Yu-Wei Fan (范祐維)

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. Starting Fall 2019, I will be a Morrey Visiting Assistant Professor at UC Berkeley.

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

	-	Weil-Petersson geometry on the space of Bridgeland stability conditions, with Atsushi Kanazawa and Shing-Tung Yau. [ Abstract ] Accepted by Comm. Anal. Geom.. (arXiv:1708.02161) 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 Hansol Hong, Siu-Cheong Lau and Shing-Tung Yau. [ Abstract ] To appear in Adv. Theor. Math. Phys., 22 (2018), no. 5. (arXiv:1706.02942) 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.
	-	Entropy of an autoequivalence on Calabi-Yau manifolds. [ Abstract, Slides ] Math. Res. Lett., 25 (2018), no. 2, 509-519, doi. (arXiv:1704.06957) 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.
	-	Systoles, Special Lagrangians, and Bridgeland stability conditions. [ Abstract, Video ] arXiv:1803.09684. 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.
	-	On entropy of P-twists. [ Abstract ] arXiv:1801.10485. 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.

Teaching

Spring 2019: Course Assistant, Theoretical multivariable calculus and real analysis, Harvard University.
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).