Inflating polyhedral surfaces

Can you have a non-convex polyhedron with bigger volume than a convex
polyhedron with isometric surface? Imagine you start blowing air into
a polyhedron with a bendable but non-stretchable surface. What can be
said about the limiting shape? These are the key questions I will
consider. I will start the talk by discussing the history of the
problem, presenting examples, and surveying earlier work on
realization of surfaces. In the second part of the talk I will discuss
my recent results on volume-increasing deformations of polyhedral
surfaces.

Fejes Tóth Lecture Series
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László Fejes Tóth (1915-2005) was a Hungarian mathematician who is
widely regarded as one of the founding fathers of the field called
Discrete Geometry that lies on the border line of mathematics and
computer science. His books "Lagerungen in der Ebene auf
der Kugel und in der Ebene", Springer (1954) and "Regular Figures",
Pergamon Press, Oxford (1964) have not only layed a broad foundation for
discrete geometry but also, via introducing an impressive number of open
research problems, generated a great interest in the new field for
generations of mathematicians. The Center for Computational and Discrete
Geometry is pleased to announce a lecture series in honor of the legacy
of László Fejes Tóth.