Mathematics Colloquium

Upcoming Colloquium

The Heritage of C. F. Gauss: Classifying Geometric Inequalities
Dr. Bogdan Suceavă, CSU Fullerton

September 20, 2024
12:00pm-1:00pm in FO3-200A

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Abstract

In 1827, C.F. Gauss obtained a relation that he described as "remarkable;" the fact that the curvature of a surface depends only on the elements of the first fundamental form. More than a century later, J. F. Nash's Theorem proved that any Riemannian manifold can be embedded into a Euclidean ambient space with dimension sufficiently large. In 1968, S.-S. Chern pointed out that a key technicality in applying Nash's Theorem effectively is finding useful relationships between intrinsic and extrinsic elements which characterize immersions. After 1993, when a groundbreaking work written by B.-Y. Chen on this theme was published, many explorations pursued the investigations of geometric inequalities between intrinsic and extrinsic quantities. With all these developments in mind, we propose a classification of geometric inequalities in the geometry of submanifolds in five classes; some of these relations might be well-known, while others are rather new.

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Bogdan Suceavă studied mathematics at the University of Bucharest (B.Sc. 1994, M.Sc. 1995) and at Michigan State University (Ph.D., 2002). Since 2002, he has worked at Cal State Fullerton, where he wrote most of his over 80 papers in mathematics. He is one of the recipients of a 2020 MAA Polya Award for Expository Writing (for a paper written with A. Glesser, M. Rathbun, and I.M. Serrano). In the fall of 2011, Suceavă established the Fullerton Math Circle, an outreach program of our CSUF Math Department, focused on developing problem-solving skills in mathematics for K-12 students. Suceavă is the recipient of the Cal State Fullerton 2023 L. Donald Shields Excellence in Scholarship and Creativity Award, and an honorary research professor with the Babeş-Bolyai University in Cluj-Napoca, Romania.