PhD Oral Exam - Ting-Han Huang, Mathematics & Statistics

When studying for a doctoral degree (PhD), candidates submit a thesis that provides a critical review of the current state of knowledge of the thesis subject as well as the student’s own contributions to the subject. The distinguishing criterion of doctoral graduate research is a significant and original contribution to knowledge.

Once accepted, the candidate presents the thesis orally. This oral exam is open to the public.

Abstract

In this thesis, we generalize the p-adic Gross-Zagier formula of Darmon-Rotger on triple product p-adic L-functions to finite slope families. First, we recall the construction of triple product p-adic L-functions for finite slope families developed by Andreatta-Iovita. Then we proceed to compute explicitly the p-adic Abel-Jacobi image of the generalized diagonal cycle. We also establish a theory of finite polynomial cohomology with coefficients for varieties with good reduction. It simplifies the computation of the p-adic Abel-Jacobi map and has the potential to be applied to more general settings.

Finally, we show by q-expansion principle that the special value of the L-function is equal to the Abel-Jacobi image. Hence, we conclude the formula.