Joseph Slote is a Ph.D. student at the California Institute of Technology, advised by Dr. Chris Umans. Joseph is expected to graduate in 2025.

In this talk, Joseph proves a Remez-type inequality for multivariate polynomials having a constant independent of dimension, the first of its kind. This motivates a notion of “norm design.” This is based on the joint work of L. Becker, O. Klein, J. Slote, A. Volberg, and H. Zhang, preprint available at arXiv:2310.07926.

Keywords: Remez inequality, dimension-free estimates

MSC2020: 46B10, 46B09, 46B07, 60E15.