Toric gravitational instantons in gauged supergravity
Benetti Genolini, P Gauntlett, J Jiao, Y Luscher, A Sparks, J Physical Review D volume 111 (24 Feb 2025)

Tribute bands are ten a penny, but parody bands, where the songs are imitative but original, are rarer and none reached the brilliance of Neils Innes' Beatles parody, the Rutles. So good in fact that the Beatles themselves loved them (Beatle George Harrison funded the documentary) and the songs are now widely recognised on their own merits. Let's be natural.

Low energy levels of harmonic spheres in analytic manifolds
Rupflin, M Journal of Functional Analysis volume 289 issue 6 (14 Apr 2025)
Machine learning for classifying chronic kidney disease and predicting creatinine levels using at-home measurements
Metherall, B Berryman, A Brennan, G Scientific Reports volume 15 issue 1 (05 Feb 2025)
Holographic Carrollian currents for massless scattering
Ruzziconi, R Saha, A Journal of High Energy Physics volume 2025 issue 1 (29 Jan 2025)
Certifiably robust policies for uncertain parametric environments
Schnitzer, Y Abate, A Parker, D Proceedings of the 31st International Conference on Tools and Algorithms for the Construction and Analysis of Systems (TACAS 2025) volume 15698 63-83 (01 May 2025)
Fri, 21 Feb 2025
15:00
L4

Monodromy in bi-parameter persistence modules

Sara Scaramuccia
(University of Rome Tor Vergata)

Note: we would recommend to join the meeting using the Teams client for best user experience.

Abstract

Informally, monodromy captures the behavior of objects when one circles around a singularity. In persistent homology, non-trivial monodromy has been observed in the case of biparameter filtrations obtained by sublevel sets of a continuous function [1]. One might consider the fundamental group of an admissible open subspace of all lines defining linear one-parameter reductions of a bi-parameter filtration. Monodromy occurs when this fundamental group acts non-trivially on the persistence space, i.e. the collection of all the persistence diagrams obtained for each linear one-parameter reduction of the bi-parameter filtration. Here, under some tameness assumptions, we formalize the monodromy behavior in algebraic terms, that is in terms of the persistence module associated with a bi-parameter filtration. This allows to translate monodromy in terms of persistence module presentations as bigraded modules. We prove that non-trivial monodromy involves generators within the same summand in the direct sum decomposition of a persistence module. Hence, in particular interval-decomposable persistence modules have necessarily trivial monodromy group.

The work is under development and it is a joint collaboration with Octave Mortain from the École Normale Superieure, Paris.
 
[1] A. Cerri, M. Ethier, P. Frosini, A study of monodromy in the computation of multidimensional persistence, in: Proc. 17th IAPR Int. Conf. Discret. Geom. Comput. Imag., 2013: pp. 1–12.
Subscribe to