First of all I would like to thank and congratulate you people for this great webpage. It is really good to find a site like this, where people is trying to help just because they want/like to.

Now, my question. From my english knowledge, I undestand that when we use TO + VERB, the verb is always in infinitive form, so I've written: "This corresponds to find..." while some person (also no native english speaker) claims that I should write "This corresponds to finding" ("there are some rare exception," he says). What would you say about it?

Thank you very much in advance...
Not rare exceptions, Enemorales, but often idiomatic. 'To' + dictionary form of the verb occurs whenever we are using the infinitive:

I want to see you.
I like to ski.
My intention is to find gold.

When 'to' is a preposition or a part of a phrasal/prepositional verb, then it is followed by a noun instead (and '-ing' verbs can act as nouns):

I am used to seeing him every Tuesday.
He agreed to my taking ski lessons.
The discovery of money on the street corresponds to finding gold.
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Just wanted to thank you!!
Thanks for your kind explanation. The propositional verb has been a headache for me for so long.

I wonder if you or anybody can tell me what is "dictionary form of the verb" and what is a phrasal verb. I was taught that "agree to do" is a phrase, but to me here "agree" and "do" both are verbs, there is no way for me to identify the function of "to" in this phrasal verb but to memorize!! That is hard for a foreigner.

And there are so many phrasal verbs in English (not to mention the vocabulary).If I cannot get the phrasal verb right, I can never speak good English.
In this case, the verb would definitely be in the jerend form. I think there is much confusion about how to conjugate/not conjugate verbs after prepositions because people tend to use incorrect prepositions/prepositions incorrectly in the first place. In the example" "She helped me to understand the homework," the "to" is unnecessary, possibly even incorrectly used. In this case, "to understand" is the infinitive form. Whereas in other languages the infinitive form automatically includes and implies the "to", we don't always use this in English. It would be perfectly normal, possibly even more correct to say "She helped me understand the homework."
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The to of the infinitive is optional after help. It must be deleted after let, make, and have, however, and after the modal verbs.

helped me (to) do something
let me do something
make me do something
have me do something

can/could/shall/should/... do something