So it wasn’t gravitational waves after all: the Nobel prize for physics went to David Thouless, Duncan Haldane and Michael Kosterlitz. That’s the easy part. The motivation needs a little unpacking:
For theoretical discoveries of topological phase transitions and topological phases of matter.
We all know and love a few phases of matter: solid, liquid and gas (maybe plasma if you want to get kinky). Phase transitions happen when, changing temperature or other conditions, matter goes from one form to the other, like melting ice. But there are more phases and more transitions transitions, some involving electrical and magnetic properties of materials.
That’s what the newly-minted Nobel laureates where after. They studied the sudden changes in electrical conductance—the efficiency in carrying electric currents—that some cold materials (I mean -270-odd Celsius) undergo when the temperature changes slightly. This effect is impossible to deal with using quantum mechanics, because it has to do with collective behavior of electrons rather than single ones.
Instead, Thouless, Haldane and Kosterlitz used topology. Topology is the branch of math that deals with properties that stay the same when stretching, twisting and bending stuff, but not puncturing, ripping or gluing it. Topologically speaking, a donut is the same as a pipe—we can turn one into the other—but is different from a ball, because we’d have to sew its hole shut.
Topological features like the number of holes must come in integer numbers: there’s no such thing as a half-hole! So they change in jumps, like that weird conductance. So the scientists theorized that topological transformtions (though not really holes appearing), were behind it.
The unusual part of the award is that the discoveries haven’t been applied quite yet: they are purely theoretical. However, they opened the floodgates for the research on materials that exploit these properties. For one, topological materials are an avenue towards the dream of building a quantum computer. During the press conference, Haldane explained that topology could protect the fragile signals in quantum computers from disruption due to impurities in the material itself.