To create a little flower is the labour of ages.
William Blake, Proverbs of Hell

Contact information CV Texts Errata Notes from talks Code Teaching Getting me to do stuff for you
Lego minifig

Contact information

Paul Seidel
MIT Room 2-276
77 Massachusetts Avenue
Cambridge, MA 02139
USA

Email: pseizzzdel@mit.edu with the zzz removed

Curriculum Vitae

Short: I am Professor of Mathematics at MIT. Or, much longer. Or maybe, you're looking for this or this instead?

Texts

Some research and expository texts not available on the arXiv.

  • My thesis
  • Lecture notes on Categorical dynamics and symplectic topology
  • Charting one's course through mirror symmetry, written for a general audience

    • Errata

    Corrections to published papers. I hope they 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 (Lemma 2.1)
  • Fukaya categories and Picard-Lefschetz theory (Section 8g)
  • 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
  • Fukaya A-infinity structures associated to Lefschetz fibrations. IV (Section 8)
  • Fukaya A-infinity structures associated to Lefschetz fibrations. IV 1/2 (Sections 3 and 4)

    • Notes from talks

    Reproduced with no attempt at improving them.

  • The exponential type conjecture for the quantum connection (2024)
  • Fukaya categories of Calabi-Yau hypersurfaces (2021)
  • Quantum Steenrod operations (2020)
  • The symplectic topologist as a dynamicist (Part of Zabrodsky lectures, 2019)
  • Lagrangian tori and mirror symmetry (Artin lecture, 2018)
  • Fields of definition of Fukaya categories of Calabi-Yau hypersurfaces (2017)
  • Growth and complexity of iterations (2016)
  • Lefschetz fibrations in symplectic topology (2015)
  • Lefschetz pencils and TQFTs (2015)
  • Noncommutative geometry of Lefschetz pencils (2014)
  • Steenrod squares and symplectic fixed points (2014)
  • Picard-Lefschetz theory and hidden symmetries (2013)
  • Categorical dynamics (2012)
  • How complicated are symplectic manifolds? (2011)
  • Constructing open symplectic manifolds from Lefschetz fibrations (2010)
  • Morse lectures (2010): Cotangent bundles and their relatives, Symplectic topology and q-intersection numbers, Symplectic topology as sheaf theory?

    • Code

    Code quality is dreadful; I offer no apologies.

  • The paper "Homological mirror symmetry for the quartic surface" relied on a variety of computations (2002, partly revised 2011)
  • cotangents2.py (Python 3 code for my paper "Symplectic homology as Hochschild homology", 2006)
  • genustwo.py (Python 3 code for my paper "Homological mirror symmetry for the genus two curve", 2009)
  • puncturedtorus.py (Python 3 code adapted from the previous one, computing Hochschild homology of graded algebras, 2010)
  • Code from the example computations in "Fukaya categories associated to Lefschetz fibration 2 1/2" (2015): lambda-infinity.py, solving-the-linear-ode.py, characteristic-polynomial.py (Python 3 using SymPy)
  • Code from the example computations in "Covariant constancy of quantum Steenrod operations", with Nicholas Wilkins (2020): The cubic (del Pezzo) surface; A threefold (intersection of two quadrics in projective five-space (Python 3 using SymPy)
  • From joint work with Dan Pomerleano (2022): An analysis of the formal behaviour of the quantum connection of the cubic (del Pezzo) surface at infinity (Python 3 using SymPy)

    • Teaching

    I concocted a one-of-a-kind undergraduate class, 18.900 Geometry and Topology in the plane. With Semyon Dyatlov and Bjorn Poonen, I am putting together 18.090 Introduction to Mathematical Reasoning (not tremendously innovative in itself, but a new thing at MIT). Over the years, I have tried to mess with the content of existing classes, like 18.01 Calculus (unsuccessfully, on the whole) and 18.100B Real Analysis (partial success), 18.906 Algebraic Topology II (jury is still out).

    Also: my groundbreaking insights into educational software tools.

    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: the exam is 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. For junior career steps (applying to graduate school or postdoctoral positions), I expect you to ask me, at the latest, one month before any deadline. I'll tell you if we need to have an in-person meeting to discuss your work. I need to receive all the necessary material three 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. For senior career steps (tenure-track applications, or promotions to tenure), double all the lengths of time mentioned above.

    Occasionally, I may decline to write a recommendation letter... that doesn't mean you're doomed! Maybe I just don't understand well enough what you're doing (strangely, getting tenure doesn't endow one with the power of all-comprehension).

  • 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 (mathematically complete, but possibly lacking some polish) one month before the defense; and the final version (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.

  • PhD supervision. Too complicated to explain - come and talk to me instead (once you've received an offer from MIT to do a PhD here).

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