Traditionally, mathematics studies precise solutions: one has for example an equation with an unknown quantity ‘x’, and wants to know precisely which value(s) of x make it true. Often in the real world, good approximate solutions will always be very close to precise solutions, and are therefore just as good for practical purposes. However, sometimes very good approximate solutions to a problem can exist without there being any actual solution at all: for example, this is a fundamental phenomenon in parts of semi-conductor physics that are closely related to the ‘K-theoretic’ methods used in this project.
Professor Rufus Willett has been awarded a grant by NSF with the title “Approximation and K-theory”. From the abstract: