A common approach to problem-solving is to split a problem into smaller sub-problems, solve each of the smaller problems, and assemble the answers into a solution to the original problem. This last step is often very difficult, as there are multiple ways of gluing the pieces of the solution together. The mathematical area of K-theory studies the different ways of putting such solutions back together, as well as the relations behind differently-assembled pieces.
Mathematician Inna Zakharevich has received a 5-year, $450,000 grant from the National Science Foundation to investigate novel connections between fields through a K-theoretic perspective; she studies how geometric objects, known as polytopes, varieties and manifolds, can be cut apart and reassembled. Zakharevich is an assistant professor of mathematics and LCP Ho Sesquicentennial Faculty Fellow.
LIGO/Caltech/MIT/Sonoma State (Aurore Simonnet)
An artist's conception of a precessing binary black hole. The black holes, which will ultimately spiral together into one larger black hole, are shown here orbiting one another in a plane. The black holes are spinning in a non-aligned fashion, which means they are tilted relative to the overall orbital motion of the pair. This causes the orbit to precess like a top spinning along a tilted axis.
