Singularity Theory Courses and Certifications

ICTP Mathematics

F-Singularities — Applications of Characteristic P Methods to Singularity Theory

Explore applications of characteristic p methods in singularity theory, focusing on F-singularities and their role in commutative algebra and algebraic geometry.

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

Institut des Hautes Etudes Scientifiques (IHES)

Birational and Singularity Invariants from Non-Commutative Hodge Theory

Explore new additive invariants of smooth projective varieties called Hodge atoms, their applications to birational equivalence, and novel singularity invariants in algebraic geometry.

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

IMSA

Geometric Problems in Machine Learning and Singularity Theory - Applications to Neural Networks

Explore geometric aspects of machine learning through matrix multiplication and singularity theory, focusing on Bayesian Learning Theory and computational challenges in Linear Neural Networks.

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

Centre International de Rencontres Mathématiques

Motivic Milnor Fibre and Logarithmic Geometry

Delve into advanced mathematical concepts exploring motivic and topological Milnor fibre through logarithmic geometry, focusing on regular functions with normal crossing singularities.

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

IMSA

Three Problems on Characteristic Classes of Singular Varieties

Explore three fundamental research problems in characteristic classes of singular varieties, including smoothings, vector field indices, and Milnor classes in advanced mathematics.

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

International Centre for Theoretical Sciences

Mirror Symmetry for Character Varieties and Field Theory by Sergey Galkin

Explore mirror symmetry for character varieties, using threespace mirrors to construct SU(2) character variety mirrors on Riemann surfaces, with applications in topological field theory and random walks.

• YouTube
• 3 hours 12 minutes
• On-Demand
• Free Video

Institut des Hautes Etudes Scientifiques (IHES)

The Geometric Ideas of René Thom Related to Manifolds with Singularities

Explore René Thom's groundbreaking papers on transversality, cobordism, and manifolds with singularities, revealing their geometric insights and impact on mathematical understanding.

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

ICTP Mathematics

Singularity Invariants in Positive Characteristic

Explore singularity invariants in positive characteristic mathematics, focusing on advanced concepts and their applications in algebraic geometry and related fields.

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

IMSA

Surface Quotient Singularities and Big Cotangent Bundle

Explore hyperbolic properties of surfaces with big cotangent bundle, including the Green-Griffiths-Lang conjecture and a new bigness criterion for orbifold surface resolutions.

• YouTube
• 1 hour 14 minutes
• On-Demand
• Free Video

IMSA

Geometry, Topology, Group Actions, and Singularities in the Americas

Explore the intersection of geometry, topology, group actions, and singularity theory in this conference talk, fostering collaboration among experts across the Americas and beyond.

• YouTube
• 1 hour 14 minutes
• On-Demand
• Free Video

IMSA

Andras Nemethi- Multivariable Poincaré Series of Complex Singularities

Explore multivariable Poincaré series in complex singularities with Andras Nemethi. Delve into advanced mathematical concepts at the intersection of geometry, topology, and singularity theory.

• YouTube
• 1 hour 7 minutes
• On-Demand
• Free Video

IMSA

Semistable Reduction - A Progress Report

Explore recent advancements in resolving singularities of complex varieties, including functorial weak semistable reduction and the proof of the semistable reduction conjecture.

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

IMSA

Blow Up Formulae and Invariants II - Dimension Theory

Explore numerical invariants in meromorphic connections, their relation to singularity theory, and applications to non-rationality criteria for Fano varieties.

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

Joint Mathematics Meetings

Extremal Singularities

Explore extremal singularities in algebraic geometry, focusing on hypersurface singularities, cone singularities, and their classification, with insights into cubic surfaces and characteristic p phenomena.

• YouTube
• 58 minutes
• On-Demand
• Conference Talk

IMSA

Fractal Dimensions of Critical Loci in Algebraic Geometry

Explore fractional dimensions in mathematics, focusing on critical loci of holomorphic functions. Discover theories from algebraic geometry, singularity theory, and more, with the smallest non-zero dimension at 1/3.

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