Analysis, Applied Math and Geometry Seminar

Link to Previous Semesters


Fall 2024

Tuesdays, 11:00 am
Morrill 109
29 October 2024

Boya Liu:

8 October 2024

Nikita Barabanov:


1 October 2024

Mariangel Alfonseca: On many questions related to Ulam's floating body problem (Part 2)
24 September 2024

Mariangel Alfonseca: On many questions related to Ulam's floating body problem

Croft, Falconer and Guy posed a series of questions generalizing Ulam's floating body problem: Given a convex body K in R^3, we consider its plane sections with certain given properties,
(V): Plane sections which cut off a given constant volume,
(A) Plane sections which have a given constant area,
(I) Plane sections which have equal constant principal moments of inertia,
(P) Plane sections which have a given constant perimeter,
(H) All the planes are at a constant distance from the origin, etc.

In particular, Ulam's floating body problem is equivalent to problem (V,I): If all plane sections of the body K which cut off equal volumes have equal constant moments of inertia, must K be an Euclidean ball?
We discuss the different nature of the problems asking 2 or 3 of the above conditions to hold. Their answers require a variety of techniques from analysis, geometry and differential equations.