346 citations · 1.2k across the 23 of their papers we have counts for
6 papers · 1 filter
Linear and quadratic ranges in representation stability
Thomas Church, Jeremy Miller, Rohit Nagpal +1
We prove two general results concerning spectral sequences of -modules. These results can be used to significantly improve stable ranges in a large portion of the stab…
Bounding the homology of FI-modules
Thomas Church
The main theorem of Church-Ellenberg [arXiv:1506.01022] is a sharp bound on the homology of FI-modules, showing that the Castelnuovo-Mumford regularity of FI-modules over Z can be…
Homology of FI-modules
Thomas Church, Jordan S. Ellenberg
We prove an explicit and sharp upper bound for the Castelnuovo-Mumford regularity of an FI-module V in terms of the degrees of its generators and relations. We use this to refine a…
FI-modules over Noetherian rings
Thomas Church, Jordan S. Ellenberg, Benson Farb +1
FI-modules were introduced by the first three authors in [CEF] to encode sequences of representations of symmetric groups. Over a field of characteristic 0, finite generation of an…
FI-modules and stability for representations of symmetric groups
Thomas Church, Jordan S. Ellenberg, Benson Farb
In this paper we introduce and develop the theory of FI-modules. We apply this theory to obtain new theorems about: - the cohomology of the configuration space of n distinct ordere…
Representation theory and homological stability
Thomas Church, Benson Farb
We introduce the idea of *representation stability* (and several variations) for a sequence of representations V_n of groups G_n. A central application of the new viewpoint we intr…