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I've heard lots of speakers use "hopefully" at the end of their lectures.

Consider this example

We have learned that Britain’s weather is very changeable and hopefully we have learned how to describe the weather in more detail using phrases and expressions. Thanks very much for watching!

where "hopefully" is used to describe "have learned ...", which does not make any sense.

"learn" is an action, which had already happened before the speaker say that.

Cambridge Dictionary gives these definitions about "hopefully"

used, often at the start of a sentence, to express what you would like to happen

in a hopeful way

why does the speakers express they would like the action of learning to happen after the action had happened?

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There is a rhetorical effect of using "we" instead of "you". But you should understand the first example to mean

You have learned that Britain’s weather is very changeable and hopefully you have learned how to describe the weather in more detail.

The speaker is expressing their "hope" that you have learned something. The speaker is telling the listeners that she would like them to have learned this fact. There is no reason why she can't tell us that hope at the end of the lecture.

But, again, this is a rhetorical effect. The purpose of this is not really to tell you about the speakers hopes, but just to remind you of the content and help you remember it.

So the underlying meaning is

Now, you know that Britain’s weather is very changeable, and you should know how to describe the weather in more detail...

It just sounds much friendlier to express this in terms of "hope" and "we"

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