44 citations · 71 across the 13 of their papers we have counts for
20 papers
Transport based embeddings with topological guarantees
Erik Carlsson, John Carlsson
Point clouds arising in image collections, samples from Markov chain Monte Carlo, or states of a random walk, often have a simple underlying geometry which is obscured by noise, hi…
Alpha shapes in kernel density estimation
Erik Carlsson, John Carlsson
For every Gaussian kernel density estimator associated to a point cloud , we def…
GKM spaces, and the signed positivity of the nabla operator
Erik Carlsson, Anton Mellit
We show that the Frobenius character of the equivariant Borel-Moore homology of a certain positive -version of the unramified affine Springer fiber studied by Goreski,…
A new construction for sublevel set persistence
Erik Carlsson, John Carlsson
We construct a filtered simplicial complex associated to a subset , a function with compactly supported sublevel sets…
A combinatorial formula for the nabla operator
Erik Carlsson, Anton Mellit
We present an LLT-type formula for a general power of the nabla operator applied to the Cauchy product for the modified Macdonald polynomials, and use it to deduce a new proof of t…
Affine Schubert calculus and double coinvariants
Erik Carlsson, Alexei Oblomkov
We define an action of the double coinvariant algebra on the equivariant Borel-Moore homology of the affine flag variety in type , which has an explici…