Stress the points that nobody should miss and
give opportunities to catch up

A human brain is not a machine. When listening to a talk people will inevitably lose concentration at some point, and they will forget a definition or statement they heard a minute ago. In order to deal with this problem there are two major measures you need to take.

Firstly, when presenting a statement or definition that plays a key role in your talk, try to make sure that nobody will miss it. You could for example try to attract your audience's attention by getting more excited, or just by saying that what follows is important; when I come to such a point in my talks I like saying something very explicit like: "my whole talk is based on this definition, so please make sure you understand it or otherwise you will miss everything" and then repeat the definition. It is also a good idea to leave such a statement or definition visible for a long time, e.g. by putting it on several slides.

Secondly, it is very important to give people that for some reason lost the thread an opportunity to catch up again. This can be achieved, for example, by stopping within a long proof to recapitulate and remind them what stage of the proof you just completed (for this it would be helpful to have a list of the main steps of the proof visible somewhere, and point to elements of this list as proving progresses). When giving them such a re-entry opportunity you need to say so loudly enough to "wake" them up; if you say it in the same monotone voice as everything else it will not work.

A. Georgakopoulos: How to give a talk that is not too bad.

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