Sums in Progressions to Squarefree Moduli Among Polynomials Over a Finite Field
Explore polynomial sums in progressions to squarefree moduli over finite fields, covering Fourier analysis, polynomial anatomy, and arithmetic functions.
The Restriction Problem and the Polynomial Method - Lecture I
Explore Stein's restriction conjecture, the Kakeya conjecture, and the polynomial method in harmonic analysis. Learn about wave packet decomposition and its applications in studying hypersurface-supported functions.
On the Riemann Zeta-Function, Fourier Optimization and Quadratic Forms
Explore the Riemann zeta-function, Fourier analysis, and quadratic forms in number theory. Delve into Selberg's theorem, Berry's conjecture, and representation of integers by quadratic forms.
Nikodym Sets and Maximal Functions Associated with Spheres - Lecture 1
Explore advanced harmonic analysis concepts: Nikodym sets and maximal functions associated with spheres. Gain insights from expert Jongchon Kim in this comprehensive lecture.
Nikodym Sets and Maximal Functions Associated with Spheres - Lecture 2
Explores advanced concepts in harmonic analysis, focusing on Nikodym sets and maximal functions related to spheres. Builds on previous lecture, deepening understanding of these mathematical structures.
Sharp Fourier Restriction onto the Parabola and the Cubic Monomial - Lecture 1
Explore sharp Fourier restriction estimates for parabola and cubic monomial curves, advancing understanding in harmonic analysis and algebraic geometry applications.
Sharp Fourier Restriction onto the Parabola and the Cubic Monomial - Lecture 2
Explores sharp Fourier restriction estimates for parabola and cubic monomial curves, advancing understanding of harmonic analysis and polynomial methods in mathematical research.
The Variance of a General Class of Multiplicative Functions in Short Intervals
Explore the variance of multiplicative functions in short intervals, applying Fourier analysis and rational point counting to derive asymptotic estimates for k-free numbers and other functions.
Distance Problems and Their Many Variants - Lecture 2
Explores distance problems in harmonic analysis, focusing on variants and recent developments. Discusses polynomial methods and discrete approaches, offering insights for researchers in the field.
Nikodym Sets and Maximal Functions Associated with Spheres - Lecture 2
Explores advanced concepts in harmonic analysis, focusing on Nikodym sets and maximal functions related to spheres. Builds on recent developments in the field.
How Much Math Do You Need to Know to Solve an Initial Value Problem - SIAM PDE Seminar
Explore mathematical techniques for solving nonlinear Schrödinger equations, from harmonic analysis to dynamical systems, focusing on long-time dynamics and energy transfer in initial value problems.
Fourier Analysis of Equivariant Quantum Cohomology II - 1-27-2024
Explore advanced concepts in Fourier analysis and equivariant quantum cohomology, building on previous research in homological mirror symmetry and mathematical physics.
Fourier Analysis of Equivariant Quantum Cohomology - Part I
Explore Teleman's conjecture, equivariant quantum cohomology, and Fourier spectral analysis in symplectic geometry. Gain insights into D-module decomposition for projective bundles and blowups.
Towards a Formalized Proof of Carleson's Theorem
Explores formalizing Carleson's theorem on Fourier series convergence, discussing its significance, challenges, and recent generalizations in metric spaces using the Lean theorem prover.
Fourier Uniformity of Multiplicative Functions
Explore Fourier uniformity of multiplicative functions, its connection to prime number distribution, and related conjectures like Chowla and Sarnak in this advanced mathematics lecture.
A Summary of Methods for Solving Differential Equations Involving Automorphic Forms
Explore advanced techniques for solving differential equations with automorphic forms, enhancing mathematical problem-solving skills in complex analysis and number theory.
Introduction to Green's Function: 2-D Example - Evaluating Constants - Part 1
Explore Green's Function in 2D, focusing on evaluating constants. Learn key concepts and techniques for solving complex mathematical problems.
Microlocalization and General Linear Combinations
Explore advanced mathematical concepts of microlocalization and general linear combinations in this concise talk by Bradley Dirks from the Institute for Advanced Study.
Singular Integrals - Classical and Dunkl Setting
Explore singular integrals in classical and Dunkl contexts, gaining insights into advanced mathematical concepts and their applications in analysis.
A Gentle Introduction to Hardy Spaces
Explore Hardy spaces through a gentle introduction, covering fundamental concepts and applications in complex analysis and functional theory.
The Method of Gauge Transform II
Explorez la méthode de transformation de jauge et son application aux problèmes spectraux périodiques et ergodiques avec Jeffrey Galkowski.