Ian M. Adelstein
I am interested in geometric analysis and global differential geometry. Most of my research has focused in two main areas: closed geodesics and the spectrum of the Laplacian. I study the characterization problem on round spheres via the existence of certain minimizing closed geodesics. Here I use techniques from comparison geometry, Morse theory, the calculus of variations, and critical point theory. In spectral geometry I study inverse problems in the presence of symmetry. I've shown that constant sectional curvature and non-orbifold singularities are inaudible properties of the G-invariant spectrum.
Here is my arxiv page.
Here is my CV.
I am a passionate educator and create an engaging and inclusive classroom when I teach. I employ active pedagogy and have a dynamic teaching style that is adaptable to diverse students, classrooms, and material. I've enjoyed teaching across the undergraduate mathematics curriculum, and have a strong belief that when math is taught in an engaging and supportive environment every student is capable of learning and success. If you are a student, please stop by my office DL 419 anytime; if you are an educator, I am always excited to chat about teaching.