Research

Research interests: Number Theory and Algebraic Geometry.
More specifically: Modular forms, Shimura varieties and Zeta values.



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
Preprint, pdf.

\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) 
Algebra Number Theory 11 (2017), no. 8, 1921--1951, pdf, journal.

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. 
Algebraic Number Theory, Oberwolfach reports, Report No. 32/2014, pdf.
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