We will construct counterexamples to previously conjectured metric formulations of Kwapień's theorem from Banach space theory. The key new ingredient in our construction is a novel rigidity theorem for metric transforms of nonpositively curved Alexandrov spaces. Time permitting, further geometric and algorithmic applications of this rigidity will also be discussed. The talk is based on joint work with M. Mendel (Open University of Israel) and A. Naor (Princeton).

Let me also mention that Alexandros is this year's laureate of the Barbara and Jaroslav Zemanek award. The award ceremony will be held at IM PAN on Wednesday at 14:15. Alexandros' lecture will be preceded by an introductory lecture delivered by Rafał Latała. Here is the web page of the event: https://www.impan.pl/pl/instytut/aktualnosci/1744-uroczystosc-wreczenia-nagrody-imienia-barbary-i-jaroslava-zemankow-2