Number theory
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 point. 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.
Here is my talk at ICM 2022: The arithmetic of quadratic twists of elliptic curves.
