Annotated Slides – Micha A. Perles 90th Birthday Meeting

Akiva Kadari, Pablo Soberon and the cascade conjecture The cascade conjecture is discussed in this post. I proposed the conjecture back in 1974, inspired by work by Meir Katchalski (though the name “Cascade Conjecture” only came into use over the last decade or two). Akiva Kadari, a master’s student of Micha Perles, proved the planar case in his M.Sc. thesis. Although the proof was ready in the early-to-mid 1980s, writing the thesis was delayed until 1990, when Micha was on sabbatical and I stepped in as a co-supervisor. (Akiva himself was present in the lecture.) This is the conjecture Recently. Pablo Soberón proved a remarkable weaker version of the conjecture using topological methods—we will devote a dedicated post to it soon. Very recently, Pablo also disproved the last open case of Grünbaum’s famous mass partition conjecture. Yaacov Kupitz and Geometric graph theory Yaacov Kupitz once decided to spend a year abroad and got in touch with the famous mathematician John Conway. Just…