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.
Theory Seminar - Face Numbers, Isabella Novik
Face numbers in centrally symmetric polytopes and spheres: exploring upper bounds, recent developments, and open problems in combinatorial geometry. Insights into maximum face counts and structural properties.
Gauge Equivariant Convolutional Networks and the Icosahedral CNN
Explore gauge equivariant CNNs on manifolds, focusing on icosahedral surfaces. Learn how this approach improves image segmentation and climate pattern analysis with enhanced efficiency and performance.
Building Manifolds from Error Correcting Codes - IPAM at UCLA
Explore the intersection of error correcting codes and manifold construction, delving into quantum error correction, topology, and complex mathematical concepts.
From Turaev to Rokhlin via VOA Characters and Curve Counting
Explore q-series invariants of 3-manifolds, their properties, and connections to topology, vertex algebras, and enumerative problems. Gain insights into Spin-C structures and related mathematical concepts.
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.
Wall Finiteness Obstruction for DG Categories II
Exploration of Wall finiteness obstruction theorem for DG categories, including applications to phantom DG categories and derived categories of algebraic varieties. Discusses extensions to algebras over DG operads.
Special Lecture Series on Numerical Geometry - Tristan Collins
Explore complete Calabi-Yau metrics on Fano manifolds with singular divisors, focusing on two-component cases and discussing potential generalizations to more complex scenarios.
An Application of Symplectic Topology to Algebraic Geometry
Explore symplectic topology's application to algebraic geometry, connecting Rouquier's triangulated category dimension to Krull dimension via homological mirror symmetry.
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.
Lattice Cohomology - Part 1
Explore topological lattice cohomology in plumbed 3-manifolds, its connection to Heegaard Floer theory, and its applications in analyzing surface singularities and geometric structures.
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.