George Willis, Pierre-Emmanuel Caprace - A Totally Disconnected Invitation to Locally Compact Groups
Explore topological groups, focusing on locally compact and totally disconnected types. Discover recent advances in theory, simple groups, local structure, and comparisons with linear groups.
Integrable Fluctuations in One-Dimensional Random Growth
Explores recent findings on asymptotic fluctuations in KPZ universality class, covering random growth models, directed polymers, and particle systems. Discusses solvability, explicit formulas, and integrable differential equations.
KPZ Limit Theorems
Explores KPZ universality in particle systems, growth models, and polymers, discussing limit theorems, integrable methods, and recent results on periodic domains.
Tianyi Zheng- Asymptotic Behaviors of Random Walks on Countable Groups
Explore asymptotic behaviors of random walks on countable groups, covering Kesten's theorems, entropy, and applications to group theory and graph analysis.
Andrew Thomas - Functional Limit Theorems for Euler Characteristic Processes
Explore functional limit theorems for Euler characteristic processes in Vietoris-Rips complexes, covering strong law of large numbers and central limit theorem in the thermodynamic regime.
Takashi Owada - Limit Theorems for Topological Invariants of the Dynamic Multi-Parameter Simplicial Complex
Explore topological invariants in dynamic multi-parameter simplicial complexes, covering connectivity, probability, and limiting processes in applied algebraic topology.
Homological Percolation: The Formation of Giant Cycles
Explore homological percolation, analyzing giant cycles in random structures and their phase transitions. Learn to differentiate signal from noise in persistence diagrams and discover connections to Euler characteristic curves.
Role of Mathematics in Data Science and How to Learn - Data Science
Explore the essential mathematical concepts for data science, including statistics, probability, and normal distribution, with practical examples and problem-solving exercises.
Persistence and First-Passage Properties of Stochastic Processes by Satya N Majumdar
Explore stochastic processes, focusing on persistence and first-passage properties. Covers applications in chemistry, finance, astrophysics, and more. Examines Markov processes and run-and-tumble particle models.
The Selberg Sieve - Lecture 1
Explore the Selberg sieve method in number theory, covering heuristics, probability, and applications to twin primes. Learn about sieve techniques for detecting primes in sequences.
Ricci Curvature and Functional Inequalities for Interacting Particle Systems
Explore entropic Ricci curvature bounds and their applications to interacting particle systems, focusing on functional inequalities and convergence rates to equilibrium in nonnegative curvature scenarios.
Determinantal Point Processes - II
Exploration of determinantal point processes, covering theorems, Young graphs, Markov chains, and related mathematical concepts with applications in random matrix theory.
Color-Position Symmetry in Interacting Particle Systems
Explore color-position symmetry in particle systems, covering probability, partition functions, and stochastic processes. Gain insights into ASEP and simulation techniques.
Percolation on Hyperbolic Poisson-Voronoi Tessellations
Explore percolation on hyperbolic Poisson-Voronoi tessellations, resolving conjectures about critical probability behavior and its dependence on Poisson process intensity.
Tomasz Tkocz - Khinchin Inequalities With Sharp Constants
Explore sharp moment comparison inequalities for weighted sums of i.i.d. random variables, covering classical and recent results on Khinchin inequalities and their applications.
Panorama of Mathematics - Laure Saint-Raymond
Explore particle dynamics, chaos theory, and statistical mechanics in large systems. Gain insights into ergodicity, entropy, and the Boltzmann equation with mathematician Laure Saint-Raymond.
Panorama of Mathematics - Darrell Duffie
Explore price transparency in over-the-counter financial markets, focusing on federal funds, contacting investors, uncertainty, and benchmark manipulation.
Statistics and Data Analysis for Cosmology - Lecture 1
Explore probability concepts in cosmology, including joint and conditional probability, PDFs, independence, Bayes' theorem, and data modeling for analyzing cosmic phenomena.
Dynamical Phase Transitions in Markov Processes by Hugo Touchette
Explore dynamical phase transitions in Markov processes, contrasting with equilibrium transitions and examining a Brownian motion model showcasing localization-delocalization phenomena.
The Planar Stochastic Heat Equation and the Directed Landscape
Explore stochastic heat equations and directed landscapes in probability theory, focusing on models, solutions, and applications in mathematical physics and statistical mechanics.
The Medical Test Paradox and Redesigning Bayes' Rule
Explore the medical test paradox and a redesigned Bayes' rule, focusing on likelihood ratios and Bayes factors to enhance understanding of conditional probability in diagnostic testing.