Computing Homology Groups - Algebraic Topology - NJ Wildberger
Explore homology groups in algebraic topology, focusing on examples like circles and disks. Learn about connectivity, loops, and higher-dimensional holes in spaces.
Simplices and Simplicial Complexes - Algebraic Topology
Explore higher-dimensional geometry through simplices and simplicial complexes. Learn about convex combinations, orientations, and the fundamental concept of homology in algebraic topology.
An Introduction to Homology - Algebraic Topology
Explore higher-dimensional topology through homology groups, cycles, and spanning trees. Learn to compute and characterize independent cycles in graphs using algebraic techniques.
An Informal Introduction to Abstract Algebra
Informal introduction to abstract algebra, covering fields, rings, and vector spaces. Explores key concepts and examples, from basic number systems to advanced constructions, providing essential background for algebraic topology.
Two-Dimensional Surfaces - The Sphere - Algebraic Topology
Explore the two-dimensional sphere's significance in algebraic topology, including its relation to stereographic projection and the inversive plane in Euclidean geometry.
Homeomorphism and the Group Structure on a Circle - Algebraic Topology 2 - NJ Wildberger
Explore homeomorphisms, group structures on circles, and projective geometry in this algebraic topology lecture, blending fundamental concepts with novel approaches and historical insights.
One-Dimensional Objects - Algebraic Topology
Explore one-dimensional objects in algebraic topology, focusing on lines and circles. Learn about their diverse representations and fundamental properties in this introductory lecture.
Introduction to Algebraic Topology - Algebraic Topology - NJ Wildberger
Explore the foundations of algebraic topology, its historical roots, and key concepts like homeomorphism and fundamental objects. Tackle challenging problems in this dynamic field of mathematics.
Log Symplectic Pairs and Mixed Hodge Structures
Explores log symplectic pairs, their connection to hyperkaehler variety degenerations, and classification of pure weight pairs. Discusses analogies with log Calabi-Yau surfaces and implications for mixed Hodge structures.
Nonrational Toric Geometry III - Quasifolds, Foliations, Combinatorics and One-parameter Families
Explores nonrational toric geometry through quasifolds, foliations, and combinatorics, extending classical toric geometry to new contexts and examining one-parameter families of toric quasifolds.
Nonrational Toric Geometry II - Quasifolds, Foliations, Combinatorics and One-parameter Families
Explore complex toric quasifolds, their structure, and relation to rational toric varieties. Learn about extending constructions to nonsimple convex polytopes in symplectic and complex settings.
On the Nielsen Realization Problem and Cohomology of Mapping Class Groups of Non-orientable Surfaces
Exploración del problema de realización de Nielsen y cohomología de grupos de clases de mapeo en superficies no orientables, con aplicaciones en topología y teoría de grupos.
Homology Planes and Fundamental Groups
Explore homology planes and fundamental groups in complex surfaces, focusing on an algorithm for line arrangements and its applications to log-general type surfaces with infinite fundamental groups.
Higgs Bundles on Elliptic Surfaces and Logarithmic Transformations
Explore Higgs bundles on elliptic surfaces and their transformations, examining vector bundles' importance in mathematics and the impact of logarithmic transformations on these structures.
Windows and Geometric Invariant Theory
Explore windows theory in algebraic geometry, its applications to GIT constructions, and its impact on derived categories and stability conditions in various mathematical contexts.
Pencils on Algebraic Surfaces with Prescribed Classes of Irreducible Components
Exploring bounds on reducible fibers in curve pencils on projective surfaces, with focus on irreducible components' classes in Neron-Severi group. Generalizes results on fundamental groups of line arrangement complements.
Braids and Configuration Spaces
Explore topology, homotopy, and braid groups in this talk on configuration spaces. Discover connections between fundamental groups, loop spaces, and unordered configurations in mathematics.
Greg Malen - Collapsibility of Random Clique Complexes
Explore k-collapsibility in random clique complexes, examining dimensional faces, strong connectivity, and homology implications for topological data analysis.
Category Weight Estimates of Minimal Triangulations
Explore LS-category methods for estimating minimal triangulations of manifolds and polyhedra, focusing on lower bounds for vertex counts in space triangulations.
Decomposing Simplicial Complexes - Without Losing Pieces
Explore simplicial complex decomposition, its impact on homotopy type, and applications in Vietoris-Rips complexes. Learn about obstruction complexes and their role in understanding topological changes.
Intrinsic Topological Transforms via the Distance Kernel Embedding
Explore topological transforms for abstract metric spaces using distance kernel embedding, combining persistent homology with Euclidean embeddings for enhanced shape analysis and discrimination.