firstname.lastname@example.org with the zzz removed
(a primitive line of defense against spam)
MIT Room 2-276 *new*
77 Massachusetts Avenue
Cambridge, MA 02139
To create a little flower is the labour of ages.
William Blake, Proverbs of hell
I am Professor in the MIT Department of Mathematics. You can look at my complete cv here.
Here are some unpublished texts, which are not available on the arXiv:
Lecture notes on Categorical Dynamics and Symplectic Topology
Charting one's course through mirror symmetry, written for a general audience (2017)
Here are some corrections to published papers. Given the length of time that has passed from publication to correction, my best hope is that the errata do not introduce mistakes that are worse than the original...
pi1 of symplectic automorphism groups and invertibles in quantum homology rings
A biased view of
symplectic cohomology (Equation 3.20)
A biased view of symplectic cohomology (Section 8b)
Fukaya categories and Picard-Lefschetz theory (Remark 11.1)
Lefschetz fibrations and exotic symplectic structures on cotangent bundles of spheres (with M. Maydanskiy)
Some speculations on pair-of-pants decompositions and Fukaya categories
Here are (handwritten) notes for some of my past talks. These are delivered "as is", with no attempt at improving them. They are in chronological order:
Constructing open symplectic manifolds from Lefschetz fibrations
Morse lectures at IAS (2010):
Cotangent bundles and their relatives,
Symplectic topology and q-intersection numbers,
Symplectic topology as sheaf theory?
How complicated are symplectic manifolds? (2011)
Categorical Dynamics (2012)
Picard-Lefschetz theory and hidden symmetries (2013)
A fundamental observation about circle actions (2013)
Critical points of complex polynomials from the symplectic viewpoint (2014)
Noncommutative geometry of Lefschetz pencils (2014)
Steenrod squares and symplectic fixed points (2014)
Lefschetz fibrations in symplectic topology (2015)
Lefschetz pencils and TQFTs (2015)
Growth and complexity of iterations (2016)
Fields of definition of Fukaya categories of Calabi-Yau hypersurfaces (2017)
Lagrangian tori and mirror symmetry (2018)
Occasionally, I write programs for carrying out homological algebra computations. Some of the results are used in my papers. See here for the source code.
Getting me to do stuff for you
UROPs (undergraduate research): To do a UROP, I need to have a suitable question that I'm seriously interested in. Usually, UROP students are ones that have taken an advanced undergraduate or basic graduate course with me, so that
I know them and their level of preparation. Most UROPs I've advised have some experimental or computational component, so be prepared to code as well as do theory.
Qualifying exams: for secondary topics, I will usually agree to be your examiner if: it's about a graduate class that I have taught; or, a class that someone taught, but that person is not available (on leave, or no longer at MIT) and the material falls within my competence. Ask well ahead of time (certainly, before you start planning or preparing for the qualifying exam). Note that independently, you need to contact the graduate (co)chair to get approval for your choice of exam topics.
Recommendation letters: I expect you to ask me, at the latest, one month before any deadline. I need to receive all the necessary material two weeks before the deadline. I will need a research statement (for graduate school applicants: statement of mathematical interests), unless I know you and your work exceptionally well.
Some additional (commonsense) considerations concerning letter-writing: occasionally, I may decline to write a reommendation letter... for instance, maybe I just don't quite understand what you're doing (strangely, getting tenure doesn't endow one with the power of all-comprehension). If the application is for postdoctoral level positions or above, we should probably meet in person to discuss your work (unless I already know it well); setting up such a meeting may require additional time. It needs to be clear beforehand that the meeting is for the purpose of writing a letter, so that I ask the right questions and take notes (I strongly prefer not to do Skype discussions for this purpose).
Thesis defense committees: Again, ask me well ahead of time, and be aware that the decision rests with me. Once we've agreed, I need to receive a preliminary version of your
thesis (essentially complete, but possibly lacking some polish or details) one month before the defense;
and the final version (with all details and fully polished) two weeks before the defense. If you miss either deadline,
I will not serve on your committee, no matter what we agreed to beforehand. The version you give me two weeks before the defense
will be the last one I will look at, and I will base my questions (at the defense) on that
PhD supervision: This is too complicated to explain on a web page - come and talk to me
instead. Note that I will almost certainly not agree to supervise you until you've come to MIT and we've had