6 citations · 18 across the 11 of their papers we have counts for
12 papers
Relative Group Trisections
Nickolas Andres Castro, Jason Joseph, Patrick K. McFaddin
Trisections of closed 4-manifolds, first defined and studied by Gay and Kirby, have proved to be a useful tool in the systematic analysis of 4-manifolds via handlebodies. Subsequen…
Interleaving Distances, Monoidal Actions and 2-Categories
Patrick K. McFaddin, Tom Needham
Interleaving distances are used widely in Topological Data Analysis (TDA) as a tool for comparing topological signatures of datasets. The theory of interleaving distances has been…
Consequences of the existence of exceptional collections in arithmetic and rationality
Matthew R. Ballard, Alexander Duncan, Alicia Lamarche +1
A well-known conjecture of Orlov asks whether the existence of a full exceptional collection implies rationality of the underlying variety. We prove this conjecture for arithmetic…
Separable algebras and coflasque resolutions
Matthew R. Ballard, Alexander Duncan, Alicia Lamarche +1
Over a non-closed field, it is a common strategy to use separable algebras as invariants to distinguish algebraic and geometric objects. The most famous example is the deep connect…
Kernels for Grassmann Flops
Matthew R. Ballard, Nitin K. Chidambaram, David Favero +2
We develop a generalization of the -construction of the first author, Diemer, and the third author for Grassmann flips. This generalization provides a canonical idempotent kerne…
Derived categories of centrally-symmetric smooth toric Fano varieties
Matthew R Ballard, Alexander Duncan, Patrick K. McFaddin
We exhibit full exceptional collections of vector bundles on any smooth, Fano arithmetic toric variety whose split fan is centrally symmetric.
The toric Frobenius morphism and a conjecture of Orlov
Matthew R. Ballard, Alexander Duncan, Patrick K. McFaddin
We combine the Bondal-Uehara method for producing exceptional collections on toric varieties with a result of the first author and Favero to expand the set of varieties satisfying…
On derived categories of arithmetic toric varieties
Matthew R. Ballard, Alexander Duncan, Patrick K. McFaddin
We begin a systematic investigation of derived categories of smooth projective toric varieties defined over an arbitrary base field. We show that, in many cases, toric varieties ad…
Zero-cycles with coefficients for the second generalized symplectic involution variety of an algebra of degree 4
Patrick K. McFaddin
We compute the group of -zero-cycles on the second generalized involution variety for an algebra of degree 4 with symplectic involution. This description is given in terms of…
The group of -zero-cycles on the second generalized Severi-Brauer variety of an algebra of index 4
Patrick K. McFaddin
In this manuscript, it is shown that the group of -zero-cycles on the second generalized Severi-Brauer variety of an algebra of index 4 is given by elements of the group $…
Patching and Quillen K-Theory
Patrick McFaddin
This paper provides an isomorphism of -groups, i.e., an exact sequence $0 \to K_n(\m…
Extended Torelli map to the Igusa blowup in genus 6, 7, and 8
Valery Alexeev, Ryan Livingston, Joseph Tenini +7
It was conjectured in \cite{Namikawa_ExtendedTorelli} that the Torelli map associating to a curve its jacobian extends to a regular map from the Deligne-Mumford moduli…