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

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。

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。

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

除了我排的不是摇滚乐，我的演唱会是黑洞拓扑学的讲座。

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？

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，而这在过去被我们认为是不可能的。

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

事实证明，这两位物学家发现的一个全新的拓扑相变中涉及到了量子涡旋！

Now you don't have to worry about what a topological qubit is.

现在您不必担心什么是拓扑量子位。

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。

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

当对象逐渐拉伸或弯曲时，拓扑属性不会改变。

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。

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。

We're taking a very different approach to our qubit, which is based on this topological qubit.

我们对我们的量子比特采取了一种非常不同的方法， 它基于这个拓扑量子比特。

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

现在，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。

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现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。

One example is called a topological insulator.

一个例子叫做拓扑绝缘体。

The Topography of Terror documentation center, near Potsdamer Platz, explains how the Nazis organized their systematic campaign of persecution and murder.

位于波茨坦广场附近的“恐怖拓扑” 文献中心，解释了纳粹如何组织其有系统的迫害和谋杀活动。

But the Nobel Laureates discovered that topological properties do exist at the quantum level.

但诺贝尔奖获得者发现，拓扑性质确实存在于量子层面。

A donut and a coffee cup look the same to a topologist because they both have one hole.

一个甜甜圈和一个咖啡杯在拓扑学家看来是一样的，因为它们都有一个洞。

For a long time, it wasn't clear whether topology was useful for describing the behaviors of subatomic particles.

长期以来，人们并不清楚拓扑学是否有助于描述亚原子粒子的行为。