Prof. Dr. Frank Sottile from Texas A&M University visited the Department of Mathematical Sciences on September 29 to deliver the 2025 Richard C. DiPrima Lecture, “Galois Groups in Enumerative Geometry.” The DiPrima Lecture honors and remembers a former faculty member who, through his research, teaching, and service as department chair, was instrumental in the transformation of our department in the 1950s-1980s to a prominent center for the application of mathematics to science and engineering concerns. Stemming from a family of Sicilian immigrants, Dr. Sottile's visit revealed a geographic connection to the DiPrima family; he noted: “An interesting aspect that I learned [when visiting RPI] was that DiPrima’s Sicilian ancestors came from the same region as mine.”
Dr. Sottile’s lively and visual presentation traced the story of how Galois theory, which originally developed in the 19th century to understand polynomial equations, has evolved into a powerful framework for studying modern problems in enumerative geometry. He explained how Galois groups capture the hidden symmetries of geometric structures and how these symmetries reveal underlying connections between algebra, geometry, and computation. To make these ideas tangible, Dr. Sottile brought 3D-printed models of several algebraic varieties, allowing the audience to see and touch the shapes he lectured on. The colorful and intricate prints provided a bridge between abstract theory and physical form, delighting students and faculty alike.
During his visit, he captivated the undergraduate Math Club and Pi Mu Epsilon Honors Society, describing how and why algebraic geometry becomes a tool for applications of mathematics, with examples ranging from describing fonts, to analyzing biased coins, to genetic equilibria. Over lunch with graduate students, he had a lively discussion about their academic journey, graduate work, and professional aspirations, all laced with threads of advice from Sottile's experiences. Students described the experience as inspiring, energizing, and deeply motivating. Chanaka Mapa Mudiyanselage reflected: “Dr. Sottile showed us how abstract ideas can illuminate the world around us. It made me see mathematics as something alive and full of possibility.”
Dr. Sottile reminded the RPI community that mathematics is not only a language of logic and rigor, but also a deeply creative science, where curiosity and structure come together to reveal new patterns and ideas. His lecture and outreach embodied the spirit of the DiPrima Lecture Series, celebrating both the depth and humanity of mathematical discovery.
Dr. Frank Sottile is a Professor of Mathematics at Texas A&M University. He earned his Ph.D. under William Fulton after distinguished studies at Michigan State University, Cambridge, and the University of Chicago. His research areas are numerical algebraic geometry, applications of algebraic geometry, algebraic geometry in spectral theory, real algebraic geometry, algebraic combinatorics, Hopf Algebras, Discrete and Computational Geometry, tropical geometry, spectral theory. Sottile has held fellowships with NSF, the Winston Churchill Foundation, the AMS, and the AAAS. Frank has taught and collaborated globally, from Berkeley and Munich to Lausanne and Stockholm.
