Hausdorff Center for Mathematics Courses

Syntaxes for Binding and Their Semantics

Explore binding syntaxes and their semantics with Guillaume Allais, delving into advanced concepts in programming language theory and formal methods.

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

Verifying Elliptic Curve Computations on Blockchain

Explore the intersection of blockchain technology and elliptic curve cryptography, focusing on verification methods for secure and efficient computations in decentralized systems.

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

Formalisation and Automation of Foundational Theories - A LogiKEy Perspective

Explores formalizing theories beyond mathematics, emphasizing legal and ethical domains for AI control. Discusses intelligent cut-introduction in proof automation and advocates for increased focus on free logic and counter-model finding.

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

Condensed Mathematics in Mathlib

Explore condensed mathematics in Mathlib with Dagur Asgeirsson, delving into advanced mathematical concepts and their implementation in the Lean theorem prover's mathematics library.

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

A Taste of ELPI - Introduction to Extensible Logic Programming Interpreter

Explore ELPI, a programming language for implementing type-checkers and elaborators. Learn its features, applications, and potential in theorem proving and meta-programming.

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

Extending the Lean User Interface with Widgets - A Tutorial

Learn to create interactive visualizations and widgets for the Lean 4 proof assistant, enhancing mathematical communication and exploration of formal proofs and computations.

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

Beautiful Formalizations and Proofs in Mechanized Mathematics

Explore the aesthetics of mathematical formalization, examining how beauty in mathematics adapts to mechanization and automation, with illustrative examples of elegant definitions and proofs.

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

From Informal to Formal Mathematics and Back - Tools for Mathematical Transformation

Tools for transforming informal mathematics to formal and vice versa, aiming to enhance mathematical understanding. Explores Lean blueprint infrastructure and Informal Lean for collaborative formalization projects and customizable proof detailing.

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

Iterated Integrals of Modular Forms in String Theory

Explore iterated integrals of modular forms in string theory, their connection to scattering amplitudes, and the concept of multiple modular values in physics.

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

Iterated Beta Integrals - Generalizing Hyperlogarithms and Beta Integrals

Explore iterated beta integrals, generalizing hyperlogarithms and beta integrals. Discover translation invariance property, yielding equalities between special values and resolving conjectures in mathematics.

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

Depth Reductions of Multiple Polylogarithms - State of the Art Around Goncharov's Depth Conjecture

Explore depth reductions of multiple polylogarithms, focusing on Goncharov's Depth Conjecture and recent advancements in proving related identities and reductions.

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

Modular Regulators and Multiple Modular Values

Explore recent advancements in computing Goncharov regulator integrals for K_4 classes on modular curves, relating them to multiple modular values and single L-values of modular forms.

• YouTube
• 1 hour 8 minutes
• Self-Paced
• Free Video

Beilinson's Conjecture for the Dwork Family

Explores Beilinson's conjecture for the Dwork family, focusing on constructing classes in higher Chow groups and computing their regulators in relation to motivic L-functions and automorphic forms.

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

K2 of Elliptic Curves over Non-Abelian Cubic and Quartic Fields

Explore K_2 of elliptic curves over non-Abelian fields, including constructions, integral elements, and numerical verification of Beilinson's conjecture. Joint work with Brunault, Hang, and Rodriguez Villegas.

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

Minimal Rank of Submatrices of Random Rectangular Matrices

Explore the minimal rank of square submatrices in random rectangular matrices, proving a conjecture on their behavior as matrix dimensions vary.

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