The new algorithm generalizes really well for tasks with different lengths, topologies, and changing objectives.

新算法对具有不同长度、拓扑结构和变化目标的任务具有很好的推广性。

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

也是一种拓扑不变量。

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数拓扑议才是书呆，数拓扑是使用抽象数的工具来研究拓扑空间的数学支。拓扑空间是一种数学结构，可以上头形式化地定义出如收敛，连通，连续等概念。

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扑相变中也涉及到量涡旋！

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 座的哪位对拓扑绝缘体的概念比较熟悉？

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

除我排队的不是摇滚乐，我的演唱是黑洞拓扑学的讲座。

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机器和拓扑材料方面开启一些重要研究。而看起来还有更多研究即将露面。

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

一个拓扑绝缘体就像两个同时起作用，而这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，科学家们正致力于研发拓扑绝缘体。其中有些人认为拓扑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奖者邓肯·霍尔丹都用拓扑学为一种新物质——拓扑绝缘体开辟道路。

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现象与数学中一个称为拓扑学的支，拓扑学关注的是物体可如何被排列与操纵。

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扑图。

And he called it Polytopia Life Lessons.

他称之为多元拓扑生活课程。

So that's the concept of retinotopy or the map in visual cortex.

这就是视网膜拓扑学或视觉皮层中的地图的概念。

This method can be super pretty, since there is a lot of color involved, and the core underlying idea applies to all sorts of math beyond this algorithm for solving equations, including a bit of topology, which I'll talk about afterwards.

这种方法可以非常漂亮， 因为涉及大量的色彩，而且其核心理念不仅适用于这个解方程的算法， 还涵盖各种数学领域，包括一些拓扑学的内容， 我稍后进行讲解。

In topology since one block of buildings surrounded by roads is considered equivalent, settlements with a wide range of shapes and sizes, from the suburbs of Las Vegas to the slums of Mumbai, can be analyzed in the same way.

拓扑学中，由于被道路包围的一栋建筑物被认为是等效的，从拉斯维加斯郊区到孟买贫民窟的各种形状和大小的定居点，可以以相同的方式进行析。

If we have two images of the topographical texture of the surface taken 59 microseconds apart, how exactly does the microchip determine the change in x and the change in y between them?

如果我们有两张相隔59微秒的表面拓扑纹理图像，微芯片究竟是如何确定它们之间的x轴变化和y轴变化的？

So if it's a specific service, maybe I want to go look at the traces, see one of those topology kind of graphs and see that, Hey, this one is not getting anything.

因此，如果这是一个特定服务， 我可能想要查看追踪信息，看看那些拓扑图，然后发现，嘿，这个服务什么都没收到。

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!

所以今年的诺贝尔奖得主机器和拓扑材料的研究中取得重要突破，看来未来还有更多精彩等着我们呢！

And he was realizing that the analysis of networks and the network topologies and network dynamics was actually really applicable to how we live our lives.

他意识到，网络析、网络拓扑结构以及网络动态实际上非常适用于我们生活的方式。