Hausdorff Center for Mathematics Courses

Functional Inequalities in Metric Geometry - Part I

Explore discrete functional inequalities as invariants in bi-Lipschitz embeddings, examining nonlinear type/cotype, convexity, and spectral gap for nonembeddability insights.

• YouTube
• 1 hour 9 minutes
• On-Demand
• Free Video

Functional Inequalities in Metric Geometry - Part II

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 16 minutes
• On-Demand
• 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
• On-Demand
• 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
• On-Demand
• 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
• On-Demand
• 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
• On-Demand
• Free Video

Numerical Multiscale Methods for Nonlinear and Randomly Perturbed Problems

Explore efficient numerical methods for complex multiscale problems, including nonlinear systems and random perturbations, using Localized Orthogonal Decomposition techniques.

• YouTube
• 50 minutes
• On-Demand
• Free Video

Multiscale Methods for High-Contrast Heterogeneous Sign-Changing Problems

Explore multiscale methods for high-contrast heterogeneous sign-changing problems, focusing on CEM-GMsFEM tailored for these scenarios. Learn about numerical effectiveness and error estimation.

• YouTube
• 44 minutes
• On-Demand
• Free Video

Challenges in Formalising Recent Results in Formal Language Theory

Explore challenges in formalizing recent results linking formal language theory and computational group theory, with insights on making proofs more amenable to formalization.

• YouTube
• 51 minutes
• On-Demand
• Free Video

On the Completeness of Interpolation Algorithms

Explore mathematical interpolation algorithms, their completeness, and applications in computational mathematics with insights from recent research publications.

• YouTube
• 22 minutes
• On-Demand
• Free Video

A View from the IMU Committee on Electronic Information and Communication

Insights into electronic information and communication in mathematics from the perspective of the IMU committee, exploring current trends and future directions.

• YouTube
• 43 minutes
• On-Demand
• Free Video

Abduction Prover in Isabelle/HOL - Automated Theorem Proving and Conjecturing

Explore abduction provers in Isabelle/HOL with Yutaka Nagashima, covering theory, practical demonstrations, and insights into automated theorem proving.

• YouTube
• 50 minutes
• On-Demand
• Free Video

Mechanising Gödel-Löb Provability Logic in HOL Light

Explore the mechanisation of Gödel–Löb Provability Logic in HOL Light, delving into formal proofs and theorem verification techniques for modal logic systems.

• YouTube
• 59 minutes
• On-Demand
• Free Video

Algebraic Theorems in PVS

Explore algebraic theorems using the PVS theorem prover. Learn to formalize and verify mathematical concepts in a rigorous computational environment.

• YouTube
• 51 minutes
• On-Demand
• Free Video

Gauss Realisability Conditions - From Error Correction to Formalization

Explore Gauss Realisability conditions, their applications in error correction, and the journey towards formalization in mathematics, offering insights into advanced mathematical concepts.

• YouTube
• 45 minutes
• On-Demand
• Free Video