Abstract: We will present the enumerative min-max theory, which relates the number of genus g minimal surfaces in 3-manifolds to topological properties of the set of all embedded surfaces of genus ≤g. As a consequence, we can show that in every 3-sphere of positive Ricci curvature, there exist ≥5 minimal tori (confirming a conjecture by B. White (1989) in the Ricci-positive case), ≥4 minimal surfaces of genus 2, and ≥1 minimal surface of genus g for all g. This is based on a joint work with Yangyang Li and Zhihan Wang. 

Brief biography: Adrian Chun-Pong Chu obtained his bachelor’s degree at the Chinese University of Hong Kong and his Ph.D. at the University of Chicago under André Neves. He is current a postdoc (H. C. Wang assistant professor) at Cornell University. His research has focused on minimal surfaces, min-max theory, and geometric flow. From a broader perspective, these topics arise from studying the space of all hypersurfaces in a given Riemannian manifold, and the area functional defined on this space.

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