I'm Noah, a postdoctoral fellow at the Max Planck Institute for Mathematics in Bonn. From 2022-2025, I was a postdoc at Imperial College London, with Yankı Lekili, and from 2019-2022, I did my PhD with Ivan Smith at the University of Cambridge.
In 2023-24 I co-organised the London Geometry & Topology Seminar along with Mykola Matviichuk.
In 2022 I spent part of the autumn term at the MSRI for their program on Floer homotopy theory.
Together with Ilaria di Dedda, Yankı Lekili and Daniil Mamaev, we organised a workshop in symplectic topology from the 7th to 9th of June 2023 at Imperial.
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
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. (2024). [arXiv]. Accepted, to appear in Trans. Amer. Math. Soc.
Obstructions to homotopy invariance of loop coproduct via parametrised fixed-point theory. Joint with Lea Kenigsberg. (2024). [arXiv].
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.
Contact
porcelli AT mpim-bonn DOT mpg DOT de
E-mails to my old (Imperial) E-mail address will not be received.
