
Explore stable homology in metric measure spaces, covering Wasserstein distance, local homology stability, and applications in data analysis and taxonomic classification.

Explores semi-Lagrangian discretisation of Monge-Ampère operator on P1 finite element spaces, discussing challenges and solutions for numerical methods in solving Monge-Ampère equations, with applications in inverse reflector problems.

Explore determinantal point processes, covering conditional measures, sign processes, gamma kernels, Palm measures, and infinite determinantal measures in this advanced mathematics lecture.

Exploration of determinantal point processes, covering theorems, Young graphs, Markov chains, and related mathematical concepts with applications in random matrix theory.

Explore advanced concepts in geometric measure theory, including zero forms, currents, and rectifiability theorems, with applications to area-minimizing problems in mathematics.

Explore advanced concepts in geometric measure theory, including currents, boundaries, and regularity theory for area-minimizing surfaces, with applications to optimal transport problems.

Explore rigidity properties of random graphs in higher dimensions and their connection to matrix completion, with insights on thresholds and optimal conditions.

Explore advanced algorithms for maximizing monotone submodular functions on integer lattices, with applications in machine learning and combinatorial optimization.

Explore over-parameterization in tensor decomposition, comparing lazy training and gradient descent approaches. Discover how gradient descent can leverage low-rank data structure beyond lazy training regimes.

Explore machine learning techniques for modeling disease spread, focusing on data preparation, model training, and interpreting results to inform public health policies.

Explore Bayesian Neural Networks, MCMC methods, and their applications in machine learning with Prof. Radford Neal. Gain insights into flexible modeling and practical implementations.

Explore vector bundles in data science, focusing on synchronization problems and topology-preserving dimensionality reduction. Applications in computational chemistry and dynamical systems are presented.

Explore rigorous data-driven methods for computing spectral properties of Koopman operators in dynamical systems, focusing on Residual Dynamic Mode Decomposition and its applications.

Explore data augmentation MCMC for Bayesian inference from privatized data, focusing on differential privacy challenges and solutions in statistical analysis.

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.

Explore X-Ramanujan graphs and their applications in computer science, focusing on advanced concepts beyond randomized rounding and the probabilistic method in graph theory.

Explore advanced techniques for outlier-robust regression, focusing on efficient algorithms and their applications in high-dimensional statistics and machine learning.

Explore approximate message passing techniques for statistical inference and estimation, focusing on applications in machine learning and data analysis.

Explore stochastic differential mean-field games in this advanced lecture, delving into mathematical models for large-scale strategic interactions and their applications in various complex systems.

Explore modified logarithmic Sobolev inequalities in this theoretical lecture by Prasad Tetali, part of a program on advances in applied probability covering high-dimensional computation and limit theorems.

Exploring cohomological methods to quantify statistical interactions in datasets, linking information theory, statistical physics, and machine learning for improved data analysis and interpretation.