Hypersurfaces Courses and Certifications

Stony Brook Mathematics

Curvature-Homogeneous Hypersurfaces in Space Forms

Explore the complete classification of curvature-homogeneous hypersurfaces in constant curvature spaces, including exotic non-homogeneous solutions discovered through advanced techniques.

• YouTube
• 1 hour 11 minutes
• On-Demand
• Free Video

INI Seminar Room 2

Moduli of Coverings Branched Along Hypersurfaces

Explore the geometry of moduli spaces and coverings branched along hypersurfaces, examining their topology, birational geometry, and connections to K-polystable log del Pezzo surfaces.

• YouTube
• 1 hour 10 minutes
• On-Demand
• Free Video

Harvard CMSA

Stable Minimal Hypersurfaces in 4-Manifolds

Explore advanced mathematical concepts of stable minimal hypersurfaces, focusing on their behavior in 4-manifolds and comparison theorems for positively curved spaces.

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

BIMSA

Optimal Transport Between Algebraic Hypersurfaces

Explore optimal transport theory applied to algebraic hypersurfaces through advanced mathematical analysis and geometric insights.

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

Stony Brook Mathematics

The Stable Bernstein Theorem for Minimal Hypersurfaces

Delve into advanced geometric analysis exploring stable minimal hypersurfaces, focusing on recent developments in the Bernstein problem and its connections to Riemannian manifold geometry.

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

IMSA

Algebraic Hyperbolicity of Hypersurfaces and Lang-Type Conjectures

Delve into algebraic hyperbolicity of hypersurfaces and Lang-type conjectures, exploring fundamental concepts and recent developments in algebraic geometry with Professor Coskun.

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

IMSA

Contact Loci of Arcs - Topology and Floer Theory in Hypersurfaces

Explore the topology of contact loci in hypersurfaces, examining their relationship with Floer theory and log minimal models while delving into motivic integration concepts.

• YouTube
• 1 hour 2 minutes
• On-Demand
• Free Video

International Centre for Theoretical Sciences

Biconservative Hypersurfaces in the Pseudo-Euclidean Space

Explore biconservative hypersurfaces in pseudo-Euclidean space through advanced differential geometry concepts and their mathematical properties.

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

International Centre for Theoretical Sciences

Generic Regularity for Minimizing Hypersurfaces Up to Dimension 11 - Lecture 3

Explore advanced regularity theory for minimizing hypersurfaces in dimensions up to 11, focusing on generic conditions and analytical techniques in geometric measure theory.

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

ICTP Mathematics

Basic Notions Seminar on Mean Curvature Flow of Closed Hypersurfaces

Explore mean curvature flow of closed hypersurfaces, from basic definitions to advanced topics, including variational aspects and key theorems like Grayson's and Huisken's.

• YouTube
• 1 hour 17 minutes
• On-Demand
• Free Video

Institute for Advanced Study

Existence Theory of Minimal Hypersurfaces - Fernando Marquez

Explore the existence theory of minimal hypersurfaces, covering minimax theorems, space of cycles, and volume spectrum. Gain insights into Ricci curvature and generic metrics.

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

ICTP Mathematics

Singularities of the Mean Curvature Flow of Mean Convex Hypersurfaces

Explore mean curvature flow singularities in mean convex hypersurfaces. Learn about extrinsic curvature flows and their applications in geometry and topology.

• YouTube
• 1 hour 2 minutes
• On-Demand
• Free Video

Fields Institute

Studying the Birational Geometry of Complex Fano Hypersurfaces via Characteristic

Explore complex Fano hypersurfaces' birational geometry through characteristic analysis, delving into advanced mathematical concepts and their applications in algebraic geometry.

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

Institute for Pure & Applied Mathematics (IPAM)

Null Hypersurfaces and the Penrose Inequality for a Perturbed Schwarzschild Black Hole

Explores the Penrose inequality in general relativity, focusing on null hypersurfaces and perturbed Schwarzschild black holes. Discusses recent breakthroughs and ongoing challenges in this field of gravitational physics.

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

IMSA

Homological Mirror Symmetry - Functorial Mirror Symmetry for Very Affine Hypersurfaces

Explore functorial mirror symmetry for very affine hypersurfaces, examining Auroux's conjectures and their modifications to account for derived structures in complement mirrors.

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