Except, instead of rock and roll music, my concert was a lecture on black hole topology.

除了我排队的不是摇滚乐，我的演唱会是黑洞拓扑学的讲座。

And for your information, the summer conference on algebraic topology at Caltech is nerd prom.

还有，给你科普一下加州理工夏天的代数拓扑会议才是书呆子舞会，代数拓扑是使用抽象代数的工具来研究拓扑空间的数学分支。拓扑空间是一种数学结构，可以在上头形式化地定义出如收敛，连通，连续等概念。

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 在座的哪位对拓扑绝缘体的概念比较熟悉？

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

事实证明，这两位物理学家发的一个全新的拓扑相变中也涉及到了量子涡旋！

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

亚原子粒子的拓扑特性也可以改变量子计算。

Now, scientists are trying to transform slums with a mathematical approach to urban design called " topology" .

在，科学家们正试图通过一种称为“拓扑”的城市设计数学方法来改造贫民窟。

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

但在一些奇异的拓扑相中，亚原子粒子可以受到保护。

First of all, topology is a branch of mathematics that focuses on fundamental properties of objects.

首先， 拓扑学是数学的一个分支，侧重于对象的基本属性。

This involved lots of weird quantum phenomena, plus a branch of math called topology, which looks at how objects can be arranged and manipulated.

这包括许多奇特的量子象与数学中一个称为拓扑学的分支，拓扑学关注的是物体可如何被排列与操纵。

Thus, the design method proposed in this study can solve the optimal problems of tree-type irrigation pipe networks with varying topologies.

因此，本研究提出的设计方法能够解决拓扑结构多变的树状灌溉管网优化问题。

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?

它也是关于 Borsuk-Ulam 定理的视频的基础，该定理被用来通过使用有关球体的拓扑事实来解决基本上是一个计数难题？

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，今年的诺贝尔奖获得者率先开展了分子机器和拓扑材料的一些重要研究，而且看起来还有更多！

The edge of such a topological insulator has perfect electron transport: no electrons travel backward, no energy is lost as heat, and the number of conducting pathways can even be controlled.

这种拓扑绝缘体的边缘具有完美的电子传输：没有电子向后移动，没有能量作为热量损失，甚至可以控制导电通路的数量。