Preprints and Publications:
With Sierra Knavel and Tom Rodewald. The Fary-Milnor theorem for Legendrian knots. In preparation.
Exotic R^4's as unions of two thickened circles. Preliminary draft here . 2026.
Irreducible Proper 2-knots From Exotic Open 2-handles. 2026. arXiv
With Shunyu Wan. Exotic R^4's, RBG Links, and End Floer Homology. 2026. arXiv
With Jen Hom and Tye Lidman. Distinguishing Exotic R^4's With Heegaard Floer Homology. 2026. arXivÂ
With M. Schweinberger. Non-Asymptotic Model Selection for Models of Network Data With Parameter Vectors of Increasing Dimension. Journal of Statistical Planning and Inference, Vol. 233. 2024. https://doi.org/10.1016/j.jspi.2024.106173
With K. Josic. Book Review: Visual Differential Geometry and Forms: a Mathematical Drama in Five Acts. SIAM Review Vol 65. Iss. 4. 2023. https://doi.org/10.1137/23N975818
Comments: The homeomorphisms in all exotic 4-manifold results to date follow from descendants of Freedman's theorem that Casson handles are homeomorphic to open 2-handles. I want to understand these homeomorphisms by explicitly describing topologically flat core disks. This is closely related to explicitly describing large exotic R^4's, which has never been done. Most of my 4-manifold research so far was inspired by this fundamental problem.
Thinking About These:
Various other problems in low-dimensional topology!