26 citations · 44 across the 14 of their papers we have counts for
15 papers
Stable homology of strata of abelian differentials
Philip Tosteson
We show that the homology of strata of abelian differentials stabilizes in a range where the number of simple zeros is large relative to the homological degree. In this range, we s…
Representation stability for moduli spaces of admissible covers
Megan Chang-Lee, Siddarth Kannan, Philip Tosteson
We prove a representation stability result for the sequence of spaces of pointed admissible -covers of stable -pointed genus- curves, for an abelian…
Homological stability and Manin's conjecture for rational curves on quartic del Pezzo surfaces
Ronno Das, Brian Lehmann, Sho Tanimoto +1
We prove a version of Manin's conjecture (over for large) and the Cohen--Jones--Segal conjecture (over ) for maps from rational curves to split qua…
Homology of spaces of curves on blowups
Ronno Das, Philip Tosteson
We consider the space of holomorphic maps from a compact Riemann surface to a projective space blown up at finitely many points. We show that the homology of this mapping space equ…
Hilbert series of representations of categories of -sets
Philip Tosteson
Let be a finite group. A contravariant functor from the category of finite free -sets to vector spaces has an associated Hilbert series, which records the underlying sequenc…
Polynomial representations of the Witt Lie algebra
Steven V Sam, Andrew Snowden, Philip Tosteson
The Witt algebra W_n is the Lie algebra of all derivations of the n-variable polynomial ring V_n=C[x_1, ..., x_n] (or of algebraic vector fields on A^n). A representation of W_n is…
Representation stability for the Kontsevich space of stable maps
Philip Tosteson
For a fixed algebraic variety , curve class , and genus , we consider the sequence of representations obtained from the homology of the Konts…
Extremal stability for configuration spaces
Ben Knudsen, Jeremy Miller, Philip Tosteson
We study stability patterns in the high dimensional rational homology of unordered configuration spaces of manifolds. Our results follow from a general approach to stability phenom…
Categorifications of rational Hilbert series and characters of modules
Philip Tosteson
We introduce a method for associating a chain complex to a module over a combinatorial category, such that if the complex is exact then the module has a rational Hilbert series. We…
Factorization statistics and bug-eyed configuration spaces
Dan Petersen, Philip Tosteson
A recent theorem of Hyde proves that the factorizations statistics of a random polynomial over a finite field are governed by the action of the symmetric group on the configuration…
Representation stability for pure braid group Milnor fibers
Jeremy Miller, Philip Tosteson
We prove a representation stability result for the Milnor fiber associated to the pure braid group. Our result connects previous work of Simona Settepenella to representation stabi…
Stability in the homology of Deligne-Mumford compactifications
Philip Tosteson
Using the the theory of FS^op modules, we study the asymptotic behavior of the homology of , the Deligne--Mumford compactification of the moduli space of curves,…
Lattice Spectral Sequences and Cohomology of Configuration Spaces
Philip Tosteson
For a topological space , we introduce a criterion for the module to be finitely generated and give several applications. For instance, if is…
The Distribution of Gaps between Summands in Generalized Zeckendorf Decompositions
Amanda Bower, Rachel Insoft, Shiyu Li +2
Zeckendorf proved that any integer can be decomposed uniquely as a sum of non-adjacent Fibonacci numbers, . Using continued fractions, Lekkerkerker proved the average number o…
The Average Gap Distribution for Generalized Zeckendorf Decompositions
Olivia Beckwith, Amanda Bower, Louis Gaudet +4
An interesting characterization of the Fibonacci numbers is that, if we write them as , , , , then every positive integer can be written un…