Research Catalog

Working Papers (Rough Drafts)

Geometric Quantitative Trading: Three Models and a Unification

Extensions of the Unified Geometric Framework

Research Overview Blurbs

Lempel-Ziv Complexity

Classic: Universal compression via incremental parsing. Algorithmic entropy bounds.
Modern: LZ ↔ RLBWT equivalence. Computation in compressed space.

Atiyah-Singer Index Theorem

Classic: Local index via heat kernel asymptotics.
Modern: Supersymmetric QM proof. Fredholm-cyclic reformulation.

Gauge Theory Formulas

Classic: Chern-Simons forms. Secondary characteristic classes.
Modern: Connes-Moscovici character. Asymptotic cyclic cocycles.

Chern Characters

Classic: Topological invariant from curvature. Index-theoretic formulation.
Modern: Entire cyclic cohomology. JLO cocycles for spectral triples.

Traces of Operators

Classic: Heat kernel eta invariants. Atiyah-Patodi-Singer index.
Modern: Breuer-Fredholm modules. Semifinite spectral flow, Type II.

Exterior Algebra

Classic: Clifford modules. Spinor bundles in index theory.
Modern: Superconnections. Path integral index formulation.

Foundational and contemporary sources for geometric methods in the working papers: spectral geometry of volatility, compressed microstructure, operator-theoretic portfolio construction.