Description
Mathematics Colloquium Talk 1.
Speaker: Anisa Chorwadwala.
Affiliation: IISER Pune.
Date and Time: Wednesday 10 July, 3:00 pm - 4:00 pm.
Venue: Room 216, Department of Mathematics.
Title: A Glimpse of Shape Optimization Problems.
Abstract: The following questions arise quite naturally from what we see
around us. Why are soap bubbles that float in air approximately spherical?
Why does a herd of reindeer form a round shape when attacked by wolves? Of
all geometric objects having a certain property, which ones have the
greatest area or volume; and of all objects having a certain property,
which ones have the least perimeter or surface area? These problems have
been stimulating much mathematical thought. Mathematicians have been
trying to answer such questions and this has led to a branch of
mathematical analysis known as “shape optimisation problems”.
A typical shape optimisation problem is, as the name suggests, to find a
shape which is optimal in the sense that it minimises a certain cost
functional while satisfying given constraints. Isoperimetric problems form
a special class of shape optimisation problems. A typical isoperimetric
problem is to enclose a given area with a shortest possible curve. In
many cases, the functional being minimised depends on solution/s of a
given partial differential equation defined on a variable domain.
The plan is to give a glimpse of a few shape optimization problems we have
worked on.