Abstract：

Finding the Noether inequality for varieties of general type is a natural problem in the study of algebraic geometry, which dates back to the work of M. Noether for surfaces. Later, Debarre proved that irregular surfaces of general type satisfy a stronger Noether inequality. Recently, J. Chen, M. Chen and C. Jiang established the optimal Noether inequality in dimension three. In this talk, I will introduce an optimal Noether inequality for almost all complex irregular threefolds of general type. This is a joint work with Y. Hu.