PSU Mark
Eberly College of Science Mathematics Department

Meeting Details

For more information about this meeting, contact Sergei Tabachnikov, Stephanie Zerby.

Title:5-dimensional geometry is not like 2-dimensional geometry (and 3 and 4 are somewhere in between)
Seminar:MASS Colloquium
Speaker:Mark Meckes, Case Western Reserve University
There are many different ways to measure how "big" a geometric shape is, and their relationships are sometimes surprising. I will discuss three different problems (Shephard's problem, the Busemann-Petty problem, and one that I proposed several years ago) asking about monotonicity relationships among volumes. For example, Shephard's problem asks, if K and L are origin-symmetric convex bodies and every shadow cast by K has bigger area than the shadow cast by L in the same direction, is the volume of K bigger than that of L? In all three problems, the answer turns out to be yes in two dimensions, but surprisingly, no in five or more dimensions. In three and four dimensions the answer is different depending on the problem.

Room Reservation Information

Room Number:MB113
Date:09 / 20 / 2012
Time:02:30pm - 04:30pm