9 citations · 22 across the 16 of their papers we have counts for
18 papers
McKay correspondence for linearly reductive finite group schemes in positive characteristic
Matthew Satriano, Jeremy Usatine
We obtain a motivic and a cohomological McKay correspondence for finite linearly reductive group schemes in arbitrary characteristic. In particular, we prove that if is a finit…
A counter-example to Batyrev's conjecture on the non-negativity of stringy Hodge numbers
Matthew Satriano, Jeremy Usatine
Batyrev's conjecture on the non-negativity of stringy Hodge numbers has been a fundamental open problem, guiding and motivating many beautiful mathematical results in motivic integ…
A cohomological interpretation for stringy Hodge numbers
Jiahui Huang, Matthew Satriano, Jeremy Usatine
We obtain a cohomological interpretation for Batyrev's stringy Hodge numbers in the full generality in which they are defined. In a previous paper, the second and third authors use…
Stringy Hodge numbers via crepant resolutions by Artin stacks
Matthew Satriano, Jeremy Usatine
In a previous paper we showed that any variety with log-terminal singularities admits a crepant resolution by a smooth Artin stack. In this paper we prove the converse, thereby pro…
Motivic integration for singular Artin stacks
Matthew Satriano, Jeremy Usatine
Let be a birational modification of a variety by an Artin stack. In previous work, under the assumption that is smooth, we proved a change of vari…
Beyond twisted arcs: a McKay correspondence for reductive groups
Matthew Satriano, Jeremy Usatine
We introduce a natural generalization of twisted maps, called \emph{warped maps}. While twisted maps play an important role in the study of Deligne--Mumford stacks, warped maps are…
Crepant resolutions of log-terminal singularities via Artin stacks
Matthew Satriano, Jeremy Usatine
We prove that every variety with log-terminal singularities admits a crepant resolution by a smooth Artin stack. We additionally prove new McKay correspondences for resolutions by…
A motivic change of variables formula for Artin stacks
Matthew Satriano, Jeremy Usatine
Let be a birational map from a smooth Artin stack to a (possibly singular) variety. We prove a change of variables formula that relates motivic integrals over a…
Gromov-Witten theory and invariants of matroids
Dhruv Ranganathan, Jeremy Usatine
We use techniques from Gromov-Witten theory to construct new invariants of matroids taking value in the Chow groups of spaces of rational curves in the permutohedral toric variety.…
Stringy invariants and toric Artin stacks
Matthew Satriano, Jeremy Usatine
We propose a conjectural framework for computing Gorenstein measures and stringy Hodge numbers in terms of motivic integration over arcs of smooth Artin stacks, and we verify this…
The motivic zeta functions of a matroid
David Jensen, Max Kutler, Jeremy Usatine
We introduce motivic zeta functions for matroids. These zeta functions are defined as sums over the lattice points of Bergman fans, and in the realizable case, they coincide with t…
Motivic zeta functions of hyperplane arrangements
Max Kutler, Jeremy Usatine
For each central essential hyperplane arrangement over an algebraically closed field, let denote the Denef-Loeser motivic zeta function of…
Hyperplane arrangements and mixed Hodge numbers of the Milnor fiber
Max Kutler, Jeremy Usatine
For each complex central essential hyperplane arrangement , let denote its Milnor fiber. We use Tevelev's theory of tropical compactifications to stu…
Motivic Volumes of Fibers of Tropicalization
Jeremy Usatine
Let be an algebraic torus over an algebraically closed field, let be a smooth closed subvariety of a -toric variety such that is not empty, and let $\math…
Gap Theorems for the Delay of Circuits Simulating Finite Automata
Connor Ahlbach, Jeremy Usatine, Nicholas Pippenger
We study the delay (also known as depth) of circuits that simulate finite automata, showing that only certain growth rates (as a function of the number of steps simulated) are…
A Combinatorial Interpretation of the Joint Cumulant
Connor Ahlbach, Jeremy Usatine, Nicholas Pippenger
In this paper, we apply the combinatorial proof technique of Description, Involution, Exceptions (DIE) to prove various known identities for the joint cumulant. Consider a set of r…
Efficient Algorithms for Zeckendorf Arithmetic
Connor Ahlbach, Jeremy Usatine, Nicholas Pippenger
We study the problem of addition and subtraction using the Zeckendorf representation of integers. We show that both operations can be performed in linear time; in fact they can be…
Barred Preferential Arrangements
Connor Ahlbach, Jeremy Usatine, Nicholas Pippenger
A preferential arrangement of a set is a total ordering of the elements of that set with ties allowed. A barred preferential arrangement is one in which the tied blocks of elements…