Yu-Wei Fan

Department of Mathematics
Harvard University
One Oxford Street, Cambridge, MA 02138

Email:
Office: Science Center 425c

I am a fifth year graduate student at Harvard, working with Shing-Tung Yau.

I have pretty broad interests in algebraic geometry, symplectic geometry, dynamical systems and mathematical physics. These days I am working on projects surrounding mirror symmetry, which is a 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.

My Curriculum Vitae.

Papers

My papers are all available on the arXiv.

2018	-	Mirror of Atiyah flop in symplectic geometry and stability conditions (with H. Hong, S.-C. Lau and S.-T. Yau). To appear in Advances in Theoretical and Mathematical Physics, 22 (2018), no. 5. [ Abstract, PDF ] We study the mirror operation of the Atiyah flop in symplectic geometry. We formulate the operation for a symplectic manifold with a Lagrangian fibration. Furthermore we construct geometric stability conditions on the derived Fukaya category of the deformed conifold and study the action of the mirror Atiyah flop on these stability conditions.
2018	-	Entropy of an autoequivalence on Calabi-Yau manifolds. Mathematical Research Letters, 25 (2018), no. 2, 509-519. [ Abstract, PDF, Journal, Notes, Slides ] 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.
2018	-	Systoles, Special Lagrangians, and Bridgeland stability conditions. Submitted. [ Abstract, PDF, Notes ] Loewner's torus systolic inequality says that the systole (least length of a non-contractible loop) on a two-torus can't be too large compare to its volume. We propose to generalize the systolic inequality from the viewpoint of Calabi-Yau geometry. This naturally leads to the notions of categorical systole and systolic ratio of a Bridgeland stability condition. Then we study the systolic problem in the case of a K3 surface.
2018	-	On entropy of P-twists. Submitted. [ Abstract, PDF ] P-twists are the mirror of Dehn twists along Lagrangian complex projective space under mirror symmetry. We compute the categorical entropy of autoequivalences given by P-twists, and show that these autoequivalences satisfy a Gromov-Yomdin type conjecture.
2017	-	Weil-Petersson geometry on the space of Bridgeland stability conditions (with A. Kanazawa and S.-T. Yau). Submitted. [ Abstract, PDF, Notes ] 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.

Teaching

Fall 2018: Course Assistant, Symplectic Manifolds and Lagrangian Submanifolds, Harvard University.
Summer 2018: Instructor, Introduction to Bridgeland stability conditions, Tsinghua University, Beijing.
Summer 2018: Coach, Yau Tsinghua Junior Math Talent Program, Tsinghua University, Beijing.
Fall 2017: Instructor, Multivariable Calculus, Harvard University.
Fall 2016: Coach, Multivariable Calculus, Harvard University.

Organized seminars

2016-2017: Yau's student seminar, Harvard University.
2015-2016: Trivial Notions Seminar, Harvard University (co-organizer).