My name is Daniel Murfet, I am an assistant professor at the University of Southern California. My research is mostly in the areas of category theory, commutative algebra and algebraic geometry, and recently I have become interested in computation.
During my PhD I wrote many careful notes on topics of interest to students in algebraic geometry. I’m guessing that’s why you’re here; I hope you find them useful.
The title of this webpage refers to the following observation of Grothendieck about his approach to solving difficult problems
“A different image came to me a few weeks ago. The unknown thing to be known appeared to me as some stretch of earth of hard marl, resisting penetration…the sea advances insensibly in silence, nothing seems to happen, nothing moves, the water is so far off you hardly hear it…yet it finally surrounds the resistant substance.“
The translation of this beautiful quote is due to Colin McLarty, from his paper “The Rising Sea: Grothendieck on simplicity and generality I“.