Coverage report

Audience

Doctoral / postdoctoral. School/early-undergrad titles are recall only.

Scale

Run python scripts/check_docs.py for live page/nav counts. The corpus is well past the original 200-page target (350+ content pages with full nav coverage).

Major research tracks (shipped)

Algebra, arithmetic, geometry

Abstract · commutative · representation · homological algebra · spectral sequences · AG · DAG · spectral AG · motivic homotopy · arithmetic geometry · analytic/algebraic NT · Langlands · geometric Langlands · \(K\)-theory · tropical · mirror · symplectic/contact · NCG · cryptography (foundations, lattice/PQ, ZK/MPC, hash/signatures, protocols)

Frontier arithmetic & geometry

Prismatic cohomology · condensed mathematics (solid/liquid, analytic rings) · higher Teichmüller (Anosov, Hitchin, maximal)

Analysis & PDE

Topology · alg. topology · measure · FA · microlocal · GMT · complex · SCV · complex geometry · Fourier · PDE · dynamics · ergodic

Probability & randomness

Probability · stochastic · SPDE · rough paths · random matrices · free probability

Foundations

Logic · category · model categories · higher categories · ∞-topoi · topos · HoTT

Physics & applied

Mathematical physics · axiomatic QFT · optimization · numerics · ML mathematics (approximation, NTK, generalization) · IT · games · discrete · statistics

Learning paths

See learning-paths.md for ordered quals-style programs.

Optional further growth

  • Full geometric Langlands (Gaitsgory–Raskin stack) working notes beyond current geometric Langlands track
  • Deeper \(p\)-adic Langlands / locally analytic representations
  • Perfectoid geometry / adic spaces as a dedicated domain (pointers exist via prismatic / condensed)
  • Synthetic differential geometry / cohesive HoTT bridge notes
  • More specialized applied tracks (control theory, combinatorial optimization monographs)

Maintenance

  1. Register pages in mkdocs.yml.
  2. python scripts/check_docs.py && mkdocs build --strict
  3. Style: writing-style.md — use **Job:** one-liner, then Core / See it / Check / Pitfalls / Refs
  4. Keep this report and index.md research map aligned when adding domains