James Pascaleff

collaborators

3 papers

math.SG2025

Speculations on higher Fukaya categories

James Pascaleff, Nicolò Sibilla

We investigate a possible theory of higher Fukaya categories associated to $n$ -shifted symplectic stacks, where $n \geq 0$ . We consider two paradigmatic cases, the shifted cotangen…

math.AT2025

Higher local systems and the categorified monodromy equivalence

James Pascaleff, Emanuele Pavia, Nicolò Sibilla

We study local systems of $(\infty, n)$ -categories on spaces. We prove that categorical local systems are captured by (higher) monodromy data: in particular, if $X$ is $(n + 1)$ -conne…

math.SG2021

Fukaya categories of higher-genus surfaces and pants decompositions

James Pascaleff, Nicolò Sibilla

In this paper we prove a local-to-global principle for the Fukaya category of a closed Riemann surface $Σ$ of genus $g \geq 2$ . We show that $Fuk (Σ)$ can be glued from the…