Singularity Theory Courses and Certifications

Centre International de Rencontres Mathématiques

Complete Outer Lipschitz Classification of Complex Surface Singularities

Explore the complete outer Lipschitz classification of complex surface singularities in this advanced mathematical presentation by Anne Pichon.

• YouTube
• 1 hour 4 minutes
• On-Demand
• Free Video

Centre International de Rencontres Mathématiques

Teissier Singularities in Positive Characteristic Mathematics

Delve into the mathematical theory of Teissier singularities and their crucial role in positive characteristics, exploring their relationship to quasi-ordinary singularities in characteristic zero resolution.

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

Centre International de Rencontres Mathématiques

Resolution of Foliated Varieties by Torus Actions - A Desingularization Approach

Delve into advanced mathematical concepts of resolving singular foliations through torus actions, focusing on principalization of ideals and desingularization of Darboux totally integrable foliations.

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

Fields Institute

Lipschitz Geometry and Combinatorics of Abnormal Surface Germs

Explore Lipschitz geometry and combinatorics of abnormal surface germs in this advanced mathematics talk by Andrei Gabrielov from Purdue University.

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

IMSA

Cohomological Connectivity of Perturbations of Map-Germs

Delve into advanced mathematical concepts exploring cohomological connectivity in holomorphic finite map-germs, focusing on perturbation theory and discriminant analysis in complex geometry.

• YouTube
• 1 hour 20 minutes
• On-Demand
• Free Video

IMSA

Le-Greuel Type Formulas on Stratified Spaces

Explore advanced mathematical concepts in Le-Greuel formulas, focusing on their extension to stratified spaces and applications in singularity theory through Nash modification and local Riemann-Roch formulas.

• YouTube
• 1 hour 3 minutes
• On-Demand
• Free Video

IMSA

Computing Higher Thom Polynomials of Multisingularities

Explore advanced mathematical concepts in computing higher Thom polynomials, focusing on singularity germs, interpolation methods, and stable envelope techniques for multisingularities.

• YouTube
• 1 hour 1 minute
• On-Demand
• Free Video

IMSA

Vanishing Arcs for Isolated Plane Curve Singularities

Delve into advanced singularity theory concepts, exploring variation operators, Milnor fiber homology, and framed mapping class groups in plane curve singularities.

• YouTube
• 1 hour 4 minutes
• On-Demand
• Free Video

IMSA

The Logarithmic Smoothness of Non-d-Semistable Normal Crossing Schemes

Explore advanced logarithmic geometry through sharp lax log structures on normal crossing schemes, extending beyond d-semistable cases with infinitesimal lifting properties.

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

IMSA

F-bundles and A-model F-bundles for Hodge Atoms

Explore F-bundles and their role in defining A-model F-bundles essential for understanding Hodge atoms in singularity theory.

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

IMSA

Mutations and Deformations of Gorenstein Toric Varieties via Log Resolutions

Explore mutations and deformations of Gorenstein toric varieties through logarithmic geometry, connecting mirror symmetry concepts with new mathematical approaches.

• YouTube
• 1 hour 1 minute
• On-Demand
• Free Video

IMSA

A'Campo Spaces and Their Applications

Explore A'Campo spaces in singularity theory, their symplectic extensions, and applications to monodromy dynamics and Zariski multiplicity conjecture.

• YouTube
• 1 hour 1 minute
• On-Demand
• Free Video

IMSA

Degenerations of del Pezzo Surfaces with Only Wahl Singularities

Explore the classification of del Pezzo surface degenerations with Wahl singularities, extending Markov number theory to complex algebraic geometry applications.

• YouTube
• 1 hour 1 minute
• On-Demand
• Free Video

IMSA

Twistor Space of Universal Unfolding of A_n Singularity and Beyond

Explore the twistor space construction connecting stability conditions and cluster Poisson varieties through A_n singularities and quiver theory.

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

IMSA

cAn Singularities Revisited

Explore quasihomogeneous cAn singularities through birational geometry and symplectic cohomology of Milnor fibres in this advanced mathematical research presentation.

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