Department of Mathematics
Science Center 425c
One Oxford Street
Cambridge, MA 02138, USA
Email: ywfan [at] math [dot] harvard [dot] edu
I am a fourth year graduate student at Harvard University.
My advisor is
I have pretty broad interests in algebraic geometry, symplectic geometry, dynamics and mathematical physics.
These days I am working on projects surrounding mirror symmetry,
which is a conjectural duality between algebraic geometry and symplectic geometry.
More specifically, I am thinking about its interplays with Bridgeland stability conditions,
wall-crossings, autoequivalences and Teichmüller theory.
- On entropy of P-twists.
P-twists are the mirror of Dehn twists along Lagrangian complex projective space.
We compute the categorical entropy of autoequivalences given by P-twists,
and show that these autoequivalences satisfy a Gromov-Yomdin type conjecture.
- Weil-Petersson geometry on the space of Bridgeland stability conditions
(with A. Kanazawa and S.-T. Yau).
We define a Weil-Petersson potential function on the space of Bridgeland stability conditions,
with the hope of further understand the stringy Kähler moduli space of Calabi-Yau manifolds.
We show that the induced Weil-Petersson metric coincides with the Bergman metric in some two-dimensional cases.
- Mirror of Atiyah flop in symplectic geometry and stability conditions
(with H. Hong, S.-C. Lau and S.-T. Yau).
We construct the mirror of Atiyah flop in symplectic geometry under mirror symmetry,
and interpret it as a change of stability conditions.
- Entropy of an autoequivalence on Calabi-Yau manifolds.
To appear in Mathematical Research Letters.
We construct the first counterexamples of a conjecture on categorical entropy.
While the construction is purely algebro-geometric,
the reason to expect counterexamples actually comes from the symplectic side of mirror symmetry.
- I taught Math 21a (Multivariable Calculus)
in Fall 2017.
Last updated: February 1st, 2018.