30 citations · 42 across the 12 of their papers we have counts for
14 papers
Normalizations of factorizations over convex cones and their effects on extension complexity
Adam Brown, Kanstantsin Pashkovich, Levent Tunçel
Factorizations over cones and their duals play central roles for many areas of mathematics and computer science. One of the reasons behind this is the ability to find a representat…
Morse theory for chromatic Delaunay triangulations
Abhinav Natarajan, Thomas Chaplin, Adam Brown +1
The chromatic alpha filtration is a generalization of the alpha filtration that can encode spatial relationships among classes of labelled point cloud data, and has applications in…
An Improved Long-Time Bishop-Gromov Theorem Using Shear
Adam R. Brown, Michael H. Freedman
The Bishop-Gromov theorem is a comparison theorem of differential geometry that upperbounds the growth of volume of a geodesic ball in a curved space. For many spaces, this bound i…
Efficient Determinant Maximization for All Matroids
Adam Brown, Aditi Laddha, Madhusudhan Pittu +1
Determinant maximization provides an elegant generalization of problems in many areas, including convex geometry, statistics, machine learning, fair allocation of goods, and networ…
Enhanced Bishop-Gromov Theorem
Adam R. Brown, Michael H. Freedman
The Bishop-Gromov theorem upperbounds the rate of growth of volume of geodesic balls in a space, in terms of the most negative component of the Ricci curvature. In this paper we pr…
Discrete Microlocal Morse Theory
Adam Brown, Ondrej Draganov
We establish several results combining discrete Morse theory and microlocal sheaf theory in the setting of finite posets and simplicial complexes. Our primary tool is a computation…
Determinant Maximization via Matroid Intersection Algorithms
Adam Brown, Aditi Laddha, Madhusudhan Pittu +2
Determinant maximization problem gives a general framework that models problems arising in as diverse fields as statistics \cite{pukelsheim2006optimal}, convex geometry \cite{Khach…
Polynomial Equivalence of Complexity Geometries
Adam R. Brown
This paper proves the polynomial equivalence of a broad class of definitions of quantum computational complexity. We study right-invariant metrics on the unitary group -- often cal…
Computing Minimal Injective Resolutions of Sheaves on Finite Posets
Adam Brown, Ondrej Draganov
In this paper we introduce two new methods for constructing injective resolutions of sheaves of finite-dimensional vector spaces on finite posets. Our main result is the existence…
Contravariant pairings between standard Whittaker modules and Verma modules
Adam Brown, Anna Romanov
We classify contravariant pairings between standard Whittaker modules and Verma modules over a complex semisimple Lie algebra. These contravariant pairings are useful in extending…
Contravariant forms on Whittaker modules
Adam Brown, Anna Romanov
Let be a complex semisimple Lie algebra. We give a classification of contravariant forms on the nondegenerate Whittaker -modules introduced b…
Probabilistic Convergence and Stability of Random Mapper Graphs
Adam Brown, Omer Bobrowski, Elizabeth Munch +1
We study the probabilistic convergence between the mapper graph and the Reeb graph of a topological space equipped with a continuous function $f: \mathbb{X} \rightarro…
Arakawa-Suzuki functors for Whittaker modules
Adam Brown
In this paper we construct a family of exact functors from the category of Whittaker modules of the simple complex Lie algebra of type to the category of finite-dimensional m…
Sheaf-Theoretic Stratification Learning from Geometric and Topological Perspectives
Adam Brown, Bei Wang
In this paper, we investigate a sheaf-theoretic interpretation of stratification learning from geometric and topological perspectives. Our main result is the construction of strati…