Topology

concepts · 12 notes linked

Related: Quanta Magazine · Knot Theory · Mathematics · Argonne National Laboratory · Computational Simulation · Lek Heng Lim · University Of Chicago · Machine Learning

Notes

• A Powerful New 'QR Code' Untangles Math's Knottiest Knots | Quanta Magazine — New computable knot invariant both strong and fast visualized as hexagonal QR code
• An Applied Mathematician Strengthens AI With Pure Math | Quanta Magazine — Applying topology and algebraic geometry to explain and improve neural networks
• First Shape Found That Can't Pass Through Itself | Quanta Magazine — First proven convex polyhedron that cannot pass through a copy of itself
• Flow Proof Helps Mathematicians Find Stability in Chaos | Quanta Magazine — New proof classifies Anosov flows using only periodic trajectory data
• How Quantum Physics Describes Earth's Weather Patterns | Quanta Magazine — Earth modeled as topological insulator explaining equatorial Kelvin waves
• Math and the Beaches of Rio — History of Fields Medal and Stephen Smale's horseshoe map work in Rio
• Math's 'hairy ball theorem' shows why there's always at least one place on Earth where no wind blows — Hairy ball theorem and its real-world consequences in physics and engineering
• New Knot Theory Discovery Overturns Long-Held Mathematical Assumption — Wendt's 1937 additivity conjecture for knot unknotting numbers disproven after 88 years
• Novel insight reveals topological tangle in unexpected corner of the universe — Hopfion topological structure discovered in ferroelectric nanoparticles via simulation
• Topology 101: The Hole Truth — Introduction to how topologists formally count holes via homology and Betti numbers
• Ultrafast reversible self-assembly of living tangled matter — California blackworms form tangles slowly but untangle in milliseconds via helical waves
• What Is a Manifold? | Quanta Magazine — Explainer on mathematical manifolds, their definition, and broad applications