Lecture

Surface Classification

Related lectures (29)

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

Local Homeomorphisms and Coverings

Covers the concepts of local homeomorphisms and coverings in manifolds, emphasizing the conditions under which a map is considered a local homeomorphism or a covering.

Holomorphic Functions: Taylor Series Expansion

Covers the basic properties of holomorphic maps and Taylor series expansions in complex analysis.

Hamiltonian Homeomorphisms on Surfaces

Explores the action of Hamiltonian homeomorphisms on surfaces and discusses related mathematical concepts.

Real Surfaces: Defects and Reconstructions

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

Topology of Riemann Surfaces

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

Fundamental Groups

Explores fundamental groups, homotopy classes, and coverings in connected manifolds.

Open Mapping Theorem

Explains the Open Mapping Theorem for holomorphic maps between Riemann surfaces.

Building surfaces from equilateral triangles

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

Meromorphic Functions & Differentials

Explores meromorphic functions, poles, residues, orders, divisors, and the Riemann-Roch theorem.

Differential Forms Integration

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

Polygonal Presentations: Classification of Surfaces

Explores the classification of surfaces based on polygonal presentations and the identification of sides and vertices.

Topology of Riemann Surfaces

Covers the topology of Riemann surfaces, focusing on orientation and orientability.

Surface of Revolution

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

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.

Curves with Poritsky Property and Liouville Nets

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

Closed Surfaces and Integrals

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

Surfaces with Variable Curvature

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

Real Surfaces: Line Defects

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

Surface Integrals: Regular Parametrization

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