Zhiyu Tian


Mailing Address:
Department of Mathematics
California Institute of Technology
Pasadena, CA, 91125

E-mail: my_last_name At caltech Dot edu

Office: Sloan 372

Research Interests

Algebraic geometry. I am currently trying to understand the geometric, topolgical and arithmetic properties of algebraic varieties by studying the rational curves on them. I am also interested in birational geometry and moduli spaces and their applications to other geometric problems.


All the papers can be found on Arxiv, which might be different from (but equivalent to) the published version.


1. Symplectic geometry of rationally connected threefolds. Duke Math. Journal. Vol. 161, No.5, 2012 (Journal, arxiv)

2. Symplectic geometry and rationally connected 4-folds.  to appear in J. Reine. Angew. Math. (Crelle’s Journal)  arxiv 1208.4343

3.  (with Hong R. Zong) One cylces on rationally connected varieties.  Compositio. Math. Vol. 150, issue 03, 396-408. (Journal, arxiv )




1. Weak approximation for cubic hypersurfaces, submitted arxiv 1303.7273.


2. Towards the symplectic Grabber-Harris-Starr theorems. submitted arxiv 1208.4340


3. (with Zhiyuan Li) Moduli of complete intersection K3 surfaces. arxiv1304.3219.


4 (with Hong R. Zong) Weak approximation for isotrivial families, submitted. arxiv 1003.3502


5. R-equivalence on del Pezzo surfaces of degree 4 and cubic surfaces,  arxiv 1307.1801


6. Separable rational connectedness and stability, submitted  arxiv1312.4238.


7. (with Francois Greer and Zhiyuan Li) Picard groups on moduli of K3 surfaces with Mukai models, submitted, arxiv 1402.2330



Spring 2014

Ma 130c Algebraic geometry

Ma 132 Topics in algebraic geometry: derived categories

Spring 2013

Topics in algebraic geometry: Hodge theory

Fall 2012

Ma 120a Abstract algebra

Spring 2012

Ma 157b Riemannian geometry II (complex and algebraic geometry)

Fall 2011

Ma 130a Algebraic geometry

Ma 157a Riemannian geometry

Office Hours