**UM Math Graduate Students Seminar**

Yijia Liu

*University of Miami*

**will present**

**Almost Complex Structures**

Friday, April 20, 2012, 4:00pm

Ungar Building Room 402

**Abstract:**
The existence of a complex structure has a central role in many physical problems. But sometimes it can be quite difficult to determine whether a manifold admits a complex structure. An example in this respect is the six dimensional sphere \(S^6\). In this talk, I will introduce the notion of almost complex structure and its relation to complex structure. An interesting result is that the only almost complex spheres are \(S^2\) and \(S^6\). I will give a criteria (Wu's Theorem) for 4-manifolds and show that \(S^4\) does not admit an almost complex structure.