In the lecture I will start with the notable theorems of Radon and Tverberg and mention the following conjectural extension.
For a set X of points x(1), x(2),...,x(n) in some real vector space V we denote by T(X;r) the set of points in X that belong to the convex hulls of r pairwise disjoint subsets of X. We let t(X;r)=1+dim (T(X;r)).
Radon's theorem asserts that If t(X,1) < |X| then t(X,2) >0.
The first open case of the cascade conjecture asserts that
If t(X,1)+t(X,2) < |X| then t(X,3) >0.
In the lecture I will discuss connections with topology and with graph coloring.
Note: This talk begins with a pre-seminar (aimed at graduate students) at 3:30–4:00. The main talk starts at 4:10.
Join Zoom Meeting: https://washington.zoom.us/j/
Meeting ID: 915 4733 5974