Transseries, Model Theory, and Hardy Fields - Lecture 1
Explore advanced mathematical concepts in transseries, model theory, and Hardy fields with Professor Lou van den Dries in this graduate-level lecture series.
Surreal Numbers and Transseries - Lecture 1
Explore surreal numbers and transseries in this graduate-level lecture, delving into advanced mathematical concepts and their applications in asymptotic analysis.
From Newton to Boltzmann - Fluctuations and Large Deviations in Hard Sphere Gas Dynamics
Explore macroscopic fluctuations in hard sphere gases, including deviations from the Boltzmann equation, central limit theorem, and large deviation bounds in the Boltzmann-Grad limit.
A Generalized Central Limit Conjecture for Convex Bodies
Explore a generalized central limit theorem for convex bodies, its connection to the KLS conjecture, and implications for asymptotic convex geometry in this advanced mathematics lecture.
Dimer Models and Random Tilings - Part 1
Explore dimer models and random tilings with Cédric Boutillier. Learn about Kasteleyn's theory, combinatorial correspondences, and asymptotic methods for studying perfect matchings on lattices.
Perfect t-embeddings of Uniform Aztec Diamond Graphs
Explores t-embeddings of uniform Aztec diamond graphs, providing new formulas and asymptotic analysis to prove convergence of dimer model height fluctuations to a Gaussian Free Field.
Dimer Models and Random Tilings - Part 2
Explore dimer models, perfect matchings, and tilings with advanced mathematical tools. Delve into Kasteleyn's theory, combinatorial correspondences, and asymptotic methods for large-scale limits.
Fluctuations of Linear Eigenvalue Statistics in Sample Covariance Matrices - Tensor Product Data
Explore fluctuations in linear eigenvalue statistics of sample covariance matrices with tensor product data, comparing normal and uniform distributions on unit sphere.
Eulerian Magnitude Homology - Subgraph Structure and Random Graphs
Explore connections between magnitude homology group ranks and graph substructures. Introduces eulerian and discriminant magnitude homology, relating them to subgraph counts and random graph models.
A Survey of Central Limit Theorems in Number Theory
Explore key central limit theorems in number theory, examining their applications and implications for understanding mathematical distributions and patterns.
Hypergeometric Matrix Models and their Duals
Explore hypergeometric functions of complex matrices, their connections to algebraic combinatorics, and a novel approach to approximating these functions using Hurwitz theory concepts.
Global Asymptotics of Jack-Deformed Random Young Diagrams via Lukasiewicz Paths
Explores discrete analogues of log-gas systems, examining universal formulas for global asymptotics in various temperature regimes, using weighted lattice paths and revealing phase transition phenomena.
Growth and Tensor Products in Representation Theory - Lecture 1
Explore asymptotic counting of summands in tensor products of representations, with numerous examples to illustrate concepts in symmetric tensor categories and representation theory.
The Asymptotics of Betti Numbers in Preferential Attachment Clique Complexes
Explore the higher-order connectivity of preferential attachment networks through Betti numbers, examining growth rates and asymptotic behavior in this advanced mathematical analysis.
Asymptotic Lower Bounds for Number Fields Generated by Plane Curves
Explore asymptotic lower bounds for number fields derived from plane curves, delving into advanced mathematical concepts and their applications in algebraic geometry.
Geometry of Dimer Models
Explore the asymptotic phenomena of random dimer coverings on large planar graphs, focusing on Aztec diamonds and their connection to Riemann surface geometry in this advanced mathematics lecture.
Finite Point Blowup for the Critical Generalized Korteweg-de Vries Equation
Explore finite point blowup in critical generalized KdV equations, uncovering new blow-up dynamics and rates. Gain insights into recent advancements in nonlinear wave theory.
Computing Stokes Constants with Quantum Modularity
Explore quantum modularity's role in computing Stokes constants, delving into advanced mathematical concepts and their applications in theoretical physics.
Unique Continuation Through Natural Boundaries Using Resurgence
Explore unique continuation through natural boundaries using resurgence, delving into advanced mathematical concepts and techniques for analyzing complex functions and their behavior.
Modular Resurgence for Integrated Correlators at Large N
Explore modular resurgence in integrated correlators at large N, delving into advanced mathematical concepts and their applications in theoretical physics.
An Introduction to Resurgence Theory - Lecture 3
Explore advanced mathematical concepts in resurgence theory, delving into complex analysis and asymptotic expansions for a deeper understanding of analytical functions.