Research interests: Number Theory and Algebraic Geometry. Preprints p-converse to a theorem of Gross-Zagier, Kolyvagin and Rubin (with Ye Tian). Preprint, available upon request. Horizontal variation of Tate-Shafareivhc groups (with Haruzo Hida and Ye Tian). Preprint, pdf. Horizontal non-vanishing of Heegner points and toric periods (with Ye Tian). Preprint, pdf. Quantitative non-vanishing of Dirichlet L-values modulo p (with Hae-Sang Sun). Preprint, pdf.
On the non-vanishing of p-adic heights for CM abelian varieties, and the arithmetic of Katz p-adic L-functions (with Daniel Disegni). Preprint, pdf. On the non-triviality of the p-adic Abel-Jacobi image of generalised Heegner cycles modulo p, I: modular curves. \mathfrak{p}-rigidity and \mathfrak{p}-independence of quaternionic modular forms modulo p. Preprint, available upon request. Publications
\mathfrak{p}-rigidity and Iwasawa \mu-invariants (with Haruzo Hida)
On the non-triviality of the p-adic Abel-Jacobi image of generalised Heegner cycles modulo p, II: Shimura curves. J. Institut Math. Jussieu 16 (2017), no. 1, 189-222, pdf,
journal.
Andre-Oort conjecture and non-vanishing of central L-values over Hilbert class fields (with Haruzo Hida). Forum Math. Sigma 4 (2016), e20, 26 pp,
journal.
An l\neq p-interpolation of genuine p-adic L-functions. Res. Math. Sci. 3 (2016), Paper No. 16, 26 pp,
journal.
On the \mu-invariant of the cyclotomic derivative of Katz p-adic L-function. J. Inst. Math. Jussieu 14 (2015), no. 1, 131-148,
pdf,
journal.
The vanishing of the \mu-invariant of p-adic Hecke L-function for CM fields (with Ming-Lun Hsieh). IMRN no. 5 (2013), 1014-1027, journal.
Thesis
On the non-triviality of arithmetic invariants modulo p.June 2015, eScholarship.
Conference Proceedings p-converse to a theorem of Gross-Zagier, Kolyvagin and Rubin. Algebraic Number Theory, Oberwolfach reports, 2018, pdf. Horizontal non-vanishing of Rankin-Selberg L-values. Prime Numbers and Representation Theory, Lecture Series of Modern Number Theory: volume 2, 2017, pdf.
Non-triviality of generalised Heegner cycles over anticyclotomic towers: a survey. Chapter 8 of p-Adic Aspects of Modular Forms, World Scientific, 2016, pdf, World Scientific link.
On the non-triviality of generalised Heegner cycles modulo p. |

### Research

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