I'm Noah, a postdoctoral fellow at the University of Edinburgh. From 2025-26 I was a postdoc at the Max Planck Institute for Mathematics in Bonn and from 2022-2025 I was a postdoc at Imperial College London, with Yankı Lekili. From 2019-22, I did my PhD with Ivan Smith at the University of Cambridge.

Some open problems

Here is a list of open problems regarding the connections between Floer theory and homotopy theory, assembled collaboratively at an IML workshop.

Research

My research is in symplectic topology. Broadly, I am interested in algebraic invariants built from spaces of holomorphic curves. Some things I like to think about are Fukaya categories, Floer homotopy theory, string topology and algebraic K-theory of spaces.

Publications/preprints

Bulk-deformations, Floer complex bordism, and Grothendieck-Riemann-Roch. Joint with Kenneth Blakey. (2026). [arXiv].

Bordism from quasi-isomorphism. Joint with Ivan Smith. (2025). [arXiv].

Open-closed maps and spectral local systems. Joint with Ivan Smith. (2025). [arXiv].

On the parametrised Whitehead torsion of families of nearby Lagrangian submanifolds. Joint with Sylvain Courte. (2025). [arXiv].

Spectral Floer theory and tangential structures. Joint with Ivan Smith. [arXiv] (2024). [Journal] Trans. Amer. Math. Soc. 379 (2026), no. 07, 4737–4808.

Obstructions to homotopy invariance of loop coproduct via parametrised fixed-point theory. Joint with Lea Kenigsberg. [arXiv] (2024). [Journal] J. Topol., 19: e70066 (2026).

C0 Lagrangian monodromy. [arXiv] (2024). [Journal] Bull. London Math. Soc. (2025).

Bordism of flow modules and exact Lagrangians. Joint with Ivan Smith. (2024) [arXiv].

Lagrangian intersections and cuplength in generalised cohomology theories. Joint with Amanda Hirschi. [arXiv] (2022). [Journal] Math. Res. Lett. Vol. 32, Issue 1 (2025).

Families of relatively exact Lagrangians, free loop spaces and generalised homology. [arXiv] (2022). [Journal] Sel. Math. New Ser. 30, 21 (2024). 

See this list on the arXiv. Comments/corrections are always welcome.

Oberwolfach report: Normal invariants of nearby Lagrangians, based on joint work with Ivan Smith.

Contact

nporcell AT ed DOT ac DOT uk (note the absence of the last letter of my name).

E-mails to my old (Imperial or MPIM) E-mail addresses will not be received.