**UBC Mathematics Department**

*http://www.math.ubc.ca*

## Colloquium Abstract: Dr. Gang Tian, MIT

* Minimal surfaces in 4-manifolds*

Abstract: One can associate two topological numbers to any surface
*Sigma* in a 4-manifold *M*, namely, the euler number
and the self-intersection number of the surface. If *M* is
complex and *Sigma* is holomorphic, the sum *a_M(Sigma)
* of those two topological numbers is the same as *c_1(M)
(Sigma)*, where *c_1(M)* denotes the first Chern class of
*M*. In this talk, we discuss recent results on the topological
number *a_M(Sigma)* for any minimal surface *Sigma* in
a general Riemannian 4-manifold. In particular, we will show that
*a_M* is always negative under certain pinched curvature
conditions. Finally, we will discuss a theorem for minimal surfaces in
symplectic 4-manifolds and its consequences.

*Coffee, tea and cookies will be served in Math Lounge (Annex) Room 1115

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