Lectures related to The Two-Holed Torus

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.

Simplicial and Cosimplicial Objects: Examples and Applications

Covers simplicial and cosimplicial objects in category theory with practical examples.

Limits and colimits in Top

Covers the concepts of limits and colimits in the category of Topological Spaces, emphasizing the relationship between colimit and limit constructions and adjunctions.

Sets and Operations: Introduction to Mathematics

Covers the basics of sets and operations in mathematics, from set properties to advanced operations.

Meromorphic Functions & Differentials

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

Simplicial Sets: Introduction and Products

Introduces simplicial sets and explores the construction of products with a geometric interpretation.

Definition of Indefinite Integral MOOC: Analysis I MOOC: Analysis I (part 7) : Indefinite and definite integrals, integration (selected chapters)

Explains the definition and properties of indefinite integrals, highlighting the relationship between primitives and the set of all primitives of a function.

A Conjecture of Erdös: Proof by Moreira, Richter and Robertson

Presents a short proof of a conjecture by Erdös, exploring related questions and detailed proof of the proposition.

Signal Representations

Explores wavelets as orthonormal bases for piecewise constant signals over unit intervals.

Thermodynamic formalism for coarse expanding dynamical systems

Explores thermodynamic formalism for weakly coarse expanding dynamical systems, covering equilibrium states, visual metrics, and symbolic coding.

Normed Spaces Log in to Mediaspace to watch this video

Covers normed spaces, dual spaces, Banach spaces, Hilbert spaces, weak and strong convergence, reflexive spaces, and the Hahn-Banach theorem.

Graph Sketching: Connected Components Log in to Mediaspace to watch this video

Covers the concept of graph sketching with a focus on connected components.

Untitled Log in to Mediaspace to watch this video

Weak Derivatives: Definition and Properties Log in to Mediaspace to watch this video

Covers weak derivatives, their properties, and applications in functional analysis.

Construction of Solutions by Dirichlet-Laplace Log in to Mediaspace to watch this video

Explores the construction of solutions by Dirichlet-Laplace in general domains.

Approximation by Smooth Functions Log in to Mediaspace to watch this video

Discusses approximation by smooth functions and the convergence of function sequences in normed vector spaces.

Algebraic Geometry: Forms and Maps Log in to Mediaspace to watch this video

Covers the concept of forms in algebraic geometry and the implications of constructing Bloch(A) from glued copies of A.

Quantum Eigenfunctions Log in to Mediaspace to watch this video

Covers quantum eigenfunctions and the importance of A and B commuting for the same set of eigenfunctions.

Wireless Receivers: OFDM Log in to Mediaspace to watch this video

Covers the fundamentals of Orthogonal Frequency Division Multiplexing (OFDM) in wireless communication systems.

Equivalence Relations and Construction of R Log in to Mediaspace to watch this video

Covers the construction of R and equivalence relations in sequences and linear recurrences.