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UNCW Department of Mathematics and Statistics Colloquium Announcement “On Hilbert’s 16th Problem” Professor Jibin Li Department of Mathematics Zhejiang Normal University Abstract: In this talk, the study progress on Hilbert's 16th problem is presented. The relationship between Hilbert's 16th problem and bifurcations of planar vector fields is discussed. The material is stated in 8 sections. Section 1: Introduction: what is Hilbert's 16th problem? Section 2: The first part of Hilbert's 16th problem. Section 3: The second part of Hilbert's 16th problem. Section 4: Focal values, saddle values and finite cyclicity in a fine focus, closed orbit and homoclinic loop. Section 5: Finiteness problem. Section 6: The weakened Hilbert's 16th problem. Section 7: Global and local bifurcations of Z q equivalent vector fields. Section 8: The rate of growth of Hilbert number H(n) with n. Time: November 03, 2008, 2:00 pm – 3:30 pm Teatime: 3:30 pm – 4:00 pm Location: 219 Bear Hall