Hausdorff Center for Mathematics Courses

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.

• YouTube
• 1 hour
• Self-Paced
• Free Video

The Restriction Problem and the Polynomial Method - Lecture 2

Explore Stein's restriction conjecture, Kakeya conjecture, and polynomial method in harmonic analysis. Understand wave packet decomposition and intersection of tubes in Fourier analysis.

• YouTube
• 58 minutes
• Self-Paced
• Free Video

The Polynomial Method for Point Counting and Exponential Sums

Explore how auxiliary polynomials aid in counting points on curves over finite fields and estimating exponential and character sums.

• YouTube
• 1 hour 1 minute
• Self-Paced
• Free Video

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.

• YouTube
• 53 minutes
• Self-Paced
• Free Video

Marina Iliopoulou- Three Polynomial Methods for Point Counting, Lecture III

Explore advanced polynomial techniques for solving geometric problems, including Dvir's method, polynomial partitioning, and slice rank method in finite-field settings.

• YouTube
• 1 hour 1 minute
• Self-Paced
• Free Video

Roger Heath-Brown- The Determinant Method, Lecture II

Explore the p-adic Determinant Method theorem and its proof in algebraic geometry, advancing understanding of rational points on varieties.

• YouTube
• 54 minutes
• Self-Paced
• Free Video

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.

• YouTube
• 1 hour 4 minutes
• Self-Paced
• Free Video

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.

• YouTube
• 53 minutes
• Self-Paced
• Free Video

An Introduction to Auxiliary Polynomials in Transcendence Theory - Lecture II

Explore advanced transcendence theory concepts, focusing on auxiliary polynomials and their applications in proving Baker's Theorem and the Masser-Waldschmidt theorem on logarithmic matrices.

• YouTube
• 1 hour 1 minute
• Self-Paced
• Free Video

An Introduction to Auxiliary Polynomials in Transcendence Theory

Explore transcendence theory, focusing on Baker's Theorem and the structural rank conjecture. Learn complex analysis and commutative algebra techniques for proving key results in number theory.

• YouTube
• 59 minutes
• Self-Paced
• Free Video

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.

• YouTube
• 57 minutes
• Self-Paced
• Free Video

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.

• YouTube
• 59 minutes
• Self-Paced
• Free Video

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.

• YouTube
• 59 minutes
• Self-Paced
• Free Video

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.

• YouTube
• 1 hour 1 minute
• Self-Paced
• Free Video

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.

• YouTube
• 1 hour 3 minutes
• Self-Paced
• Free Video