Danny Calegari

activity

20242026

collaborators

6 papers

math.DS2026

Laminations and External Angles for Similarity Pairs

Danny Calegari, Alden Walker

A {\em similarity pair} is the dynamical system in $C$ generated by two maps $f : z \to sz - 1$ and $g : z \to sz + 1$ for $∣ s ∣ < 1$ . Associated to the dynamical system is an attrac…

math.DS2026

Quasimorphisms and Pseudo-Anosov flows

Danny Calegari, Jonathan Zung

We describe two connections between the theory of quasimorphisms and pseudo-Anosov flows without perfect fits on closed hyperbolic 3-manifolds. First we show that for every such fl…

math.GT2026

CaTherine wheels

Danny Calegari, Ino Loukidou

A CaTherine wheel is a surjective continuous map $f : S^{1} \to S^{2}$ such that for every closed interval $I \subset S^{1}$ the image $f (I)$ is homeomorphic to a disk, and $f (\partial I)$ …

math.PR2026

CaTherine wheels from trees and Liouville quantum gravity

Danny Calegari, Ewain Gwynne

A CaTherine wheel is a space-filling curve $f : S^{1} \to S^{2}$ such that for every closed interval $J \subset S^{1}$ , $f (J)$ is homeomorphic to a closed disk and $f (\partial J)$ is conta…

cs.LG2025

Triangulating PL functions and the existence of efficient ReLU DNNs

Danny Calegari

We show that every piecewise linear function $f : R^{d} \to R$ with compact support a polyhedron $P$ has a representation as a sum of so-called `simplex functions'. Such representation…

math.DS2024

Big mapping class groups and rigidity of the simple circle

Danny Calegari, Lvzhou Chen

Let $I^$ denote the mapping class group of the plane minus a Cantor set. We show that every action of $I^$ on the circle is either trivial or semi-conjugate to a unique minimal act…