Hausdorff Center for Mathematics Courses

Fourier Interpolation

Explore Fourier uniqueness and interpolation pairs, examining recent progress in explicit constructions and existence results for reconstructing functions from restricted data sets.

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

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.

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

Blow Up Solution for the Energy Critical Heat Equation

Explore classical results and recent developments in blow-up phenomena for critical Fujita equations, including infinite and finite-time blow-up, using the inner-outer method.

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

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.

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

The Restriction Problem and the Polynomial Method - Lecture IV

Explore Stein's restriction conjecture, Kakeya conjecture, and the polynomial method in restriction theory. Understand wave packet decomposition and intersection of tubes in hypersurfaces.

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

The Restriction Problem and the Polynomial Method - Lecture III

Explore Stein's restriction conjecture, Kakeya conjecture, and the polynomial method in restriction theory. Understand wave packet decomposition and intersection of tubes in hypersurfaces.

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

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