3 papers
math.CO2026
Singular Hodge theory for combinatorial geometries
Tom Braden, June Huh, Jacob P. Matherne +2
We introduce the intersection cohomology module of a matroid and prove that it satisfies Poincaré duality, the hard Lefschetz theorem, and the Hodge-Riemann relations. As applicat…
math.AG2026
Intersection cohomology without spaces
Tom Braden, Nicholas Proudfoot
We survey three settings in which dimensions of intersection cohomology groups of algebraic varieties provide deep combinatorial and representation-theoretic information, and compu…
math.CO2025
Inverse Kazhdan-Lusztig polynomials of matroids under deletion
Tom Braden, Luis Ferroni, Jacob P. Matherne +1
We provide a deletion formula for the inverse Kazhdan--Lusztig polynomial and the inverse -polynomial of a matroid. Our formulas provide analogues to the deletion formulas of Br…