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. Draft available upon request. 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. arXiv
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:
Kirby Diagrams for Large Exotic R4's and applications to topological slicing.
Plumbing 3-handles.
With Shunyu Wan. Exotic Stein structures on Exotic R4's
End Floer homology of branching Casson handles.
Explicit Exotic R4's with compactly supported diffeomorphisms.
Foliations of Exotic R4's
With Nick Castro, Mark Hughes, Seungwon Kim, Maggie Miller, and Yikai Teng. Noncompact trisections.