How does one start an email to a professor? I am curious about how it is done in Russia, but also how it should be done in Russian in the United States. Over here, especially in small classes (like my Russian class), we have relatively casual relationships with professors. In an English email, I would say, "Hello Professor Smith."
If your relationship is casual and less formal one may be addressed as
Приветствую/Здравствуйте, профессор no (sur)names
Omission of a name underscores the informality and sounds kind of cheery, merry, enthusiastic and upbeat. And if the content of the message is somber or deals with a request of some sort, then it conversely sounds more appealing, cordial, intimate, hopeful and ingratiating.