Speaker: Mikhail Sodin (Tel Aviv University)

Title: A curious Lagrange-Ivanov-Yomdin-type lemma

Abstract: Suppose 𝑓 is an 𝑚-smooth function on the unit ball that is small
(for instance, vanishes) on an epsilon-net 𝐸 for a sufficiently
small epsilon. Then the maximum of 𝑓 is controlled by the 𝐿¹-
norm of its 𝑚 − 𝑡ℎ derivative and its uniform norm on 𝐸. This
estimate is dimensionless. The proof is not long and uses only
undergraduate analysis.

The talk is based on an ongoing joint work with Aleksei Kulikov
and Fedor Nazarov on multi-dimensional Fourier uniqueness.