“will have seen yesterday”

This is a part of a sentence:

As many of you will have seen yesterday, . . .

What does it mean? The words will and yesterday seem to be in contradiction.

Is that a correct sentence?

This use of the future perfect is a standard construction used in English to express an assumption, expectation or presumption.

If someone asks, "Where is Fred?", then I might respond:

He has gone to the bank.

This would indicate that I know for certain where he has gone - perhaps he told me so. However, if he didn't say anything, but I happen to know that he usually goes to the bank on a Thursday, I might instead say:

He will have gone to the bank.

The reason the tense is used in this way (to my mind, at least) is as follows: we are implying that, at the point in the future when we discover for certain where he has gone, we will discover "he has gone to the bank" - and hence the construction is roughly equivalent to [When we find out where he has gone] he will have gone to the bank.

The usage in the question is similar. If the speaker had said

As many of you saw yesterday...

that would imply that he knows that the audience saw [whatever it was] yesterday - again, perhaps he spoke to the people concerned, or was there at the time. Instead, by saying

As many of you will have seen yesterday...

he conveys that he does not know for certain, but confidently assumes this to be the case based on habit, common sense or some such: perhaps he knows that many of the audience were in the right place at the right time to see [whatever this momentous spectacle happened to be].

The British National Corpus reports many examples of such use - searching for "you will have *d", there are plenty of examples of the future perfect being used with this meaning, including You will have noted/noticed (24), you will have gathered/found (16), and plenty more with other verbs; searching with other subjects reveals many more examples, but it gets harder to filter out those that use the future perfect in this way rather than other uses. Even so, searching for "will have *d" and looking through the first page of results reveals that this construction is extremely common, perhaps even the most common use of the future perfect.

(I also tried checking COCA for US usage, to see if this is more common in the UK, but alas I was unable to due to "database errors".)

As has been noted elsewhere on ELU, English doesn't really have a "future tense". But just because we normally use the modal/auxiliary verb "will" to indicate future, doesn't mean that's all it can do. To claim that OP's example is illogical or ungrammatical is just spurious pedantic rationalisation.

When talking about an imaginary event, or a past event that might not have happened (i.e. - we don't know, or it's conditional), we normally use the form "would have" + past participle.

To indicate that a past event actually happened, we normally use "will have" + past participle...

As you will have noticed, he's got new glasses.

[Edited: In short, as you will have seen yesterday is technically correct and natural in speech; but, since the same meaning could be conveyed in fewer words, and because it may be slightly confusing at times, perhaps as you saw yesterday would be better in a polished text. ]

1.) As many of you saw yesterday, she sucked.

This is a simple situation, in which I describe what you saw yesterday.

2.) As many of you will agree, she sucked.

Here I presume that you will agree that she sucked, if I ask your opinion at some point in the fture. The "if I ask your opinion" is implicit. You will agree is equivalent in meaning to "it will turn out that you agree".

[Edited:

3.) As many of you will have seen, she sucked yesterday.

Now how should this be parsed? The use of will to indicate future probability is quite unremarkable on its own, as seen in (2.) above.

It is the combination with have seen that makes it complex. At some point in the future, if I ask, it will turn out that you saw that she sucked yesterday. So there is actually no real problem.

4.) As many of you will have seen yesterday, she sucked.

I parse this similarly to (3.), but with yesterday in a different position: at some point in the future, if I ask, it will turn out that you saw yesterday that she sucked.

Here yesterday modifies only (that) you say, not it will turn out; this different scope of yesterday is invisible in will have seen, but it is there. The cause of confusion is that our subconscious might want to apply yesterday to the whole clause, including will, while in fact it applies only to (that) you saw. ]