The Hilbert curve (also known as the Hilbert space-filling curve) is a continuous fractal space-filling curve first described by the German mathematician David Hilbert in 1891, as a variant of the space-filling Peano curves discovered by Giuseppe Peano in 1890. Because it is space-filling, its Hausdorff dimension is 2 (precisely, its image is the unit square, whose dimension is 2 in any definition of dimension; its graph is a compact set homeomorphic to the closed unit interval, with Hausdorff dimension 2). The Hilbert curve is constructed as a limit of piecewise linear curves. The length of the th curve is , i.e., the length grows exponentially with , even though each curve is contained in a square with area . (Wikipedia).
This shows a 3d print of a mathematical sculpture I produced using shapeways.com. This model is available at http://shpws.me/2toQ.
From playlist 3D printing
This shows a 3d print of a mathematical sculpture I produced using shapeways.com. This model is available at http://shpws.me/8pkP
From playlist 3D printing
Anthony Licata: Hilbert Schemes Lecture 7
SMRI Seminar Series: 'Hilbert Schemes' Lecture 7 Kleinian singularities 2 Anthony Licata (Australian National University) This series of lectures aims to present parts of Nakajima’s book `Lectures on Hilbert schemes of points on surfaces’ in a way that is accessible to PhD students inter
From playlist SMRI Course: Hilbert Schemes
More identities involving the Riemann-Zeta function!
By applying some combinatorial tricks to an identity from https://youtu.be/2W2Ghi9idxM we are able to derive two identities involving the Riemann-Zeta function. http://www.michael-penn.net http://www.randolphcollege.edu/mathematics/
From playlist The Riemann Zeta Function
Joshua Ciappara: Hilbert Schemes Lecture 10
SMRI Seminar Series: 'Hilbert Schemes' Lecture 10 Representations of Heisenberg algebras on homology of Hilbert schemes Joshua Ciappara (University of Sydney) This series of lectures aims to present parts of Nakajima’s book `Lectures on Hilbert schemes of points on surfaces’ in a way tha
From playlist SMRI Course: Hilbert Schemes
Emily Cliff: Hilbert Schemes Lecture 3
SMRI Seminar Series: 'Hilbert Schemes' Lecture 3 The universal family on H Emily Cliff (University of Sydney) This series of lectures aims to present parts of Nakajima’s book `Lectures on Hilbert schemes of points on surfaces’ in a way that is accessible to PhD students interested in rep
From playlist SMRI Course: Hilbert Schemes
Emily Cliff: Hilbert Schemes Lecture 6
SMRI Seminar Series: 'Hilbert Schemes' Lecture 6 GIT stability, quiver representations, & Hilbert schemes Emily Cliff (University of Sydney) This series of lectures aims to present parts of Nakajima’s book `Lectures on Hilbert schemes of points on surfaces’ in a way that is accessible to
From playlist SMRI Course: Hilbert Schemes
Space-Filling Curves (2 of 4: Hilbert Curve)
More resources available at www.misterwootube.com
From playlist Exploring Mathematics: Fractals
Some identities involving the Riemann-Zeta function.
After introducing the Riemann-Zeta function we derive a generating function for its values at positive even integers. This generating function is used to prove two sum identities. http://www.michael-penn.net http://www.randolphcollege.edu/mathematics/
From playlist The Riemann Zeta Function
Coding in the Cabana 3: Hilbert Curve
It's the third episode of Coding in the Cabana! On this snowy day, I attempt to animate the path of the classic "space filling curve" known as the Hilbert Curve. 💻https://thecodingtrain.com/CodingInTheCabana/003-hilbert-curve.html 🔗Hilbert Curve on Wikipedia: https://en.wikipedia.org/wik
From playlist Coding in the Cabana
Hilbert's Curve: Is infinite math useful?
Space-filling curves, and the connection between infinite and finite math. Help fund future projects: https://www.patreon.com/3blue1brown An equally valuable form of support is to simply share some of the videos. Home page: https://www.3blue1brown.com Supplement with more space-filling cu
From playlist Explainers
Geometry and Topology in Quantum Mechanics - Mathematical Properties by N. Mukunda
DISCUSSION MEETING GEOMETRIC PHASES IN OPTICS AND TOPOLOGICAL MATTER ORGANIZERS: Subhro Bhattacharjee, Joseph Samuel and Supurna Sinha DATE: 21 January 2020 to 24 January 2020 VENUE: Madhava Lecture Hall, ICTS, Bangalore This is a joint ICTS-RRI Discussion Meeting on the geometric pha
From playlist Geometric Phases in Optics and Topological Matter 2020
Ekaterina Amerik: Rational curves and contraction loci on holomorphic symplectic manifolds
VIRTUAL LECTURE RECORDED DURING SOCIAL DISTANCING Recording during the meeting "Varieties with Trivial Canonical Class " the April 06, 2020 by the Centre International de Rencontres Mathématiques (Marseille, France) Filmmaker: Guillaume Hennenfent Find this video and other talks given by
From playlist Virtual Conference
The cohomology groups...Jacobians of planar curves - Luca Migliorini
Luca Migliorini University of Bologna; Member, School of Mathematics February 18, 2015 I will first discuss a relation between the cohomology groups (with rational coefficients) of the compactified Jacobian and those of the Hilbert schemes of a projective irreducible curve CC with planar
From playlist Mathematics
Richard Thomas - Vafa-Witten Invariants of Projective Surfaces 4/5
This course has 4 sections split over 5 lectures. The first section will be the longest, and hopefully useful for the other courses. 1. Sheaves, moduli and virtual cycles 2. Vafa-Witten invariants: stable and semistable cases 3. Techniques for calculation --- virtual degeneracy loci, c
From playlist 2021 IHES Summer School - Enumerative Geometry, Physics and Representation Theory
The computational theory of Riemann–Hilbert problems (Lecture 1) by Thomas Trogdon
ORGANIZERS : Alexander Abanov, Rukmini Dey, Fabian Essler, Manas Kulkarni, Joel Moore, Vishal Vasan and Paul Wiegmann DATE & TIME : 16 July 2018 to 10 August 2018 VENUE : Ramanujan Lecture Hall, ICTS Bangalore This program aims to address various aspects of integrability and its role in
From playlist Integrable systems in Mathematics, Condensed Matter and Statistical Physics
Cannon-Thurston maps: naturally occurring space-filling curves
Saul Schleimer and I attempt to explain what a Cannon-Thurston map is. Thanks to my brother Will Segerman for making the carvings, and to Daniel Piker for making the figure-eight knot animations. I made the animation of the (super crinkly) surface using our app (with Dave Bachman) for coh
From playlist GPU shaders
Geometry of Teichmüller curves – Martin Möller – ICM2018
Dynamical Systems and Ordinary Differential Equations Invited Lecture 9.4 Geometry of Teichmüller curves Martin Möller Abstract: The study of polygonal billiard tables with simple dynamics led to a remarkable class of special subvarieties in the moduli of space of curves called Teichmüll
From playlist Dynamical Systems and ODE
Anthony Henderson: Hilbert Schemes Lecture 4
SMRI Seminar Series: 'Hilbert Schemes' Lecture 4 Kleinian singularities 1 Anthony Henderson (University of Sydney) This series of lectures aims to present parts of Nakajima’s book `Lectures on Hilbert schemes of points on surfaces’ in a way that is accessible to PhD students interested i
From playlist SMRI Course: Hilbert Schemes