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会议才是书呆子舞会，代数是使用抽代数的工具来研究空间的数学分支。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。

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相变中也涉及到了量子涡旋！

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 在座的哪位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.

除了我排队的不是摇滚，我的演唱会是黑洞学的讲座。

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数学中一个称为学的分支，学关注的是物体可如何被排列操纵。

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

亚原子粒子的特性也有望革新量子计算领域。

Incredibly complex topology to try and load bounce all this stuff.

极其复杂的结构，试图让所有这些东西加载反弹。

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， 因为涉及了大量的色彩，而且其核心理念不仅适用于这个解方程的算法， 还涵盖了各种数学领域，包括一些学的内容， 我稍后会进行讲解。

HPE prefers something known as a dragonfly topology, a two-layer system in which groups of chips are connected to each other in clusters and those clusters are wired up to each other in turn.

惠普企业更倾向于使用一种称为“蜻蜓”的结构，这是一种两层系统， 在该系统中， 芯片组相互连接形成集群， 而这些集群又彼此相连。

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 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在分子机器和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，从我们架构设计上的角度来看， 确实非常出色。

AWS Systems Manager for SAP now supports SAP NetWeaver-based ABAP applications deployed in distributed and HA topologies, so you can get up and running faster.

AWS系统管理器在支持在分布式和高可用性中部署的基于SAP NetWeaver的ABAP应用，因此您可以更快地启动和运行。

If you want to understand the topology of something, you look at the functions, you do Durham cohomology, and you get the topology.

如果你想理解某个事物的结构，你就研究它的函数， 进行杜伦上同调计算，从而得到其结构。

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“学”的数学方法来改造贫民窟。

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结构多变的树状灌溉管网优化问题。

For me, so what I'm saying is, I get a little bit of the joy of kind of learning something purely as a scientist, something completely outside of what I do, mathematics.

我来说，我的意思是，我能感受到一种纯粹作为科学家去学习某些完全超出我专业领域——数学之外的东西的趣。比如他感兴趣的规范理论，那种非常高级的几何学。

So let's take a little sidestep through topology proof land; I think you'll agree this is a really satisfying line of reasoning.

所以让我们稍微偏离一下， 进入证明的世界；我想你会觉得这条推理路线非常令人满意。

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

但在某些奇异的相态中，亚原子粒子能够得到保护。

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

首先，学是数学的一个分支，专注于研究物体的基础性质。