Max Hill joined our department this January as a Temporary Assistant Professor.
Let me first say: welcome to our department! What type of mathematics are you interested in?
Max: I am interested in applications of probability theory and algebraic statistics to further our understanding of evolution and the tree of life.
Do you have a favorite open problem?
Max: A favorite open problem? I am really interested in the following open conjecture, which I learned about from Olivier Gascuel last year:
Suppose you have ‘perfect data’ for some set of taxa (i.e., you have infinitely long DNA sequences from them!) and that you know the topology of their evolutionary tree. Then Gascuel conjectures that under standard DNA substitution models, the likelihood function has no local maxima other than the global maxima.
While at first this conjecture seems rather artificial, whether or not this it is true turns out to have important implications for widely-used maximum likelihood estimation algorithms—namely, whether they are consistent.
What types of courses are you most excited to teach?
Max: I learn a lot every time I teach a new course. Even when it’s something I think I am really familiar with, I find myself making new connections. This, along with interacting with my students, are two of the main joys for me of teaching math. This semester I am so happy to be teaching Math 372 (Probability and Statistics), because I really just love the ‘flavor’ of the subject, with dice and coins and betting games and all of that, which are things that make the subject come alive to me.
What have you liked the most about Hawai’i so far?
Max: About the island: The mountains and the warm breeze. About UH Manoa: Working with Dr Gross and her students has been great; they have made this a wonderful environment for me to grow and do research here. About the city: I really like Don Quijote.
Can you tell us something about yourself that might be surprising?
Max: I really like to sail, though I’ve never said on the ocean (yet).