Embeddings of Kac-Moody Affine Grassmannian Slices
Explorez les développements récents dans la théorie des représentations géométriques, en se concentrant sur les tranches de Grassmanniennes affines de type Kac-Moody et leur construction via les branches de Coulomb.
The Method of Gauge Transform II
Explorez la méthode de transformation de jauge et son application aux problèmes spectraux périodiques et ergodiques avec Jeffrey Galkowski.
Quantitative Global Theory of One-Frequency Quasiperiodic Operators - Part II
Explorez la théorie quantitative globale des opérateurs quasipériodiques à une fréquence, en examinant la réductibilité et ses implications dans les problèmes spectraux.
Quantitative Global Theory of One-Frequency Quasiperiodic Operators - Part I
Explore quantitative global theory of one-frequency quasiperiodic operators, covering dynamic approaches, prototypical models, and applications in spectral problems.
The Method of Gauge Transform - Lecture 4
Explorez la méthode de transformation de jauge et ses applications dans les problèmes spectraux périodiques et ergodiques avec Jeffrey Galkowski de l'University College London.
Spherical Functions and Mirror Symmetry
Explore spherical functions and mirror symmetry in mathematics, bridging quantum physics and the Langlands Program through innovative interdisciplinary approaches.
Highlights from the History of Probability
Explore key milestones in probability theory, from Hilbert's problems to martingales, with insights on Brownian motion, Central Limit Theorem, and stochastic processes.
Operator Algebras, Bi-Unitary Connections and Tensor Networks - Lecture 4
Explore tensor categories as quantum symmetries, using Jones subfactor theory and bi-unitary connections to study 2D topological order and tensor networks.
Operator Algebras, Bi-Unitary Connections and Tensor Networks - Lecture 2
Explore tensor categories as quantum symmetries, using Jones subfactor theory and bi-unitary connections to study 2D topological order and tensor networks.
Operator Algebras, Bi-Unitary Connections and Tensor Networks - Lecture 1
Explore tensor categories as quantum symmetries, using Jones subfactor theory and bi-unitary connections to study 2D topological order and tensor networks.
The Method of Gauge Transform - Lecture 3
Explore advanced mathematical concepts in periodic and ergodic spectral problems, focusing on the Gauge transform method.
Causal Effects - Introduction to the Potential Outcomes Framework
Explore the Potential Outcomes Framework and three types of causal effects in this introductory video on causal inference, laying the groundwork for future discussions on observational data analysis.
S-duality and Lie Super-algebras
Explore geometric realization of quantum simple Lie super-algebras, S-duality, and connections to geometric Langlands correspondence and relative Langlands duality.
Operator Algebras, Tensor Categories and Tensor Networks in Topological Order
Explore tensor networks in topological order using operator algebra techniques. Discover quantum symmetries and their mathematical representation through tensor categories.
Curvature-Homogeneous Riemannian 3-Manifolds and Integrable Systems
Explore curvature-homogeneous Riemannian 3-manifolds, surveying known examples and recent discoveries. Delve into connections with integrable systems, particularly Toda lattices, to construct new explicit examples.
Knot Invariants from Finite Dimensional Integration
Explore finite dimensional integration for computing powerful knot invariants, surpassing traditional methods in efficiency and rigor while challenging established notions in knot theory.
Metric SYZ Conjecture for Calabi-Yau Manifolds - ICBS 2024
Explore special Lagrangian torus fibrations on Calabi-Yau manifolds, focusing on recent progress and the Fermat family of hypersurfaces.
A Finite Dimensional Proof of the Verlinde Formula
Explore a purely algebro-geometric proof of the Verlinde formula, examining recurrence relations for curve genus and parabolic points in generalized theta function spaces.
Quasi-Dynamic System Representation of Multiple Nonlinear Regression
Explore evolutionary game theory and allometric scaling to model nonlinear relationships between variables, overcoming limitations of linear regression for complex systems analysis.
Interface and Its Fluctuation in Interacting Particle Systems - ICBS 2024
Explore particle separation in Glauber-Kawasaki dynamics, interface evolution, and fluctuations. Delve into extended research on anisotropic curvature flow and stochastic partial differential equations.
Hyperbolic and Mixed-Type Problems in Gas Dynamics and Geometry
Explore hyperbolic and mixed-type PDEs in gas dynamics and geometry, focusing on transonic flows and isometric embedding.