Alexander Lubotzky has had a close-knit relationship with computer science in his research for a while now. Opening the 6th day of ICM 2018, the Israeli professor and mathematician of the Einstein Institute of Mathematics delivered a special lecture about high-dimensional expanders, taking the concept of expander graphs above and beyond more tangible dimensions.
Computer science and pure mathematics have a mutually beneficial history that goes back several decades mainly due to expander graphs – what he describes as “highly connected sparse finite graphs.”
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The father of six explores possible paths of this obscure field of study. “Believe it or not, in the last decade or two, many computer scientists are studying cohomology,” he said enthusiastically, highlighting the relevance to ‘property testing’ algorithms in the broad area of computer science.
But, there is still quite a way to go. Lubotzky ended his lecture with an open question: “Is there a random model that will give coboundary or topological expander?” He posits that perhaps not, but it is clear that there is plenty more research to be done in this fascinating new area.