Research
My previous research has focused on the classical problem of classifying smooth 3-manifolds bounding smooth 4-manifolds, with a particular emphasis on homology 3-spheres, contractible 4-manifolds, and contractible/acyclic complex surfaces. I am currently working on a variation of this problem by focusing on smooth codimension 1 embeddings. Recently, I have become particularly interested in symmetric classical knots, knotting in higher dimensions, and contact and symplectic structures on 3- and 4-manifolds.
• Ozsváth-Szabó d-invariants of almost simple linear graphs (with Çağrı Karakurt)
Journal of Knot Theory and its Ramifications 29 (2020), no. 5, 2050029, 17 pp. (Journal) (arXiv) (Mathscinet)
• More Brieskorn spheres bounding rational balls
Topology and its Applications 286 (2020), 107400, 10 pp. (Journal) (arXiv) (Mathscinet)
• Classical and new plumbed homology spheres bounding contractible manifolds
To appear in International Journal of Mathematics (arXiv)
• Almost simple linear graphs, homology cobordism and connected Heegaard Floer homology (with Çağrı Karakurt)
Acta Mathematica Hungarica 168 (2022), no.2, 454–489 (Journal) (arXiv) (Mathscinet)
• A survey of the homology cobordism group
Bulletin of the American Mathematical Society New Series 61 (2024), no. 1, 119–157 (Journal) (arXiv) (Mathscinet)
• On homology planes and contractible 4-manifolds (with Rodolfo Aguilar Aguilar)
Published online in Bulletin of the London Mathematical Society and in press (arXiv)