Research interests 

I challenge problems in geometry and topology, which are inspired by Gromov's conjectures, by investigating applications of Cheeger-Gromov L2-invariants and Atiyah-Singer ρ-invariants. 

Papers

• Quantitative asphericalization and bounds on rho-invariants, in preparation.

• Generalized Baumslag-Dyer-Heller groups, in preparation.

• Gromov linearity problem over virtually acyclic groups (joint with James F. Davis), in preparation.

• Quantitative bordism over acyclic groups and Cheeger-Gromov ρ-invariants (joint with Jae Choon Cha), arXiv preprint, arXiv:2404.11885 (Apr. 18, 2024), submitted.

• Bounds on Cheeger-Gromov invariants and simplicial complexity of triangulated manifolds (joint with Shmuel Weinberger), Journal für die reine und angewandte Mathematik (Crelle's Journal) vol. 808 (2024), pp. 271-297. (arXiv preprint arXiv:2301.08870)

• Enhanced bounds for rho-invariants for both general and spherical 3-manifolds, Journal of Topology and Analysis vol. 16 no. 3 (2024), pp. 409–459. (arXiv preprint arXiv:2103.12889)