Here’s a list of things that are incredibly interesting and I couldn’t live without learning. I’m hoping to learn plasma physics to get to the point where I can hang with people doing real research and maybe apply my creativity. Also, I have some pretty cool ideas for superconductivity, but I’m not sure if they’re original.
To Learn Over the Next Six Months
Language
- Japanese
- Kanji
- Learn more about written languages (devanagari, etc)
Math
- Retake Coursera Crypto I
- Study some of Crypto papers on deck
- Finite Element Analysis
- Helmholtz Decomposition
- Master Gradient/Curl/Divergence/Laplacian
- Branched Ray Tracing Algorithms
- Wallpaper Group
- Matroids
- Halting Problem
- Knot Theory (Racks and Quandles)
- Distributive Lattice
- Various Emergent Crystal Structures
- Symmetry Groups and Isometry Groups
- Quantum Harmonic Oscillators
- Einstein Solids
- Groups/Rings/Fields
- Polynomials and Ring Theory
- Galois Theory
- Dyandic Tensor
- Wavelets
- λ-Rings
- Grothendieck
- n-Category Theory (& omega… lol)
- … probably start with just regular Category Theory though
- Like braiding … what’s that?
- Then build up to Ross Street’s work
- Sheaf theory and applications
- Hermitian Operators
- Symplectic Operators
- Hamintonian Mechanics
- Ergodic Hypothesis …..
- Tensor Fields
- Manifolds & Reimann Manifolds
- Jacobian Matrix
- Using a self-similar 3D flower of life to approximate integral (Laplacian)
- Diffusion Theorum
Electromagnetism
- E & M basics
- Skyrmions
- Permittivity
- Band Theory! (lots of great ideas for solid state chem here)
- Quantum Hall Effect
- Other Thermo-Electric effects
Superconductance
- Flux pinning
- Flux tubes
- BCS Theory
- Ginzburg-Landau Theory
- Abrikosor Vortices
- Type 1/1.5/2 Superconductors
- London Penetration Depth
- Superconducting Coherence Length
- Husimi Q Representation
- Quantum Vortex
- Magnetic Flux Quantum
- Current Density
- Flux Pumping
- Debye Model
- Correlation to Phononic Properties
- Correlation to Lattice Arrangment & Dimensionality (1D,2D,3D)
- Space Group
- Crystoallographic Point Group
- Broullouin Zone
- Bloch Wave & Oscillations & MoM Method
Plasma Physics
Basics:
- DC/AC Conductivity
- Photo/Tunnel Ionizations
- Langmuir Probe
- DC & RF Discharge
Plasma Instabilities:
- Plasma waves: EM, Langmuir, Surface Plasma, & Ion Acoustic
- 2 Stream Instability Propagation
- Weibel Instability
Plasma Confinement:
- Single Particle Motion
- Motion in Magnetic Fields (inhomogenous/curved)
- Magnetic Moment Confinement
- Mirror Confinement
- Tokamak Confinement
Applications:
- Medium/Short Wave Communications
- Processing of Materials
- Laser Ablation
- Laser-Driven Fusion
- Magnetic Fusion
& Magnetohydrodynamics
Mostly just want to fuse some hot things.