Low energy levels of harmonic spheres in analytic manifolds
 Rupflin, M Journal of Functional Analysis

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Celebrate Green Action Week (10–14 February)

Bring your own cup or container and enjoy 50p off any hot drink or meal. This offer is valid all week (10–14 February). 

And try our freshly baked Lemon Drizzle Cake, made using surplus lemons and milk. It's a delicious way to enjoy a sustainable treat while supporting our efforts to reduce food waste. Available during Green Action Week.

Annual Strachey Lecture

Shafi Goldwasser (Berkeley (USA), MIT (USA), Weizmann (Israel)) - Privacy, Verification, Robustness: A Cryptographer's perspective on ML

4 March, 11:00 am, Oxford University Museum of Natural History, Parks Road, Oxford, OX1 3PW

The Strachey Lectures are a series of termly computer science lectures named after Christopher Strachey, the first Professor of Computation at the University of Oxford.

Complexity Cluster Event

Glen Callater Room, H B Allen Centre, Keble College, Wednesday, 12 February 2025. All welcome. Coffee from 4.10 pm.

Public Lecture: Helge Holden (Chair of the Abel Prize Committee) - The Abel Prize 

Workshops: Jose Carrillo - Aggregation-Diffusion Equations for Collective Behaviour in the Sciences;

François Caron - Frequentist, Assisted by Bayes, Prediction-Powered Inference;

Andras Juhasz - The Unknotting Number, Hard Unknot Diagrams, and Reinforcement Learning

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)
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.
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