2 Expository Talks by Prof. Francois Petit (Sheaves and Persistence & Metric Aspects of Sheaf Theory)

Speaker: Prof. Francois Petit (FCRESS, France)

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Title 1: Sheaves and Persistence

Abstract: In this talk, we will give a brief historical overview of sheaf theory and highlight several of its fundamental concepts. We will then show how sheaf theory arises naturally in topological data analysis (TDA), presenting the various flavors of sheaf-theoretic frameworks used in TDA and exploring their relationships. Emphasis will be placed on the unifying role of sheaf theory and its connections to other approaches within TDA. Finally, considering their theoretical and computational relevance, we will discuss the properties of different types of sheaves in light of their applications in TDA.

Time: 10:00-11:00, July 17, 2025

Location: OIST, Lab 5, Floor D, Room L5D23

This talk will also be broadcast online via Zoom:
Zoom link
Meeting ID: 947 8296 0593
Passcode: 584111

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Title 2: Metric Aspects of Sheaf Theory

Abstract: One of the significant contributions of Topological Data Analysis (TDA) to sheaf theory has been the introduction of various notions of distance on categories of sheaves. These metric structures have opened new research directions, enabling the study of quantitative questions through sheaf theory and the investigation of the metric properties of classical operations and transformations in sheaf theory. Conversely, sheaf theory has also shed light on some metric questions in TDA. In this talk, we will present a selection of results illustrating the mutual contributions between TDA and sheaf theory, particularly in addressing questions of a metric nature.

Time: 10:00-11:00, July 18, 2025

Location: OIST, Lab 5, Floor D, Room L5D23

This talk will also be broadcast online via Zoom:
Zoom Link
Meeting ID: 947 8296 0593
Passcode: 584111

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These talks are part of the Thematic Program TDA PARTI: Topological Data Analysis, Persistence And Representation Theory Intertwined.