Malabika Pramanik

The Pythagorean theorem, dating back to before 500 BC, gives a formula for computing the Euclidean distance between two points. It is simply astounding that a concept so simple and classical has continued to fascinate mathematicians over the ages...

Large sets in Euclidean space should have large projections in most directions. Projection theorems in geometric measure theory make this intuition precise, by quantifying the words “large” and “most”. How large can a planar set be if it contains a...

The structure of the zero set of a multivariate polynomial is a topic of wide interest, in view of its ubiquity in problems of analysis, algebra, partial differential equations, probability and geometry. The study of such sets originated in the...

Pretend that your car is a unit line segment. How do you perform a three-point turn using an infinitesimally small area on the road? It turns out that this seemingly impossible driving stunt is related to the fundamental theorem of calculus, as well...