On January 22, 2024, Monday, at 1:00 pm, in Room 478 of IMI-BAS,

Assoc. Prof. Stoyu Barov will deliver an inaugural lecture on:

On closed sets with convex projections in separable Hilbert spaces”

Abstract.  We discuss closed sets in $R^n$ and in Hilbert space $l^2$ all of whose shadows (projections onto hyperplanes) are convex. Among other theorems,  we show that if $C$ is a closed and nonconvex set in Hilbert space $l^2$ such that the closures of the projections onto all hyperplanes are convex and proper, then $C$ must contain a closed topological copy of $l^2$.