Introduction to Vertex Algebras - From Heisenberg to Virasoro Algebras
Delve into vertex algebras, exploring Heisenberg, Kac-Moody, and Virasoro structures while understanding their connections to affine W-algebras and Zhu algebra fundamentals.
Representation Theory for Finite W-algebras
Delve into advanced representation theory, exploring Whittaker reduction, finite W-algebras, and their connection to Lie algebras through geometric and algebraic perspectives.
Construction of Finite W-algebras and Slodowy Slice Quantization
Delve into advanced mathematical concepts of Slodowy slices, nilpotent orbits, and finite W-algebras, exploring their construction, Poisson structures, and quantization methods in semisimple Lie algebras.
The Global Hecke Action - Talk 41
Delve into geometric Satake theory and explore how Rep(G^vee) actions on BunG sheaves integrate into global Hecke modifications, with applications in Betti, de Rham, and étale settings.
Moduli Spaces of Local Systems in Algebraic Varieties
Delve into advanced mathematical concepts of local systems and Galois representations, exploring construction methods and parameter spaces in Betti, deRham, and l-adic settings.
Counting Points on Bun_G - Talk 35
Delve into advanced algebraic geometry as Matthew Emerton explores G-L trace formula for Bun_G, providing a detailed proof of Conjecture 8 from Lurie's earlier lectures.
Breaking Black-Box AI
Explore failure cases of popular AI algorithms through live demos, from linear regression to deep learning. Learn to identify and address silent failures in black-box AI systems.
P-Form Symmetries in Functorial Quantum Field Theory
Explore p-form symmetries in functorial quantum field theory, focusing on implementing finite group global and gauged symmetries in TQFT using cohomology-decorated bordisms.
An Effective and Adequate Theory of Real Computation with Applications
Explore an effective theory of real computation, addressing inadequacies in current approaches and discussing applications in scientific and engineering disciplines.
Quaternionic Foundations of Quantum Mechanics and Spin 1/2 Visualization
Explore quaternionic foundations of quantum mechanics and visualize spin 1/2 behavior. Gain insights into Dirac equation, spinors, and elastic continuum model using interactive simulations and quaternion representations.
Riemann, Topology and Physics - Lecture 1
Explore interdisciplinary connections between Riemann geometry, topology, and physics in this doctoral-level lecture by Renzo Ricca at Beijing Institute of Technology.
Foundations of Type-Driven Probabilistic Modelling
Explore type-driven abstractions for probabilistic modelling, covering discrete probability and quasi-Borel spaces. Gain hands-on experience through accompanying exercises for self-study.
Probabilistic Programming Tutorial - Part 2
Explore advanced concepts in probabilistic programming, focusing on practical applications and techniques for scientific computing and data analysis.
Visualization for Data Science: Network Analysis - Part 2
Explore advanced network visualization techniques and data science principles for creating effective visual representations of complex networked systems and relationships.
Foundations of Data Analysis - Lecture 23
Dive into advanced data science concepts through comprehensive statistical analysis, probability theory, and practical applications in this university-level lecture.
Optimization of Radioimmunotherapy of Blood Cancers - Insights from Mathematical Modeling
Explore mathematical modeling approaches to optimize radioimmunotherapy treatments for blood cancers, focusing on tumor immune dynamics and therapeutic effectiveness.
The Geometry of Decision-Making
Explore the fascinating geometry of decision-making in animal behavior with Prof. Iain Couzin's insightful lecture on collective intelligence and movement.
The Mathematical Universe Behind Deep Neural Networks - Rothschild Lecture
Explore the mathematical foundations of deep neural networks, covering functional analysis, harmonic analysis, complex analysis, approximation theory, and more with Professor Helmut Bölcskei.
Elliptic Curves Associated to Two-Loop Graphs and Feynman Diagrams - Rothschild Lecture
Explore elliptic curves in two-loop Feynman diagrams, examining their emergence in cubic hypersurfaces and potential connections to elliptic dilogarithms in quantum field theory amplitudes.
Extraordinary Waves and Math: From Beaches to Photonics - Rothschild Lecture
Explore extraordinary waves, from historical solitary waves to modern solitons, and their applications in water, rogue waves, photonics, and cellular automata.
From the Origins of Twistor Theory to Bi-Twistors and Curved Space-Times
Explore the origins and evolution of twistor theory, from its quantum field theory roots to applications in curved space-times, with Professor Roger Penrose.