#Hypersurfaces

Explore a classificação das hipersuperfícies deformáveis com Luis Florit, aprofundando-se em conceitos avançados de geometria diferencial e topologia.

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1 Lesons

1 hour 45 minutes

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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.

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5 Lesons

20 minutes

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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.

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10 Lesons

24 minutes

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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.

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8 Lesons

22 minutes

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IMSA

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.

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15 Lesons

57 minutes

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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.

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8 Lesons

1 hour 16 minutes

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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.

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1 Lesons

43 minutes

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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.

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1 Lesons

59 minutes

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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.

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1 Lesons

57 minutes

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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.

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1 Lesons

1 hour 14 minutes

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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.

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1 Lesons

31 minutes

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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.

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8 Lesons

49 minutes

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International Centre for Theoretical Sciences

Nash's C^1 Isometric Embedding Theorem and the Borisov-Gromov Problem - Lecture 3

Explore Nash's C^1 isometric embedding theorem and the Borisov-Gromov problem in Riemannian geometry. Delve into surprising constructions and open questions linked to the Onsager conjecture.

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1 Lesons

1 hour 53 minutes

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Recent Developments in Constant Mean Curvature Hypersurfaces - Part I

Explore recent developments in constant mean curvature hypersurfaces, focusing on existence theory using min-max methods and discussing open problems in the field.

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23 Lesons

47 minutes

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Interplay Between Notions of Convexity in Complex, Symplectic and Contact Geometries

Explore the interplay between convexity notions in complex, symplectic, and contact geometries. Gain insights into pseudo-convexity, rational convexity, and their geometric counterparts.

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32 Lesons

1 hour 3 minutes

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Recent Developments in Constant Mean Curvature Hypersurfaces - Part II

Explore recent developments in constant mean curvature hypersurfaces, focusing on min-max theorems and the half-volume spectrum. Gain insights into advanced geometric analysis concepts.

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14 Lesons

51 minutes

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Stony Brook Mathematics

Real Loci of Non-Real Varieties - Mathematics Department Colloquium

Explore cooriented submanifolds in real algebraic geometry, focusing on their properties, intersections, and linking numbers. Gain insights into the geometry of pencils and real projective spaces.

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1 Lesons

1 hour 3 minutes

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Periods of Hypersurfaces via Effective Homology

Explore numerical approximations of periods for hypersurfaces using effective homology, enabling computation of algebraic invariants for complex projective varieties.

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1 Lesons

44 minutes

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Centre de recherches mathématiques - CRM

An Excursion into Mean Curvature Flow

Explore mean curvature flow's regularity theory, focusing on distinctions between one-dimensional and higher-dimensional flows in this geometric analysis lecture.

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1 Lesons

59 minutes

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Centre de recherches mathématiques - CRM

Complexity of Submanifolds and Colding-Minicozzi Entropy

Explore Colding-Minicozzi entropy's role in analyzing submanifold complexity and its applications to mean curvature flow singularities and hypersurface simplicity.

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1 Lesons

1 hour 2 minutes

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Minimal Surfaces and the Allen-Cahn Equation on 3-Manifolds

Explore minimal surfaces and the Allen–Cahn equation on 3-manifolds, focusing on recent results and the multiplicity-one theorem in three dimensions.

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1 Lesons

52 minutes

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Higher Gromov-Witten Invariants of Calabi-Yau Threefolds

Explore mixed-spin-p-fields method for Calabi-Yau quintics, its application to BCOV Feynman summation rule, and generalization to hypersurfaces in toric varieties.

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1 Lesons

1 hour

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Metric SYZ Conjecture for Calabi-Yau Manifolds - ICBS 2024

Explore special Lagrangian torus fibrations on Calabi-Yau manifolds, focusing on recent progress and the Fermat family of hypersurfaces.

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1 Lesons

45 minutes

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The Singular Set of Stable Minimal Hypersurfaces

Explore stable minimal hypersurfaces, their singularities, and recent findings on constructing metrics with specific singular sets in higher dimensions.

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1 Lesons

49 minutes

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Generic Dynamics of the Mean Curvature Flows

Explore generic dynamics of mean curvature flows, including perturbation of shrinkers and isolatedness of cylindrical singularities in hypersurface evolution.

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1 Lesons

47 minutes

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Centre International de Rencontres Mathématiques

Quadratic Enumerative Invariants and Local Contributions in Algebraic Geometry