Degrees and Honours
B.Sc. (Tsuda College)
Numerous visiting positions at leading research institutes including:
Bye-fellowship at Newnham College, University of Cambridge, England
Visiting Researcher at Max-Planck-Institute for Mathematics, Germany
My general areas of research interests/activities are in Arithmetic Algebraic Geometry, and Mathematical Physics: in particular, Mirror Symmetry Conjecture. The current research topics include arithmetic aspects (L-functions) of Calabi--Yau varieties defined over number fields, mirror maps of certain families of Calabi--Yau varieties, and the mirror symmetry conjecture for K3 surfaces and certain Calabi-Yau threefolds. Calabi-Yau varieties in dimension 1, 2, 3 are, respectively, elliptic curves, K3 surfaces, and Calabi-Yau threefolds, and specifically, Picard-Fuchs differential equations for pencils of K3 surfaces, the modularity conjecture for rigid Calabi--Yau threefolds, the conjecture of Beilinson and Bloch relating the order of vanishing of the L-functions at s=2 and the rank of certain Chow groups on Calabi-Yau threefolds are currently investigated.
I collaborate with a number of mathematicians, including D. Zagier (Max-Planck Institute, Bonn) on number of problems, H. Verrill (Hannover) on mirror maps of families of K3 surfaces, M-H. Saito (Kobe) on rigid Calabi-Yau threefolds, S. Hosono (Tokyo) on mirror symmetry conjecture, F. Q. GouvL a (Colby College) on the conjectures of Beilinson and of Lichtenbaum and Milne, X. Xarles (Barcelona) on intermediate Jawbians of Calabi-Yau threefolds, and with C.U. Jensen (Copenhagen) and A. Ledet (Waterloo) on constructive aspects of the Inverse Galois Problem.