19 citations · 133 across the 26 of their papers we have counts for
33 papers
Polynomial stability of the homology of Hurwitz spaces
Andrea Bianchi, Jeremy Miller
For a finite group and a conjugation-invariant subset , we consider the Hurwitz space parametrising branched covers of the plane with bran…
On rank filtrations of algebraic K-theory and Steinberg modules
Jeremy Miller, Peter Patzt, Jennifer C. H. Wilson
Motivated by his work on the stable rank filtration of algebraic K-theory spectra, Rognes defined a simplicial complex called the common basis complex and conjectured that this com…
A degree theorem for the simplicial closure of Auter space
Juliet Aygun, Jeremy Miller
The degree of a based graph is the number of essential nonbasepoint vertices after generic perturbation. Hatcher--Vogtmann's degree theorem states that the subcomplex of Auter spac…
On the codimension-two cohomology of
Benjamin Brück, Jeremy Miller, Peter Patzt +2
Borel-Serre proved that is a virtual duality group of dimension and the Steinberg module is its dualizing modu…
The free factor complex and the dualizing module for the automorphism group of a free group
Zachary Himes, Jeremy Miller, Sam Nariman +1
Answering a question of Hatcher-Vogtmann, we prove that the top homology group of the free factor complex is not the dualizing module for , at least for .
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…
Improved homological stability for certain general linear groups
Alexander Kupers, Jeremy Miller, Peter Patzt
We prove that the general linear groups of the integers, Gaussian integers, and Eisenstein integers satisfy homological stability of slope 1 when using -coefficien…
Mapping class group actions on configuration spaces and the Johnson filtration
Andrea Bianchi, Jeremy Miller, Jennifer C. H. Wilson
Let denote the configuration space of ordered points on the surface and let denote the mapping class group of . We prove that the ac…
On the generalized Bykovskii presentation of Steinberg modules
Alexander Kupers, Jeremy Miller, Peter Patzt +1
We study presentations of the virtual dualizing modules of special linear groups of number rings, the Steinberg modules. Bykovskii gave a presentation for the Steinberg modules of…
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…
On the top dimensional cohomology groups of congruence subgroups of
Jeremy Miller, Peter Patzt, Andrew Putman
Let be the level- principal congruence subgroup of . Borel-Serre proved that the cohomology of vanishes above degree . W…
FI-hyperhomology and ordered configuration spaces
Jeremy Miller, Jennifer C. H. Wilson
Using a result of Guès on FI-hyperhomology (a variant of a result of Gan-Li) and a semi-simplicial resolution of configuration spaces due to Kupers-Miller-Tran, we establish an exp…
Non-integrality of some Steinberg modules
Jeremy Miller, Peter Patzt, Jennifer C. H. Wilson +1
We prove that the Steinberg module of the special linear group of a quadratic imaginary number ring which is not Euclidean is not generated by integral apartments. Assuming the gen…
The May-Milgram filtration and -cells
Inbar Klang, Alexander Kupers, Jeremy Miller
We describe an -cell structure on the free -algebra on a point, and more generally describe how the May-Milgram filtration of lifts to a filtration of…
Stability in the high-dimensional cohomology of congruence subgroups
Jeremy Miller, Rohit Nagpal, Peter Patzt
We prove a representation stability result for the codimension-one cohomology of the level three congruence subgroup of . This is a special case of a que…
Quantitative representation stability over linear groups
Jeremy Miller, Jennifer C. H. Wilson
We introduce a technique for proving quantitative representation stability theorems for sequences of representations of certain finite linear groups over a field of characteristic…
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…
Central stability for the homology of congruence subgroups and the second homology of Torelli groups
Jeremy Miller, Peter Patzt, Jennifer C. H. Wilson
We prove a representation stability result for the second homology groups of Torelli subgroups of mapping class groups and automorphism groups of free groups. This strengthens the…
Higher order representation stability and ordered configuration spaces of manifolds
Jeremy Miller, Jennifer C. H. Wilson
Using the language of twisted skew-commutative algebras, we define \emph{secondary representation stability}, a stability pattern in the {\it unstable} homology of spaces that are…
Sharper periodicity and stabilization maps for configuration spaces of closed manifolds
Alexander Kupers, Jeremy Miller
In this note we study the homology of configuration spaces of closed manifolds. We sharpen the eventual periodicity results of Nagpal and Cantero-Palmer, prove integral homological…
Homological stability for symmetric complements
Alexander Kupers, Jeremy Miller, TriThang Tran
Conjecture F from [VW12] states that the complements of closures of certain strata of the symmetric power of a smooth irreducible complex variety exhibit rational homological stabi…
Representation stability for homotopy groups of configuration spaces
Alexander Kupers, Jeremy Miller
We prove that the dual rational homotopy groups of the configuration spaces of a 1-connected manifold of dimension at least 3 are uniformly representation stable in the sense of Ch…
A twisted homology fibration criterion and the twisted group-completion theorem
Jeremy Miller, Martin Palmer
The purpose of this note is to clarify some details in McDuff and Segal's proof of the group-completion theorem and to generalize both this and the homology fibration criterion of…
-cell attachments and a local-to-global principle for homological stability
Alexander Kupers, Jeremy Miller
We define bounded generation for -algebras in chain complexes and prove that for this property is equivalent to homological stability. Using this we prove a local-t…