Gokukoku no Brynhildr

Ryouta Murakami is a teen astronomy buff with a photographic memory. He took an interest in astronomy after a friend he had as a kid died during a trip for stargazing. One day, he notices that the transfer student in his class looks oddly familiar. She looks just like his old friend - the one who believed in aliens and kept looking for them in the skies until just before she died.