May 21, 2025
In this talk I will introduce the main topics about the new field of research called Neuroalgebraic Geometry. In particular I will focus on the definitions, results (and conjectures) contained in the papers
- J. Kileel, M. Tranger, J. Bruna, On the Expressive Power of Deep Polynomial Neural Networks, (2019).
- K. Kubjas, J. Li, M. Wiesmann, Geometry of polynomial neural networks, (2024).
- G. L. Marchetti, V. Shahverdi, S. Mereta, M. Trager, K. Kohn, An Invitation to Neuroalgebraic Geometry, (2025).
and I will talk also about my recent results on it and a list of suggested problems
The structure of this program is built upon a series of meetings throughout the academic year. Its primary objective is to provide not only a comprehensive background on the subject but also an opportunity to stay updated on the current state of research activities related to tensor decomposition, secant varieties, and other topics in algebraic geometry. Additionally, it serves as a way for sharing and exchanging ideas with experts in these areas and for connecting with young researchers who are embarking on their academic careers.
The meetings are usually scheduled to occur every three weeks between the Department of Mathematics and Computer Science "Ulisse Dini" at the University of Florence and the Department of Mathematics at the University of Bologna. Typically, each meeting lasts for one hour.
The participants include members affiliated with various institutions, including Marche Polytechnic University, Polytechnic University of Milan, Polytechnic University of Turin, University of Bologna, University of Ferrara, University of Florence, University of Milan, University of Modena and Reggio-Emilia, University of Siena, and University of Trento.
Alessandra Bernardi (Università degli Studi di Trento)
Enrico Carlini (Politecnico di Torino)
Luca Chiantini (Università degli Studi di Siena)
Cosimo Flavi (Università degli Studi di Firenze)
Alessandro Gimigliano (Alma Mater Studiorum – Università di Bologna)
Massimiliano Mella (Università degli Studi di Ferrara)
Giorgio Ottaviani (Università degli Studi di Firenze)
Pierpaola Santarsiero (Alma Mater Studiorum – Università di Bologna)
The concept of organizing a series of meetings focused on tensors and secant varieties has been a recurring initiative every academic year since 2014, when the first edition was launched as part of the program entitled Geometria Algebrica Numerica.
Over the years, this program has witnessed the active involvement of numerous professors and young researchers. In addition to the core members of the research groups at each institution, who continue to hold regular seminars, this initiative has also had the privilege of welcoming experts in algebraic geometry from institutions around the world. These experts have generously offered to present their contributions and share their latest research findings on occasion.
For any question and information about the cycle of seminars, to be added to the mailing list or to get the link to partecipate to the eventual online connection for the meetings, please write to pierpaola.santarsiero@unibo.it