And it's what's called a topological invariant.

也是一种拓不变量。

Turns out, quantum vortices also involved in an entirely new topological phase transition discovered by these two physicists!

事实证明，这两位物理学家发现的一个全新的拓相变中也涉及到了量子涡！

All right, let's begin. Show of hands, who here is familiar with the concept of topological insulators?

好吧 开始上课 请举手告诉我 在座的哪位对拓绝缘体的概念比较熟悉？

So this year's Nobel Laureates have pioneered some important research into molecular machines and topological materials, and it looks like there's a lot more on the horizon!

因此，今年的诺贝尔获得在分子机器和拓材料方面开启了一些重要研究。而看起来还有更多研究在即将露面。

A topological insulator acts like both at the same time, which we used to think was impossible!

一个拓绝缘体就像两个同时起作用，而这在过去被我们认为是不可能的。

Nowadays, scientists are working to develop topological insulators, and some think they could be as important for future technologies as semiconductors are today.

当前，科学家们正在致力于研发拓绝缘体。其中有些人认为拓绝缘体对于未来的技术就像今天的半导体一样重要。

Thouless and the final winner, Duncan Haldane, are both also using topology to pave the way for a new kind of material: topological insulators.

索利斯及最后一位的获肯·霍尔丹都用拓学为一种新物质——拓绝缘体开辟了道路。

What's really weird--One really weird finding about these lobes is that they include topological maps.

真正奇怪的是——关于这些波瓣的一个非常奇怪的发现是它们包含拓图。

They then used their topological algorithm to figure out which areas were inaccessible by roads, then generated the most cost effective ways to build roads and connect them to outside services.

他们然后使用了拓算法来确定哪些区域无法通过道路到达，接着成了最经济有效的建路方式，并将这些区域与外界服务连接起来。

So this year’s Nobel Laureates have pioneered some important research into molecular machines and topological materials, and it looks like there’s a lot more on the horizon!

所以今年的诺贝尔得主在分子机器和拓材料的研究中取得了重要突破，看来未来还有更多精彩等着我们呢！

So all these little things that that it would enable, like from a kind of a topological perspective of what we do architecturally is pretty spectacular.

因此， 所有这些小功能都能实现，从我们架构设计上的拓角度来看， 确实非常出色。

It also underlies the video on the Borsuk-Ulam theorem being used to solve What was basically a counting puzzle by using topological facts about spheres?

它还支撑了一个关于使用博苏克-乌拉姆定理来解决基本上是一个计数谜题的视频，这个谜题是通过球体的拓学事实来解答的。

But they nevertheless have some of these ideas like topological gravity aspects are emphasized in the context of loop quantum gravity in some form.

然而，它们确实包含了一些概念，比如拓重力方面，在某种形式的圈量子引力背景下得到了强调。

These topological qubits would be more stable, leading to more accurate computation and a better quantum computer.

这些拓量子比特将更为稳定，从而实现更精确的计算和更出色的量子计算机。

Topological properties don't change when an object is gradually stretched or bent.

拓性质在物体逐渐拉伸或弯曲时保持不变。

Euler characteristic is counting the number of points minus the number of edges plus the number of faces minus, so you can count the alternating sequence of properties of the space, which is a topological property of a space.

欧拉特征数是计算点的数量减去边的数量加上面的数量再减去，如此交替计算空间的各种属性，这是空间的一种拓性质。

The topological properties of subatomic particles could also transform quantum computing.

亚原子粒子的拓特性也有望革新量子计算领域。

In fact, I wrote a paper about topological string theory and some connections potentially loop quantum gravity, which could be part of that.

事实上， 我撰写了一篇关于拓弦理论及其与圈量子引力潜在联系的论文，这些可能也是其中的一部分。

One example is called a topological insulator.

一个典型的例子就是拓绝缘体。

But in some exotic topological phases, the subatomic particles can become protected.

但在某些奇异的拓相态中，亚原子粒子能够得到保护。