Polygonal Presentations: Classification of Surfaces

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Related lectures (28)

Topology of Riemann Surfaces

Covers the topology of Riemann surfaces and the concept of triangulation using finitely many triangles.

Graph Algorithms: Modeling and Traversal

Covers graph algorithms, modeling relationships between objects, and traversal techniques like BFS and DFS.

Bounding the Poisson bracket invariant on surfaces

Covers the concept of bounding the Poisson bracket invariant on surfaces, exploring joint work with A. Logunov and S. Tanny.

Building surfaces from equilateral triangles

Explores the construction of Riemann surfaces from equilateral triangles and the dynamics of finite-type maps.

Graph Representation and Traversal

Introduces graph theory basics, graph representation methods, and traversal algorithms like BFS and DFS.

Differential Forms Integration

Covers the integration of differential forms on smooth manifolds, including the concepts of closed and exact forms.

Developable Surfaces and Parametrization

Explores developable surfaces, parametrization, equations verification, and conformally flat surfaces.

Surface Classification

Covers the classification of surfaces using polygonal presentations and homeomorphism.

Surface Orientation Analysis

Discusses surface orientation analysis, normal vectors, and Green's identities application.

Connected Sum of Torus and RP2

Explores the connected sum of surfaces, focusing on torus and RP2, highlighting the resulting homeomorphism with the sphere.

Graph Traversal: BFS and DFS

Covers Breadth-First Search, Depth-First Search, and topological sort in graphs.

Surface Properties: Understanding Semiconductors and Nanomaterials

Covers the significance of surface properties in semiconductors and nanomaterials, including surface energy, reconstruction, and the effects of surface states on electronic behavior.

Curves with Poritsky Property and Liouville Nets

Explores curves with Poritsky property, Birkhoff integrability, and Liouville nets in billiards.

Closed Surfaces and Integrals Log in to Mediaspace to watch this video

Explains closed surfaces like spheres, cubes, and cones without covers, and their traversal and removal of edges.

Surface of Revolution Log in to Mediaspace to watch this video

Explains the parametric equations of surfaces of revolution generated by curves in space.

Real Surfaces: Defects and Reconstructions Log in to Mediaspace to watch this video

Explores the difference between ideal and real surfaces, defects, and surface reconstructions.

Surface Integrals: Regular Parametrization Log in to Mediaspace to watch this video

Covers surface integrals with a focus on regular parametrization and the importance of understanding the normal vector.

Surfaces with Variable Curvature Log in to Mediaspace to watch this video

Explores surfaces with variable curvature, discussing their construction and properties.

Shells I Log in to Mediaspace to watch this video

Covers linear pressure vessels, thin shells, and critical buckling pressure, emphasizing the dimensional reduction from 3D to 2D.

Real Surfaces: Line Defects Log in to Mediaspace to watch this video

Explores line defects in real surfaces and their influence on surface energy.

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