Hypersurfaces Courses and Certifications

A Homological Interpretation of Higher Du Bois and Higher Rational Singularities

Explore homological interpretations of higher Du Bois and rational singularities, focusing on hypersurfaces and characteristic classes. Gain insights into advanced algebraic geometry concepts.

• YouTube
• 57 minutes
• On-Demand
• Free Online Course

Michael Penn

Differential Forms - Integrating M-Forms

Explore the concept of integrating differential m-forms on m-dimensional hypersurfaces in R^n, including theory and practical examples to enhance understanding of this advanced mathematical topic.

• YouTube
• 20 minutes
• On-Demand
• Free Online Course

ICTP Mathematics

Singularities of the Mean Curvature Flow of Mean Convex Hypersurfaces - Lecture 5

Explore singularities in mean curvature flow of convex hypersurfaces, covering max inequality, weak solutions, surgeries, and Type 2 singularities with intuitive explanations.

• YouTube
• 1 hour 16 minutes
• On-Demand
• Free Online Course

Institute for Pure & Applied Mathematics (IPAM)

Entropy and C^0 Stability of Hypersurfaces - IPAM at UCLA

Explore entropy's role in hypersurface complexity, focusing on sphere rigidity, stability properties, and generalizations in higher dimensions. Gain insights into cutting-edge research in geometric analysis.

• YouTube
• 24 minutes
• On-Demand
• Free Online Course

Institute for Pure & Applied Mathematics (IPAM)

Topological Properties of Hypersurfaces with Low Entropy - IPAM at UCLA

Explore topological properties of hypersurfaces with low entropy, focusing on Colding-Minicozzi entropy, mean curvature flow, and closed hypersurfaces in this advanced mathematics lecture.

• YouTube
• 22 minutes
• On-Demand
• Free Online Course

ICTP Mathematics

Singularities of the Mean Curvature Flow of Mean Convex Hypersurfaces - Lecture 2

Explore singularities in mean curvature flow of convex hypersurfaces, focusing on advanced mathematical concepts and their implications in geometric analysis.

• YouTube
• 1 hour 14 minutes
• On-Demand
• Free Online Course

International Mathematical Union

Entropy in Mean Curvature Flow

Explore entropy in hypersurfaces and its role in mean curvature flow. Survey recent progress on conjectures about sharp lower bounds and extensions in geometric complexity.

• YouTube
• 43 minutes
• On-Demand
• Free Online Course

ICTP Mathematics

F-Signature of Some Hypersurfaces

Explore F-signature of hypersurfaces with A. Caminata, delving into advanced mathematical concepts and their applications in algebraic geometry.

• YouTube
• 31 minutes
• On-Demand
• Free Online Course

Hausdorff Center for Mathematics

The Restriction Problem and the Polynomial Method - Lecture IV

Explore Stein's restriction conjecture, Kakeya conjecture, and the polynomial method in restriction theory. Understand wave packet decomposition and intersection of tubes in hypersurfaces.

• YouTube
• 59 minutes
• On-Demand
• Free Online Course

Hausdorff Center for Mathematics

The Restriction Problem and the Polynomial Method - Lecture III

Explore Stein's restriction conjecture, Kakeya conjecture, and the polynomial method in restriction theory. Understand wave packet decomposition and intersection of tubes in hypersurfaces.

• YouTube
• 57 minutes
• On-Demand
• Free Online Course

Insights into Mathematics

Curvature for General Algebraic Surfaces - Differential Geometry Lecture 29

Explore curvature formulas for general algebraic surfaces, extending from paraboloids to general quadrics. Learn to compute curvatures for hypersurfaces in affine space.

• YouTube
• 49 minutes
• On-Demand
• Free Online Course