# Research

My research area is geometric topology. Some of my interests include low-dimensional topology; manifolds, fiber bundles, and characteristic classes; group actions and Nielsen realization; mapping class groups, diffeomorphism groups, and arithmetic groups.

Collaborators: Alina al Beaini, Mauricio Bustamante, Lei Chen, Jeffrey Giansiracusa, Junzhi Huang, Manuel Krannich, Alexander Kupers, Jean-Francois Lafont, Kathryn Mann, Nick Salter, Daniel Studenmund, Genevieve Walsh

## Research articles

Note: frequently the version on this page is more up-to-date than the version on the arXiv.

Counting flat cycles in the homology of locally symmetric manifolds

with D. Studenmund arxiv: 2206.11986Geometric cycles and characteristic classes of manifold bundles

with appendix by M. Krannich Comment. Math. Helv. 96 (2021) 1, 1-45.Characteristic classes of bundles of K3 manifolds and the Nielsen realization problem

with J. Giansiracusa and A. Kupers Tunis. J. Math. 3 (2021) 1, 75-92.Borel’s stable range for the cohomology of arithmetic groups

J. Lie Theory. 29(2019) 4, 1093-1102.Hyperbolic groups with boundary an n-dimensional Sierpinski space

with J. Lafont J. Topol. Anal. 11 (2019) 1, 233–247.Characteristic classes of fiberwise branched covers via arithmetic groups

Michigan Math. J. 67 (2018), 31–58.## Other articles

Surface bundles in topology, algebraic geometry, and group theory

with N. Salter AMS Notices, Feb. 2020.## Notes

Local coefficients and Poincare duality pdf