It is often said that a geometer has only two basic tools to
study a space: to slice it or to project it. Cartography provides a
vivid example: contour lines are simply the intersections of a
landscape with horizontal planes. In the nineteenth...
Recently, a number of formulas reminiscent of Weyl's law have
been discovered in the context of symplectic geometry. Various
three-manifold invariants, defined by building on ideas originating
in Morse theory, have been at the heart of these...
The algebraic structure of various groups of homeomorphisms and
diffeomorphisms was studied extensively in the 1960s and 1970s,
when it was shown that these groups are (mostly) simple. A notable
open case concerned the group of area-preserving...
