🍩 Database of Original & Non-Theoretical Uses of Topology

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  1. The Persistence of Painting Styles (2025)

    Reetikaa Reddy Munnangi, Barbara Giunti
    Abstract Art is a deeply personal and expressive medium, where each artist brings their own style, technique, and cultural background into their work. Traditionally, identifying artistic styles has been the job of art historians or critics, relying on visual intuition and experience. However, with the advancement of mathematical tools, we can explore art through more structured lens. In this work, we show how persistent homology (PH), a method from topological data analysis, provides objective and interpretable insights on artistic styles. We show how PH can, with statistical certainty, differentiate between artists, both from different artistic currents and from the same one, and distinguish images of an artist from an AI-generated image in the artist's style.

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  2. SuPerPoV: Score and Evolution of the Stratospheric Polar Vortex via Persistent Homology (2026)

    Jake Cordes, Barbara Giunti, Zheng Wu
    Abstract Classifying the stratospheric polar vortex provides predictability for surface weather on extended-range timescales definitions of these events proposed in over 60 years of study depend on empirically chosen parameters and yield different results when one of them changes. Moreover, as previous definitions are based on static thresholds, it is not straightforward to use them to study the spatiotemporal evolution of the vortexe introduce SuPerPoV, a score system that computes displacement and split ratiossing tools from applied topology. The computation is entirely threshold-free, open source, and does not require familiarity with applied topology. The scores generally recovers previous definitions and are output for a user-defined number of days, thus showing the evolution of the event. SuPerPoV offers a paradigm shift in the study of the polar vortex, hopefully bringing a deeper understanding of the polar vortex and related extreme events, such as sudden stratospheric warmings.

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