96 citations · 190 across the 19 of their papers we have counts for
25 papers
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…
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…
Perverse sheaves on symmetric products of the plane
Tom Braden, Carl Mautner
For any field , we give an algebraic description of the category of perverse sheaves on the -fold symmetric product of the p…
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 applicati…
A semi-small decomposition of the Chow ring of a matroid
Tom Braden, June Huh, Jacob P. Matherne +2
We give a semi-small orthogonal decomposition of the Chow ring of a matroid M. The decomposition is used to give simple proofs of Poincaré duality, the hard Lefschetz theorem, and…
Kazhdan-Lusztig polynomials of matroids under deletion
Tom Braden, Artem Vysogorets
We present a formula which relates the Kazhdan-Lusztig polynomial of a matroid , as defined by Elias, Proudfoot and Wakefield, to the Kazhdan--Lusztig polynomials of the matroid…