The School of Data, Mathematical, and Statistical Sciences (SDMSS) Colloquium series offers a platform for research scholars, faculty, students, and industry experts to share and exchange ideas, fostering discussion and networking across mathematics, statistics, and data science.
Professor Annalisa Calini from College of Charleston will speak at this week's colloquium on "Soliton equations and geometric flows for Legendrian and transverse curves in the 3-sphere."
Abstract:
I will begin with two canonical examples of integrable geometric flows for curves—the vortex filament flow in Euclidean geometry and the NLS equation, and Pinkall’s flow in centro-affine geometry and the KdV equation—highlighting the role of moving frames in integrability.
In the rest of the talk, I will focus on Legendrian and transverse curves in the 3-sphere endowed with the standard contact structure, and describe how a well-known integrable model of short wave-long wave interaction arises from a simple geometric flow on transverse curves.
This talk is based on recent work with Tom Ivey (College of Charleston) and a long-standing collaboration with Emilio Musso (Politecnico di Torino, Italy).
Speaker Bio: Annalisa Calini received her Laurea in Physics from the Uni- versity of Milano, Italy, and her Ph.D. in applied mathematics from the University of Arizona. She is a Professor of Mathematics at the College of Charleston, where she has served on the faculty for many years. She has held appointments as Program Officer in Applied Mathematics at the National Science Foundation and currently serves as Deputy Editor of Studies in Applied Mathematics.
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