Dr. Nico Lombardi 

The general research framework for the application to the "Regular Fellowship" at the Hanse-

Wissenschaftskolleg — Institute for Advanced Study explores an important question in

geometry, focusing on how the volume of certain shapes, known as convex bodies, behaves

under specific conditions. Convex bodies are geometric shapes, like spheres or cubes, that

cannot have holes or indentations. The main research topic of this application is to better

understand how the volume of these shapes changes when they are combined in particular

ways, with an additional focus on how they project onto a flat surface, called hyperplanes. More

specifically, the research examines what happens when two convex bodies have the same

projection onto a hyperplane. The aim is to find out how the interaction and combination of

these convex bodies behave under the projection constraint, revealing new geometric

properties that could be useful in areas ranging from mathematics to computer science and

beyond.