Hausdorff Center for Mathematics Courses

Computation and Formalization - Case Studies in Computational Number Theory

Explore case studies in computational number theory, examining the interplay between computation and formalization in mathematical research and problem-solving.

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

Diagrams and Proofs in Mathematics

Explore the intersection of visual reasoning and mathematical proofs, examining how diagrams enhance understanding and facilitate logical arguments in mathematics.

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

Formalizing Post-Rigorous Mathematics

Explore post-rigorous mathematics and its formalization with Emily Riehl, delving into advanced concepts and their applications in modern mathematical research.

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

Natural Theorem Proving with Naproche-ZF

Explore natural theorem proving using Naproche-ZF, a powerful tool for formalizing mathematical proofs in a language close to human reasoning.

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

Insights into Search Interfaces for Mathematicians

Explore innovative search interfaces tailored for mathematicians, enhancing research efficiency and knowledge discovery in mathematical domains.

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

Large Language Models and Neural Methods in Autoformalisation - Challenges and Complementary Approaches

Explore the role and challenges of LLMs/neural methods in autoformalisation, with insights on complementary symbolic approaches for parsing natural languages.

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

Autoformalisation - Bridging the Gap Between Informal and Formal Proofs

Explore autoformalisation techniques to transform informal mathematical proofs into rigorous, machine-verifiable formal proofs, enhancing theorem-proving capabilities.

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

Hypergraph Rewriting as a Foundation for Diagrammatic Calculus

Explore hypergraph rewriting as a computational foundation for diagrammatic calculus, covering various algebraic structures and featuring a Mathematica paclet implementation.

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

Formalizing Deligne's Theorem in Number Theory

Explore Deligne's theorem in number theory, focusing on its formalization and implications for mathematical research and understanding.

• YouTube
• 1 hour 2 minutes
• Self-Paced
• Free Video

A cb-Bohnenblust-Hille Inequality with Constant One and Its Applications in Learning Theory

Explore the cb-Bohnenblust-Hille inequality with constant one and its applications in quantum learning theory, including extensions to learning low-degree quantum objects.

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

Structure Theorems in Boolean Harmonic Analysis - Part 3

Explore structure theorems in Boolean Function Analysis, including FKN theorem, Friedgut's junta theorem, and sharp threshold theorems, with focus on biased hypercube and symmetric group.

• YouTube
• 1 hour 7 minutes
• Self-Paced
• Free Video

Signal Recovery, Restriction Theory, and Applications - Lecture 4

Explore signal recovery techniques using Fourier transforms and restriction theory. Delve into improved recovery conditions for multiple transmissions and continuous aspects of the problem.

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

Vector-Valued Concentration on the Symmetric Group

Explore vector-valued concentration inequalities for the symmetric group, examining implications for Banach space geometry and building on recent advancements in discrete hypercube analysis.

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

Functional Inequalities in Metric Geometry - Lecture 4

Explore discrete functional inequalities as invariants for bi-Lipschitz embeddings, examining nonlinear type/cotype, convexity, and spectral gap to deduce nonembeddability results for various graphs.

• YouTube
• 1 hour 14 minutes
• Self-Paced
• Free Video

Numerical Investigation of Vortex Formation in Bose-Einstein Condensates

Explore numerical modeling of vortex patterns in Bose-Einstein condensates using finite elements, focusing on mesh size requirements for accurate approximations of superfluid behavior.

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