Research Interests:
Analytic torsion, Quillen metrics, and their applications to automorphic forms and moduli spaces

Current Researches:
(1) Construction of invariant for varieties of Calabi-Yau type by using analytic torsion
(2) Determination of the analytic torsion invariant as an explicit function on the moduli space
(3) Branched covering and Quillen metrics
(4) Determination of the boundary behavior of analytic torsion
(5) An algebraic expression for the Borcherds Phi-function

Selected Publications:
[1] Discriminant of theta divisors and Quillen metrics,
J. Differential Geom. 52 (1999), 73--115.
[2] K3 surfaces with involution, equivariant analytic torsion,
and automorphic forms on the moduli space,
Invent. Math. 156 (2004), 53--117.
[3] On the singularity of Quillen metrics,
Math. Ann. 337 (2007), 61--89.
[4] (with H. Fang & Z. Lu) Analytic torsion for Calabi--Yau threefolds,
J. Differential Geom. 80 (2008), 175--259.
[5] K3 surfaces with involution, equivariant analytic torsion,
and automorphic forms on the moduli space II,
J. reine angew. math. 677 (2013), 15--70.

Awards:
Takebe Prize (Mathematical Society of Japan, 1997)
Geometry Prize (Mathematical Society of Japan, 2007)