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.

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