Tootfinder

Projective Delineability for Single Cell Construction
Jasper Nalbach, Lucas Michel, Erika \'Abrah\'am, Christopher W. Brown, James H. Davenport, Matthew England, Pierre Mathonet, Na\"im Z\'ena\"idi
https://arxiv.org/abs/2508.00512

Projective Delineability for Single Cell Construction
The cylindrical algebraic decomposition (CAD) is the only complete method used in practice for solving problems like quantifier elimination or SMT solving related to real algebra, despite its doubly exponential complexity. Recent exploration-guided algorithms like NLSAT, NuCAD, and CAlC rely on CAD technology but reduce the computational effort heuristically. Single cell construction is a paradigm that is used in each of these algorithms. The central property on which the CAD algorithm is bas…

The magnetic and spin-down properties of slowly rotating fully convective M dwarfs
Victor See, Louis Amard, Stefano Bellotti, Sudeshna Boro Saikia, Emma L. Brown, Jean-Francois Donati, Rim Fares, Adam J. Finley, Colin P. Folsom, \'Elodie M. H\'ebrard, Moira M. Jardine, Sandra V. Jeffers, Baptiste Klein, Lisa T. Lehmann, Stephen C. Marsden, Sean P. Matt, Matthew W. Mengel, Julien Morin, Pascal Petit, Katelyn Smith, Aline A. Vidotto, Ian A. Waite

The magnetic and spin-down properties of slowly rotating fully convective M dwarfs
The evolution of the magnetism, winds and rotation of low-mass stars are all linked. One of the most common ways to probe the magnetic properties of low-mass stars is with the Zeeman-Doppler imaging (ZDI) technique. The magnetic properties of partially convective stars has been relatively well explored with the ZDI technique, but the same is not true of fully convective stars. In this work, we analyse a sample of stars that have been mapped with ZDI. Notably, this sample contains a number of sl…

Self-lensing binaries as probes of Supernova physics
Grzegorz Wiktorowicz, Matthew Middleton, Aleksandra Olejak, Cordelia Dashwood-Brown, Madeleine-Mai Ward, Adam Ingram
https://arxiv.org/abs/2509.11726

Self-lensing binaries as probes of Supernova physics
Self-lensing (SL) in binary systems has the potential to provide a unique observational window into the Galactic population of compact objects. Using the $\mathtt{startrack}$ and COSMIC population synthesis codes, we investigate how different supernova mechanisms affect the observable population of SL systems, with particular attention to the mass gap (2$\mathrm{-}$5 M$_\odot$) in compact object distributions. We test three supernova remnant formation models with different convective growth tim…

Higher tensor categories and their extensions: notes from the Scottish Talbot On Algebra and Topology
Diogo Andrade, Julia Bierent, Jennifer Brown, Tudor Caba, Matthew Cellot, Jonathan Davies, Adrien DeLazzer Meunier, Jannik Gr\"one, Benjamin Ha\"ioun, Alea Hofstetter, Theo Johnson-Freyd, David Jordan, Tessa Kammermeier, Patrick Kinnear, Cameron Krulewski, Theodoros Lagiotis, Leon Liu, Adri\`a Mar\'in Salvador, Nivedita, David Reutter, Lorenzo Riva, Iordanis Romaidis, Ja…

Higher tensor categories and their extensions: notes from the Scottish Talbot On Algebra and Topology
These lecture notes are the product of a week-long learning workshop on the work of Johnson-Freyd and Reutter on the problem of the existence of minimal nondegenerate extensions of braided fusion categories (arXiv:2105.15167). They recount the mathematical arguments of the original paper from an expository angle, with background material covering the algebra and homotopy theory required to understand the statement and follow the proof. The notes are aimed at newcomers to the field of (braided) …