Symmetries of Manifolds - Lecture 3
Explore symmetries of manifolds in topology and geometry. Delve into classical and recent results, methods, and emerging conjectures about symmetry spaces of simple manifolds like spheres and discs.
Symmetries of Manifolds - Lecture 2
Delve into symmetries of manifolds, exploring classical and recent results on spaces of symmetries for simple manifolds like spheres and discs, with insights into emerging conjectural perspectives.
Symmetries of Manifolds - Lecture 1
Explore symmetries of manifolds in topology and geometry. Delve into classical and recent results, methods, and emerging conjectures about symmetry spaces of simple manifolds like spheres and discs.
Algebraic Structure of Area-Preserving Homeomorphism Groups - Lecture 4
Explore the algebraic structure of area-preserving homeomorphism groups, focusing on Fathi's question and the simplicity conjecture for compact surfaces. Delve into link spectral invariants and Lagrangian Floer homology.
Topology
Explore fundamental concepts of topology, including metric spaces, convergence, compactness, continuity, and connectedness, with applications to real-world mathematical problems.
Space of Actions of Groups on the Real Line
Explore group actions on the real line, delving into mathematical concepts and theories presented by Bertrand Deroin in this insightful conference talk.
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.
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.
Danny Ruberman- Diffeomorphism Groups of 4-Manifolds
Exploring unique 4-dimensional phenomena: infinite families of homeomorphic but non-diffeomorphic manifolds, and exotic behavior in diffeomorphism and homeomorphism groups.
Topology - Lecture 2
Explore fundamental concepts of topology, including topological spaces, continuity, and homeomorphisms, with a focus on mathematical rigor and abstract reasoning.
Topology - Lecture 14
Explore advanced concepts in topology with Bruno Zimmerman, delving into complex mathematical structures and their properties in this comprehensive lecture.
Homeomorphisms of Euclidean Space
Explore recent advances in understanding the topological group of homeomorphisms of Euclidean space, including methods and emerging conjectures in geometric topology.
The Ham Sandwich Theorem and the Continuum - Algebraic Topology Lecture 14
Explore the Borsuk-Ulam theorem, Ham Sandwich theorem, and their applications in algebraic topology. Learn how these concepts relate to continuous maps and homeomorphisms in affine spaces.
Introduction to Topology in Mathematics History
Explore topology's historical development, from Euler's polyhedron discoveries to Poincaré's insights. Learn about key concepts like Euler characteristic, Riemann surfaces, and surface classification in this mathematical journey.
Characterisation of Area-Strict Limits of Planar BV Homeomorphisms
Explore area-strict limits of planar BV homeomorphisms, focusing on cavitations, fractures, and the no-crossing condition in elastic deformations.
Finitely Presented Simple Groups of Homeomorphisms of the Reals
Explore Thompson's groups and finitely generated simple groups of homeomorphisms, with insights into joint research on finitely presented examples.
Random Embeddings of Graphs in Surfaces - Lecture
Explore random 2-cell embeddings of graphs in surfaces, from basic concepts to recent developments in Random Topological Graph Theory.
Manifolds, Covers, Fundamental Groups, and Group Actions by Homeomorphisms - Lecture 2
Explore manifolds, covers, fundamental groups, and group actions by homeomorphisms in this advanced mathematics lecture, delving into key concepts of geometric topology.
Weak Limit of Homeomorphisms in W1,n-1: Invertibility and Lower Semicontinuity
Explore weak limits of homeomorphisms, examining invertibility and lower semicontinuity in W1,n-1 spaces through variational and geometrical methods.
Homeomorphic Sobolev Extensions of Parametrizations of Jordan Curves
Explore homeomorphic Sobolev extensions of Jordan curve parametrizations, examining conditions for finite energy deformations and recent findings in this mathematical field.
Symplectic Mapping Class Groups: Structural Properties from Smooth to C⁰
Explore structural properties of symplectic mapping class groups, from smooth to C⁰, with an overview of key concepts and open questions in this mathematical field.