Should I reach out to potential advisors before applying?

[StatCramer]

Hi All,

Hope everyone is staying safe.

I am applying for Statistics PhD programs for fall 2021 cycle. I am interested in spatiotemporal statistics with environmental and ecological applications. Most universities have only one or two professors working in this area, so I'm wondering whether I should reach out to them before applying? I'm planning on mentioning them by name in my statement of purpose (is this wise?) but a bit scared that they might simply reject me if they are not taking any new students to work with them right now. And I don't even know how to initial such an email. Can I simply ask them whether they are taking new students? I am currently working with a well known professor in this field on my master's thesis whom is going to provide me with a recommendation. Should I mention his name in the statement of purpose?

Thank you

[Casorati]

It doesn't hurt to mention their name in SOP or reach out to them briefly before applying. But most schools admit students at the department level so contacting them/mentioning their names in SOP won't affect your chances in general. Also, students typically choose their supervisor(s) during the second year and I don't think you need to stick to a particular area. It is generally easy to switch research areas in statistics as long as you have strong math background.