Which supervised learning algorithms are available for matching?
You can try to frame this problem as a recommender systems situation. Where you have your users (prospective students) and items (alumni) and want to recommend to the users one item. 

It's not a perfect fit as you want just one item for each user and you don't have previous match data for each user. However you could investigate this idea a bit further. I'm applying these techniques to the recruitment problem, I'm matching users with job offers and I'm having some success. 

Try to read a bit about recommender systems, to start I recommend chapter 9 of mining massive data sets, it's really introductory, but gives a good overview of the most common techniques.