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 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分支。拓扑空间是一种数结构，可以在上头形式化地定义出如收敛，连通，连续等概念。

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

了我排队的不是摇滚乐，我的演唱会是黑洞拓扑的讲座。

Topology was originally studied as a branch of purely abstract mathematics.

拓扑最初是作为纯抽象数的一个分支来研究的。

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

首先， 拓扑是数的一个分支，侧重于对象的基本属性。

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

现在，科家们正试图通过一种称为“拓扑”的城市设计数方法来改造贫民窟。

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

长期以来，们并不清楚拓扑是否有助于描述亚原子粒子的行为。

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中一个称为拓扑的分支，拓扑关注的是物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。

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·霍尔丹都用拓扑为一种新物质——拓扑绝缘开辟了道路。

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

因此， 让我们稍微回避一下拓扑证明领域；我想你会同意这是一个非常令满意的推理思路。

So that's the puzzle, remember it, and now let's take a seemingly unrelated sidestep to the total opposite side of the math universe: Topology.

这就是谜题，记住它，现在让我们从一个看似无关的话题转向数宇宙的完全相反的一面：拓扑。

They call it topology optimization, where they try to make a part that is as strong as possible while using as little material as possible.

他们称之为拓扑优化，即在尽可能少用材料的前提下，努力制造出强度最高的部件。

These electrons then bounce off, and, in the process, create secondary electrons, back-scattered electrons and X-Rays, which we measure to get details as to the surface topology and chemical composition.

然后这些电子反弹，并在此过程中产生二次电子、背散射电子和 X 射线，我们通过测量这些电子来获取有关表面拓扑和化成分的详细信息。

But when the topology gods close a door, they open a window, because the Borsuk-Ulam theorem guarantees that no matter what, there must be some other antipodal pair that now land on each other.

但是，当拓扑之神关上一扇门时，他们也会打开一扇窗， 因为博尔苏克-乌拉姆定理保证，无论如何，一定有其他一些对映对落在彼此身上。

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.

在拓扑中，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分析。

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， 因为涉及很多颜色，并且核心基本思想适用于此求解方程的算法之外的各种数，包括一些拓扑， 我将在后面讨论。