Visual companions to the papers
Constructions,
made explicit.
A picture can show a relation before anyone understands its proof, and a numerical example can expose a distinction a formula hides. Each companion makes one construction from the research explicit, with the assumptions and limits of its model stated beside it.
01 · Topology
From a knot to a complex.
Cut a knot along a sphere and a three-dimensional problem becomes a count of intersecting curves.
Five guided moves · Worked trefoil example
02 · Algebraic geometry
A sphere disappears. Another takes its place.
Pass through a singularity, then see why the global relations decide what can happen.
Three experiments · Local geometry and global topology
03 · Gauge theory
Four dimensions. Two languages.
A space changes. Two mathematical languages describe the change, and the question is whether they agree.
Six guided moves · Geometry, maps and comparison
04 · Quantitative finance
Give the hierarchy an expected return.
Change the forecast. Watch four portfolio rules decide what to hold.
Four experiments · Weights computed in your browser