Comments: I have been thinking about Exotic R4's and Casson handles a lot recently. Every homeomorphism in every known exotic 4-manifold result comes from descendants of Freedman's theorem that Casson handles are homeomorphic to 2-handles. My goal is to understand Casson handles further and try to see what the topologically flat core disk looks like. Most of my 4-manifold research so far was inspired by this fundamental problem.
Preprints:
Irreducible Proper 2-knots From Exotic Open 2-handles. 2026. Draft available upon request.
With Shunyu Wan. Distinct Slice R4's Made from the Same Pieces. 2026. Draft available upon request.
With Jen Hom and Tye Lidman. Distinguishing Exotic R^4's With Heegaard Floer Homology. 2026. arxiv
Writing These Up:
With Sierra Knavel and Tom Rodewald. The Legendrian Fary-Milnor Theorem.
Thinking About These:
Kirby Diagrams for Large Exotic R4's and applications to topological slicing.
Plumbing 3-handles.
Decomposing exotic R4's into simple spaces.
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.
Older:
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