Topology in Condensed Matter: Tying Quantum Knots | DelftX on edX | Course About Video

SPEAKER: If you watch this video,
you have probably read, in the news, about the topological
insulators and the electrons becoming massless on their
surface while carrying current which is protected
from dissipation. Or you have heard how Majorana particles
split a single electron into halves and allow it to construct a quantum
computer insensitive to noise. So why exactly do these
systems have robust properties? The answer to this is topology. It studies everything that
cannot be changed gradually. So this mug and this donut are exactly
identical from a topological point of view since they have
the same number of holes. In condensed matter systems, expressions
like this are the quantities that cannot be smoothly changed. While such topological
invariance cannot be visualized, all the robustness of topological
protection derives from their existence. However, even without
using advanced math, careful analysis allows us
to understand essentially all of the important results. Often we find that it is even
more fruitful than trying to stay as strict and
formal as possible. Focusing on the main ideas that explain
how topology works in condensed matter systems allows us to avoid a
lot of errors and confusion, which is not at all uncommon, even
among researchers in the field. We will teach you how to understand
exactly these simple ideas that serve as beacons in
navigating the field. You will hear the explanations
from active scientists. And you will see how the
actual analysis is performed. You will find that most papers
become really transparent and clear. And in many cases, you
will say to yourself, hey, I could have discovered that. In other words, once
you finish our course, you will be ready to research topology
in condensed matter on your own.

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