|My specialty is algebraic geometry. This means, roughly, the study of the geometric properties of solutions of systems of algebraic equations. What I love about this subject is the interplay among geometry, algebra, analysis, and number theory. I am especially interested in applying differential and integral calculus in an algebraic setting. I am also involved in "logarithmic geometry," which is a systematic way of dealing with two important phenomena in mathematics: compactification and degeneration. I am especially interested in p-adic geometry, including various aspects of algebraic differential equations, and p-adic cohomology, including crystalline and prismatic cohomology.|
Research Papers and Presentations
Logarithmic Algebraic Geometry and Mirror Symmetry
Current and Recent Students
"What an abbys of uncertainty whenever the mind feels that some part of it has strayed beyond its own borders; when it, the seeker,
is at once the dark regioin through which it must go seeking, where all its equipment will avail it nothing. Seek? More than that: create.
It is face to face with something which does not so far exist, to which it alone can give reality and substance, which it alone can bring into the light of day."
I love cycling, and used to be the adviser to the Cal Cycling Club:
I also love music, especially the jazz of Patricia Barber: