If you are Lieutenant Commander Data: your brother can but you can't (or, as you would say, "cannot"). Otherwise: I see that you can use contractions in your informal writing, so it would be very strange if you were not able to use them when writing your thesis. If you can't, maybe contact Oliver Sacks: he should get at least an article about this, and maybe part of a book.
More seriously: obviously you can. Should you? Speaking as someone who has both written and carefully read theses in a STEM field (mathematics): one generally needs to worry first that the content is complete and correct and second that the writing is good enough so as not to detract (or distract) from the content. The use of contractions would be at least a level below anything I would worry about when reading a thesis...provided they are used correctly.
It's best to stick to language within your comfort zone (especially as a non-native speaker). But your post above indicates to me that you have more than enough facility with English to pull off contractions if you want to. You'll be fine.