Mathematics

Lecture 05: The Large Sieve

Sharp Projection Theorems, Part 2: AD Regular Case

Lecture 10: Sum-Product Theory

Rolle's Theorem, the Cauchy Mean Value Theorem, L'Hôpital's Rule, and Taylor Expansion

Lecture 13: Open and Closed Sets; Coverings; Compactness

How to Write a Proof; Archimedean Property

A Complexity Lower Bound on Algebra Isomorphisms

Hodge-Theoretic Anabelian Geometry

Trickle-down Theorems for High-dimensional Expanders via Lorentzian Polynomials

Edge Modes on String Horizons

From the Universality to the Kähler Geometry of Random Curves

Fundamental Groups of Algebraic Varieties and the Shafarevich Conjecture

Regularity of Measures Generated by Random Dynamics and Applications

New Methods in Resolution of Singularities

Homogeneous Dynamics, Part 2: Quantitative Ratner Theorems and Projection Theory

Lecture 25: Stochastic Calculus (cont.); Stochastic Differential Equations

The Bourgain Projection Theorem, Part 1 (over the Real Numbers)

Applications of the Large Sieve to Number Theory

Lecture 04: The Fourier Method in Euclidean Space

Volatility Modeling

Stochastic Processes II

Multisummability Relative to Certain Quasianalytic Classes

Lorentzian Conformal Field Theory - Part 1

How to Sketch a Learning Algorithm