Research
My interests lie broadly in the area of geometric group theory, and most often concern properties and invariants of arithmetic groups. My research includes results on group cohomology, superrigidity, abstract commensurators, full residual finiteness growth, and commensurability growth.
Preprints
Counting flat cycles in the homology of locally symmetric spaces, D. Studenmund and B. Tshishiku, submitted.
Topological models of abstract commensurators, E. A. Bering IV and D. Studenmund, to appear in Groups, Geometry, and Dynamics.
Research Papers
Hall's universal group is a subgroup of the abstract commensurator of a free group, E. A. Bering IV and D. Studenmund, Israel J Math. (2023) https://doi.org/10.1007/s11856-023-2591-8
The dualizing module and top-dimensional cohomology group of GLn(O), A. Putman and D. Studenmund, Math. Z. 300 (2022), no. 1, 1–31.
On abstract commensurators of surface groups, K. Bou-Rabee and D. Studenmund, J. Topol. Anal. 13 (2021), no. 3, 607-622.
Arithmetic lattices in unipotent algebraic groups, K. Bou-Rabee and D. Studenmund, J. Group Theory. 23 (2020), no. 2, 299–312.
Commensurability growth of branch groups, K. Bou-Rabee, R. Skipper, and D. Studenmund, Pacific J. Math. 304-1 (2020), 43-54
Commensurability growths of algebraic groups, K. Bou-Rabee, T. Kaletha, and D. Studenmund, Math. Z. 294 (2020), no. 3-4, 1749–1757.
The topology of local commensurability graphs, K. Bou-Rabee and D. Studenmund, New York J. Math. 24 (2018), 429–442. See accompanying GAP code, Mathematica notebook, and data.
Semidualities from products of trees, D. Studenmund and K. Wortman, Geom. Topol. 22 (2018), no. 3, 1717–1758
Full residual finiteness growths of nilpotent groups, K. Bou-Rabee and D. Studenmund, Israel J. Math. 214 (2016), no. 1, 209-233
Commensurators of solvable S-arithmetic groups, D. Studenmund, Pacific J. Math. 283 (2016), no. 1, 201-221
Abstract commensurators of lattices in Lie groups, D. Studenmund, Comment. Math. Helv. 90 (2015), no. 2, 287–323
Nonarchimedean superrigidity of solvable S-arithmetic groups, D. Witte Morris and D. Studenmund, J. Algebra. 416 (2014), 184–199
Expository Papers
Abstract commensurators: a survey of constructions and computations -- to appear in the Proceedings of the Beyond Hyperbolicity Conference.
Talks
Full residual finiteness growth of nilpotent groups (slides), AMS Northeast Sectional Meeting, September 2016
Cohomology of the lamplighter group (slides), 50th Spring Topology and Dynamics Conference, March 2016
Abstract commensurators of lattices in Lie groups (slides), 47th Spring Topology and Dynamics Conference, March 2013