Mini-course on Operators on Function Spaces - Part 2
Explore advanced concepts in function spaces, including multiplication operators, Toeplitz operators, and the unilateral shift, with applications in complex analysis and operator theory.
Mini-course on Operators on Function Spaces - Part 1
Explore operators on function spaces, focusing on the Volterra operator's properties, spectrum, and related concepts in functional analysis.
Mini-course on de Branges-Rovnyak Spaces - Part 1
Explore de Branges-Rovnyak spaces, covering history, multipliers, and types of spaces. Learn about Bronzerovnik and range spaces, general lemmas, and boundary behavior.
Building Human Intelligence at Scale, to Save the Next Generation from ChatGPT
Innovative approaches to scale human intelligence and education in the era of AI, drawing from game theory and real-world problem-solving experiences across mathematics, pandemic control, and live math education.
Improved Bounds for the Sunflower Lemma
Explore recent progress on the sunflower conjecture, examining structure vs pseudo-randomness and connections to DNF simplification under random restrictions.
High Dimensional Expanders - Introduction and Motivation
Explore high-dimensional expanders, their applications in error-correcting codes, and the motivations behind this emerging field of mathematics and computer science.
Morning Session- Causality
Explore racial bias in data, examining tensions between quantitative and qualitative approaches. Experts discuss implications for fairness and accuracy in research and decision-making.
Tractable Probabilistic Circuits
Explore recent developments in tractable probabilistic circuit models, their efficient learning from data, and applications in causal inference algorithms for computing marginal probabilities and related queries.
Last-Iterate Convergence in Constrained Min-Max Optimization - SOS to the Rescue
Explore last-iterate convergence in constrained min-max optimization using Sum of Squares (SOS) techniques, with insights from Yale's Yang Cai on adversarial approaches in machine learning.
Constrained Optimization on Riemannian Manifolds
Explore advanced mathematical techniques for solving optimization problems on curved spaces, with applications in machine learning and data analysis.
Tensor Graphical Models for Complex and High Dimensional Data
Explore advanced statistical methods for analyzing complex, high-dimensional data using tensor graphical models, with applications in algorithmic inference and combinatorial structures.
Computational Optimal Transport
Explore geometric methods in optimization and sampling, focusing on computational optimal transport techniques and their applications in machine learning and data analysis.
Sampling Using Diffusion Processes, From Langevin to Schrödinger
Explore diffusion processes in sampling, from Langevin dynamics to Schrödinger bridges, with insights on geometric methods in optimization and their applications.
Geodesic Convexity and Optimization
Explore geodesic convexity and its applications in optimization, delving into geometric methods for solving complex problems in high-dimensional spaces.
Optimization on Manifolds
Learn techniques for optimizing functions on smooth manifolds, exploring applications in machine learning and data science with practical examples and toolbox demonstrations.
Breakthroughs - A Refined Laser Method and Faster Matrix Multiplication
Explore advanced techniques in matrix multiplication, including the refined Laser method, to enhance computational efficiency and speed in mathematical operations.
Deterministic Approximation of the Ising Partition Function
Explore advanced techniques for approximating the Ising partition function, focusing on deterministic methods and their applications in statistical physics and computational complexity.
X-Ramanujan Graphs
Explore X-Ramanujan graphs and their applications in computer science, focusing on advanced concepts beyond randomized rounding and the probabilistic method in graph theory.
Effective Arithmetic Geometry
Explore advanced concepts in arithmetic geometry, focusing on effective methods and their applications in number theory and algebraic geometry.
High Dimensional Robust Sparse Regression
Explore advanced techniques for robust sparse regression in high-dimensional data, focusing on sublinear algorithms and nearest-neighbor search methods.
Efficient Algorithms for Outlier-Robust Regression
Explore advanced techniques for outlier-robust regression, focusing on efficient algorithms and their applications in high-dimensional statistics and machine learning.