Lectures related to Surface Classification

Connected Sum of Torus and RP2

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.

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.

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.

Topology: Classification of Surfaces and Fundamental Groups

Discusses the classification of surfaces and their fundamental groups using the Seifert-van Kampen theorem and polygonal presentations.

Harmonic Forms: Main Theorem

Explores harmonic forms on Riemann surfaces and the uniqueness of solutions to harmonic equations.

Surface Orientation Analysis

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

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.

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 of Revolution Log in to Mediaspace to watch this video

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