Equidistribution of Expanding Translates of Curves in Homogeneous Spaces
Explores equidistribution of expanding translates of non-degenerate real-analytic curves in semisimple group spaces, extending previous work and applying to Diophantine approximation on matrices.
Don Zagier: Holomorphic Quantum Modular Forms
Explore holomorphic quantum modular forms, their connections to number theory and quantum knot invariants, and applications in odd weight Eisenstein series and Maass cusp forms.
Thermodynamical Formalism and Markoff-Hurwitz Equations
Explore connections between Diophantine geometry and fractals through Markoff-Hurwitz equations, transfer operators, and thermodynamical formalism. Discover links to various mathematical areas.
Horocycle Flow on Moduli Spaces of Translation Surfaces
Explore the intricate dynamics of horocycle flow on moduli spaces of translation surfaces in this advanced mathematics lecture by Jon Chaika.
Roger Heath Brown - The Determinant Method, Lecture III
Explore variants of the determinant method and its application to consecutive "powerful" numbers in algebraic number theory.
An Introduction to Auxiliary Polynomials in Transcendence Theory - Lecture III
Explore transcendence theory, Baker's Theorem, and the structural rank conjecture. Learn complex analysis and commutative algebra techniques for proving lower bounds on logarithmic matrices.
Roger Heath-Brown: The Determinant Method I
Explore rational points on algebraic varieties, their counting methods, and related phenomena in this advanced mathematics lecture by renowned number theorist Roger Heath-Brown.
The Orbit Method, Microlocal Analysis and Applications to L-Functions
Explore quantitative orbit method in microlocal analysis, its applications to representation theory, and implications for L-functions, including moment estimates and subconvex bounds.
New Avenues for the Circle Method - Lecture I
Explore adelic delta-method and nonabelian analogues in analytic number theory. Discover Poisson summation formulae for special varieties to generalize Fourier theory techniques.
Simon Myerson- Repulsion- A How-To Guide, Lecture III
Explore advanced techniques in polynomial analysis, focusing on repulsion methods to improve Birch's circle method for integral zeroes of multivariate polynomials.
Repulsion - A How-To Guide, Lecture I
Explore advanced techniques in polynomial analysis, focusing on repulsion methods to improve Birch's circle method for integral zeroes of multivariate polynomials.
Terence Tao - Pseudorandomness of the Liouville Function
Explore the Liouville pseudorandomness principle and its related conjectures, examining recent progress in understanding the statistical behavior of the Liouville function in number theory.
Sharp Examples for Decoupling and Related Questions
Explore open questions in decoupling, examining sharp examples and their connections to number theory and harmonic analysis. Gain insights into current challenges in the field.
Exponential Sums and Oscillatory Integral - A Unified Approach
Explore a unified approach to exponential sums and oscillatory integrals, delving into advanced mathematical concepts and techniques in this comprehensive lecture.
Relative Trace Formulas for GL - 2 - and Analytic Number Theory
Explore relative trace formulas for GL(2) and their applications in analytic number theory, delving into advanced mathematical concepts and techniques.
The Ratios Conjecture Over Function Fields
Explore the Ratios Conjecture for quadratic L-functions over function fields, including upper bounds for negative moments and partial results for various L-function ratios.
James Maynard: Half-Isolated Zeros and Zero-Density Estimates
Innovative method for detecting zeta function zeros, improving classical zero density results and providing insights into prime number distribution in short intervals.
Regularity of Free Boundaries in Obstacle Problems - Lecture II
Explore free boundary problems in PDE, focusing on regularity in obstacle problems. Learn key results, current research, and open questions in this mathematical field.
Traces of CM Values and Geodesic Cycle Integrals of Modular Functions
Explores generating series of CM value traces and geodesic cycle integrals of modular functions, covering theta lifts and applications to L-series and cycle integral rationality.
The Polynomial Method for Point Counting and Exponential Sums - Lecture IV
Explore advanced techniques for counting points on curves over finite fields and estimating exponential and character sums using auxiliary polynomial families.
Valentin Blomer: The Polynomial Method for Point Counting and Exponential Sums
Explore advanced techniques for counting points on curves over finite fields and estimating exponential sums using families of auxiliary polynomials.