Geometry Seminar

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Four hyperplanes do not always equipartition a mass in R^4

Speaker: Pablo Soberon, Baruch College and CUNY Graduate Center

Location: Warren Weaver Hall 1314

Date: Tuesday, November 10, 2026, 6 p.m.

Synopsis:

In 1960, Grünbaum conjectured that, given a measure in \(\mathbb{R}^d\), we can always find \(d\) hyperplanes that split it into \(2^d\) parts of equal size.  This conjecture was confirmed for \(d=1,2,3\) shortly after, and disproved for \(d\) at least 5 in the 80s.  The case \(d=4 \) remained “stubbornly open” despite the progress in the area.  In this talk, we discuss the construction of a counterexample and the general method behind it.

Notes:

In person and on Zoom.  Plz contact Boris Aronov if you are not NYU-affiliated and want to attend in person and/or to be put on the mailing list and get the Zoom information.