Comments: I'm 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. So I think it's a good idea to understand Casson handles further and try to see what that flat disk looks like. Most of my 4-manifold research so far was inspired by this fundamental problem.
Preprints Out:
With Jen Hom and Tye Lidman. Distinguishing Exotic R^4's with Heegaard Floer Homology. 2026. arxiv
Writing These Up:
Exotic R4’s as branched covers, exotic open 2-handles, and topologically slice links.
With Sierra Knavel and Tom Rodewald. Legendrian Fary-Milnor Theorems.
With Akash Narayanan. Do Smooth Curves Detect Minima?
With Nick Castro, Mark Hughes, Seungwon Kim, Maggie Miller, and Yikai Teng. Noncompact trisections.
(note: the Laudenbach-Poenaru theorem holds for non compact 1-handlebodies. Details available upon request.)
Thinking About These:
Kirby Diagrams for Large Exotic R4's and applications to topological slicing.
With Shunyu Wan. Exotic Stein structures on Exotic R4's
Pushing End Floer homology further: branching Casson handles and exotic planes.
Explicit Exotic R4's with compactly supported diffeomorphisms.
Foliations of Exotic R4's
Older:
S. Eli, 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
S. Eli, 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