Barbara Giunti - An introduction to Topological Data Analysis via its industrial applications

Abstract: Topological Data Analysis (TDA) is a discipline that applies the techniques of the theoretical field of algebraic topology to analyze complex, multi-dimensional data. Despite being a relatively new field, TDA has been widely and successfully applied across various domains, such as medicine, materials science, and biology.

In this seminar, I will provide a gentle introduction to the mathematical background of TDA, exemplifying its techniques using industrial applications. I will provide an intuition of some of TDA’s most successful tools, such as Mapper, Persistent Homology, and UMAP, describing their strengths and weaknesses, their successes, and, perhaps more importantly, the areas where they have potential for significant contributions but are currently underutilized.

Bio: Barbara Giunti defended her PhD thesis on Topological Data Analysis at the University of Pavia in December 2019. Afterwards, she worked for one year as a postdoctoral fellow at the University of Modena and Reggio Emilia. Between December 2020 and July 2023, she was a postdoctoral researcher at Graz University of Technology. In August 2023, Giunti joined the Departments of Mathematics and Statistics at the University at Albany as an Assistant Professor. Her work is on applied topology, and she is especially interested in parameterized chain complexes and their use in the theory, computation, and applications of Topological Data Analysis. Giunti is one of the creators and maintainers of DONUT – Database of Original & Non-Theoretical Uses of Topology, a public database of real-world applications of Topological Data Analysis.