Affine W-algebras - Lecture 4
Explore affine W-algebras construction via quantum Hamiltonian reduction. Delve into vertex algebra theory, Virasoro minimal models, and tensor categories of W-algebra representations.
Affine W-algebras - Lecture 3
Explore affine W-algebras construction via quantum Hamiltonian reduction. Delve into vertex algebra theory, Virasoro minimal models, and tensor categories of W-algebra representations.
Towards the Quantum Exceptional Series
Explore continuous families of planar algebras interpolating exceptional Lie algebras and their quantum counterparts. Discover a potential new exceptional knot polynomial through skein theoretic analysis.
Smooth 2-Groups and Their Principal Bundles
Explore smooth 2-groups and principal bundles in Lie groupoids. Learn about categorical generalizations of groups and their applications in mathematics.
Affine W-algebras - Lecture 2
Explore affine W-algebras through quantum Hamiltonian reduction. Delve into vertex algebra theory, Virasoro minimal models, and tensor categories of W-algebra representations.
Affine W-algebras - Part I
Explore affine W-algebras construction via quantum Hamiltonian reduction. Delve into vertex algebra theory, Virasoro minimal models, and tensor categories of W-algebra representations.
New Isoperimetric Inequalities and Their Applications to Systolic Geometry and Minimal Surfaces
Explore new isoperimetric inequalities for k-dimensional submanifolds, their applications to systolic geometry, and implications for minimal submanifolds in this mathematical colloquium.
W-algebras and Lax Operators - Lecture 5
Explore finite W-algebras, twisted Yangians, and Lax operators. Investigate relationships between these mathematical structures in quantum algebra and integrable systems.
W-algebras and Lax Operators - Lecture 3
Explore finite W-algebras, twisted Yangians, and Lax operators. Investigate relationships between these mathematical structures using advanced algebraic techniques.
Bayesian Markov Switching Space-Time Model for Zika in Colombia
Explorez un modèle bayésien spatio-temporel à changement de régime markovien pour l'épidémie de Zika en Colombie, examinant les facteurs d'émergence, de transmission et de persistance de la maladie.
Mathematics for Deep Neural Networks: Theory for Shallow Networks - Lecture 2 of 5
Explore universal approximation theorem, proof strategies, and approximation rates for shallow networks. Learn estimation methods and data fitting techniques.
Mathematics for Deep Neural Networks: Advantages of Additional Layers - Lecture 3
Explore the mathematical advantages of deep neural networks over shallow networks, focusing on localization, approximation capabilities, and the Kolmogorov-Arnold theorem.
Mathematics for Deep Neural Networks: Statistical Theory for Deep ReLU Networks - Lecture 4
Explore statistical theory for deep ReLU networks, focusing on risk bounds, approximation properties, and sparse connections in neural network architectures.
Mathematics for Deep Neural Networks: Energy Landscape and Open Problems - Lecture 5
Explore the energy landscape of deep neural networks and future challenges in statistical theory, focusing on gradient descent methods and important developments.
Sharp Oracle Inequalities for Non-Convex Loss - Lecture 1
Explore sharp oracle inequalities for non-convex loss in M-estimation, focusing on regularization techniques and sparsity-inducing penalties like the l₁-penalty in Lasso.
The Debiased Lasso - Lecture 3
Explore sparsity in high-dimensional statistics, focusing on confidence intervals and the Debiased Lasso method for parameter estimation and asymptotic normality.
Spectral Methods Meets Asymmetry: Two Recent Stories - Lecture 4
Explore spectral methods for asymmetric data matrices, covering top-K ranking and matrix de-noising. Learn advantages over traditional approaches in data analysis and estimation.
On the Critical Points of Steklov Eigenfunctions
Explore critical points of Steklov eigenfunctions on Riemannian manifolds, examining relationships between eigenfunction indexes, boundary behavior, and Euler characteristics.
An Overdetermined Eigenvalue Problem and the Critical Catenoid Conjecture
Explore an overdetermined eigenvalue problem on the two-sphere and its implications for characterizing the critical catenoid as a unique embedded free boundary minimal annulus.
A Weighted Reilly Formula for Differential Forms and Sharp Steklov Eigenvalue Estimates - Lecture
Explore weighted Reilly formula for differential forms and its applications in sharp Steklov eigenvalue estimates. Gain insights into spectral geometry and related open problems.
New Minimal Surfaces via Equivariant Eigenvalue Optimization - Part II
Explore equivariant optimization of Laplace and Steklov eigenvalues on surfaces to construct embedded minimal surfaces in 3-sphere and 3-ball. Discover new insights into geometric analysis and topology.