Hausdorff Center for Mathematics Courses

A Type-Theoretic Framework for Certified Meta-programming

Explore a type-theoretic framework for certified meta-programming, delving into advanced concepts and techniques in programming language theory and formal verification.

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

Local Fields in Lean

Explore local fields using the Lean theorem prover, focusing on mathematical foundations and practical applications in number theory and algebraic geometry.

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

Commutative Diagrams in Lean - Demo

Explore commutative diagrams in Lean through a hands-on demonstration, learning practical applications and techniques for mathematical proofs and theorem verification.

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

Inductive Definitions, Predicativity, and the Mahlo Universe

Explore inductive definitions, predicativity, and the Mahlo universe in type theory with Peter Dybjer. Gain insights into advanced mathematical concepts and their applications.

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

Automated Transformation of Hierarchies of Theories in Large Libraries

Explore automated transformations of theory hierarchies in extensive libraries, focusing on efficient methods for managing complex mathematical structures.

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

Annotating and Spotting in Mathematical Corpora - Concepts and Tools

Explore techniques for annotating and spotting mathematical concepts in large text corpora, enhancing research and analysis in mathematical fields.

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

Stéphane Druel: Codimension 1 Foliations with Projectively Flat Tangent Bundle

Explore complex projective manifolds and codimension 1 foliations, focusing on numerically projectively flat tangent bundles and new findings on normal bundles of regular foliations.

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

Moduli of Bundles in Low Genus, Coble Hypersurfaces and Degeneracy Loci

Explore the geometry of moduli spaces for semistable bundles, focusing on Coble hypersurfaces and their connections to Abelian varieties, K3 surfaces, and cubic fourfolds.

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

Marcello Bernardara - Semiorthogonal Decompositions as Markings and Autoequivalences

Explore semiorthogonal decompositions as markings and their role in lifting autoequivalences between triangulated categories, with applications to rational surfaces and non-commutative examples.

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

On the Classification of Compactified Jacobians of Nodal Curves

Explore modular degenerations of Jacobians when smooth curves become nodal, with insights from recent Pagani-Tommasi findings in algebraic geometry.

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

Derived Deformations of Crepant Curves

Explore advanced algebraic geometry concepts, focusing on (-3,1)-curves in CY 3-folds and their noncommutative deformation theory, with applications to string theory predictions.

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

A New Case of BSD Conjecture and Deformation of Line Bundles

Explores a new case of the BSD conjecture for elliptic curves and examines deformation of line bundles in positive and mixed characteristic, applying rigidity properties of variations of Hodge structures.

• YouTube
• 1 hour 6 minutes
• Self-Paced
• Free Video

Orbifold Fundamental Groups of Log Calabi-Yau Surface Pairs, and the Jordan Constant

Explores orbifold fundamental groups of log Calabi-Yau surface pairs, discussing their properties, structure, and connections to other mathematical concepts in algebraic geometry.

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

Weighted Blowups, Wall-Crossing and Weak Factorization

Explore stack-theoretic weighted blowups and their applications in resolution of singularities, destackification, wall-crossings, and weak factorization for more natural and efficient algorithms.

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

Brill-Noether Reconstruction for Fano Threefolds and Applications

Explore Brill-Noether reconstruction for Fano threefolds, focusing on Kuznetsov components and Bridgeland moduli spaces. Learn about applications in categorical Torelli theorems and auto-equivalences.

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