My interests include  arithmetic of elliptic curves and automorphic forms, in particular the BSD conjecture, Iwasawa theory and relative trace formulae.

Here is my CV (English / Chinese), Publications and Preprints.

Selected Publications:

1. A. Burungale; Y. Tian. A rank zero -converse to a theorem of Gross--Zagier, Kolyvagin and Rubin. Ann. of Math.

2. A. Diaconu; Y. Tian. Twisted Fermat curves over totally real fields. Ann. of Math. (2) 162 (2005), no. 3, 1353--1376.   

3. J. Li; B. Sun and Y. Tian. The multiplicity one conjecture for local theta correspondences. Invent. Math. 184 (2011), no. 1, 117--124.   

4. Y. Tian. Congruent numbers and Heegner points. Camb. J. Math. 2 (2014), no. 1, 117--161.   

    Y. Tian. Congruent numbers with many prime factors. Proc. Natl. Acad. Sci. USA 109 (2012), no. 52, 21256--21258.   

    Reviewed by J. Coates: Congruent numbers. Proc. Natl. Acad. Sci. USA 109 (2012),  no.52, 21182–21183

5. A. Burungale; Y. Tian. p-converse to a theorem of Gross-Zagier, Kolyvagin and Rubin. Invent. Math. 220 (2020), no. 1, 211--253.