Mathematics

• Statistics
  • Probability theory
  • Measure Theory
  • Stochastic Processes
• Analysis
  • real analysis
  • functional analysis
• Linear Algebra
  • Operator Theory
  • Spectral Theory
• Fourier Transforms

• Green’s Functions

• Differential Equations
• Special Functions

• Complex Variable Theory

• Category Theory

• Topology
  • General Topology
  • Algebraic Topology
• Abstract Algebra
• Differential Form
• Group Theory
  • Groups
  • Tensor
  • Spinor
  • Manifolds
    • Riemannian Manifolds
    • Fiber Bundles
  • Poincare Group, Lie Groups and Lie Algebras

• Logic and Computer Science

• Combinatorics
• Number Theory
• Algebraic Geometry

• Graph Theory

• Knot Theory

• Langlands Program

• Conformal Field Theory

Physics

• What Is Physics?
• Classical Mechanics and Relativity
• Electrodynamics and Optics
• Quantum Mechanics and Quantum Field Theory
• Thermal and Statistical Physics
• Solid State Physics
• Computational Physics

• Particles Physics, String Theory and Beyond

• Fluid Mechanics
  • Mathematical theories of lift
• A Topos Foundation for Theories of Physics(ko)