1 citations · 3 across the 10 of their papers we have counts for
10 papers
Local degrees of FI-modules through spectral sequences
Cihan Bahran
We establish bounds on the local degrees of FI-modules (in the sense of Church-Miller-Nagpal-Reinhold [CMNR18]) through a spectral sequence which only depend on the initial page an…
Notes on splitting fields
Cihan Bahran
These notes include introductory material on the notion of splitting fields for modules over a k-algebra where k is a field.
Regularity of an FI-module via the derivative functor
Cihan Bahran
We characterize the regularity of an FI-module using the derivative functors.
Improved stability ranges in the homology of Torelli and congruence subgroups
Cihan Bahran
We improve the central stability ranges for H2(Torelli subgroup of Aut(Fn)'s) as GL_n(Z)-representations, H2(Torelli subgroup of mapping class groups) as Sp_2g(Z)-representations,…
Onset of regularity for FI-modules
Cihan Bahran
In terms of local cohomology, we give an explicit range as to when the FI-homology of an FI-module attains its regularity.
Polynomial conditions and homology of FI-modules
Cihan Bahran
We identify two recursively defined polynomial conditions for FI-modules in the literature. We characterize these conditions using homological invariants of FI-modules (namely the…
Regularity and stable ranges of FI-modules
Cihan Bahran
We give refined bounds for the regularity of FI-modules and the stable ranges of FI-modules for various forms of their stabilization studied in the representation stability literat…
The commuting complex of the symmetric group with bounded number of -cycles
Cihan Bahran
For a fixed prime , we consider a filtration of the commuting complex of elements of order in the symmetric group . The filtration is obtained by imposing su…
Categorifying induction formulae via divergent series
Cihan Bahran
We show how to get explicit induction formulae for finite group representations, and more generally for rational Green functors, by summing a divergent series over Dwyer's subgroup…
An improvement in the linear stable ranges for ordered configuration spaces
Cihan Bahran
Recently, Church-Miller-Nagpal-Reinhold [arXiv:1706.03845] obtained linear stable ranges for the integral cohomology of ordered configuration spaces, in the sense of representation…