Floer Equations with neural networks Click and drag between highlighted orbits to view Floer cylinders Does not work on mobile! please play on desktop sorry Hamiltonian Select Hamiltonian: Quartic Mexican hat Saddle Floer Cylinder Start Orbit Index End Orbit Index . . Select a Floer cylinder Allow non-converging Floer cylinders An interactive applet displaying numerical solutions of Floer’s…
Does not work on mobile! please play on desktop sorry Quantum Dice Basins of attractions Flow time: 0.5 Marble sphere? Dice Roundness: 0.5 Draw dice The left hand side lets you control a collection of points $p_i \in S^2$, and their weights $w_i$. The colors show the basin of attraction of the gradient flow of the function $f: S^2\to \mathbb{R}$: \[f(x) = \prod |x-p_i|^{w_i}\] Remarkably, the…
Does not work on mobile! please play on desktop sorry --> Sun's dial n = draw labels? Save Template Scroll or click + drag to spin dials. Use the slider or the text input to create a dial for any positive number. Click “save template” to download an image, which you can print to make a physical version Joint with Dina Buric. Thanks to Jonathan Love for figuring out the key labeling Using Sun’s…
Genus 2 surfaces What does a genus 2 surface look like? I each participant submit one. There are many of the standard double tori, but also many different shapes. There are, geometrically, many different genus 2 surfaces. I didn’t have time to make a nice worksheet this week. But, here’s my notes about what I was planning on doing. Maybe they’re even readable Page 1 Page 2 Page 3 Page 4 Page 5…
Does not work on mobile! please play on desktop sorry --> Gaussian periods n = ω = Colorize Color modulus Suppose that $\omega, d$ and $n$ are positive integers satisfying $\omega^d \equiv 1 \mod n$. A Gaussian period is a function $\sigma^{\mathbb{Z}/n}_{\langle\omega\rangle}: \mathbb{Z}_n \to \mathbb{C}$ defined by the exponential sum of the powers of $\omega$:…
Does not work on mobile! please play on desktop sorry --> Torsion points of elliptic curves torsion points of order This applet shows the torsion points of an elliptic curve sitting inside of $\mathbb{CP}^2$. The left pane shows the uniformized elliptic curve, thought of as a square with edges identified. Clicking and dragging the green dot changes the modulus of the elliptic curve. For an…
Chaim goodman-strauss showed me a system for quickly and cheaply creating large, lightweight polyhedra. There are two ingredients Thin Plastic straws (coffee stirrers work wonders, back when we still believed in single use plastic) Sip n joy red sip stirrers: Link to product Tile spacers Rubi tile spacers 1/16” rigid crosses: Link to product If you get the right brands, then the stirrers fit…
Visions of the complex projective plane