Shimura varieties, focusing on inseparable morphisms, characteristic P, and applications to surfaces and general cases in algebraic geometry.
Dichotomy and Howe Duality for Exceptional Theta Correspondences
Explore exceptional theta correspondences, focusing on Howe duality for G_2 x H pairs and a dichotomy theorem. Gain insights into local data correspondence, constraints, and reductive periods.
Eisenstein Cocycles and Values of L-Functions
Explore Eisenstein cocycles, equivariant cohomology, and their applications to L-functions. Gain insights into recent constructions and their connections to theta kernels and arithmetic groups.
Ramification of Supercuspidal Parameters
Explore supercuspidal parameters in representation theory, focusing on local Langlands conjecture, Fargues-Scholze theory, and applications to automorphic forms and wild ramification.
Harish-Chandra Tempered Representations and Homogeneous Spaces by Yves Benoist
Explore Harish-Chandra tempered representations and homogeneous spaces with Yves Benoist in this interactive lecture. Engage with the speaker and deepen your understanding of advanced mathematical concepts.
Homotopy Coherence - Theme and Variations
Explore homotopy coherence theory's evolution, applications, and links to representation theory in this semi-historical survey, offering unique insights and connections in algebraic topology.
A Local Version of HMS for Parabolic Hitchin Space
Exploring coherent sheaves on Springer fibers and their relation to microlocal sheaves, with applications to mirror duality in parabolic Hitchin spaces.
Homological Mirror Symmetry - Quivers & Curves in Higher Dimensions
Explore the connection between quiver mutations, Poisson X-cluster varieties, and Calabi-Yau categories, leading to a correspondence between Donaldson-Thomas invariants and rational curve counts in higher dimensions.
Homological Mirror Symmetry - Homological Link Invariants from Floer Theory
Explore a groundbreaking connection between homological mirror symmetry and representation theory, solving the knot categorification problem and generalizing Heegard-Floer theory to simple Lie superalgebras.