Hailong "Long" Dao

Associate Professor of Mathematics
Primary office:

My research interests are focused on commutative algebra and its connections to neighbor fields such as algebraic K-theory or algebraic geometry. One of the motivations for my research is a group of questions informally known as "the homological conjectures". Surprisingly, there is an wiki entry for them, in case you are curious. For a very readable history of these questions, see this book review by Craig Huneke. 

The main reason I started working on these questions was my thesis advisor, Mel Hochster. He has been obsessed with these problems for over 30 years and some of his best work were motivated by them. Needless to say, the remaining questions are pretty hard, but it does not prevent him from trying them on his students! Three years into the program, I seriously considered switching to Economics, since compared to Serre's Positivity Conjecture, the global poverty problem seemed at least doable! Fortunately, Mel's constant encouragement and kindness (plus his enormous grant) helped me through, and now I enjoy thinking about them a whole lot more. In fact, these are beautiful problems, and it is quite easy to fall in love with them. Trouble is, your love is almost never returned (just like high school!). As often with doomed love affairs, this one did bring out some unintended consequenses, a summary of which you can find here 

Sometimes I put questions related to my research on Mathoverflow. It has been great fun! 

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