KASS seminar

Abstract: If $M$ is an arbitrary smooth compact real $n$-dimensional manifold, what is the smallest integer $N$ such that $M$ can be smoothly embedded into $\C^N$ as a polynomially convex set? This natural question was asked by Izzo and Stout in 2018. A related question is how many smooth functions on $M$ it takes to generate the uniform algebra of all continuous functions on $M$. An upper bound follows by classical works by Forstneric and Rosay. This bound was recently improved by Gupta and Shafikov. I will present a joint work in progress with Arosio and Wold to answer the above questions when $n\leq 11$.