Speaker: Dr. Ryan Alvarado, Amherst College
Title: “Geometric influences on fractional Sobolev spaces in the metric setting”
Abstract: The study of (fractional) Sobolev spaces in  the Euclidean setting has long been central to analysis, particularly in the context of the theory of partial differential equations. In recent years, there have been significant developments in extending the theory of these function spaces beyond $\mathbb{R}^n$, to the setting of metric-measure spaces. When considered in this more general setting, these function spaces exhibit a rich and complex behavior that depends heavily on geometric and measure-theoretic properties of the underlying metric-measure space.

In this talk, we will discuss the extension of the classical (fractional) Sobolev spaces to metric measure spaces, investigating how the underlying geometry affects their analytical nature. In particular, we will present new results pertaining to their (compact) embedding properties, illustrating the fundamental role that the metric-measure structure plays in shaping function space behavior. 

The Analysis and Applied Mathematics (AAM) Seminar is intended for Kennesaw State faculty working in the various areas of analysis and applied mathematics to get together to discuss their current work or related questions. Seminars often involve advanced mathematical knowledge. However, the seminars are open to anyone interested in attending.