Abstract: In the beginning of 20th century, Poincare initiated the study of topology. He proposed a fundamental conjecture in 3-dim topology: Every simply connected, closed 3-manifold is homeomorphic to the 3-sphere. Comparing with the classification of 2-dim closed manifolds, the similar classification problem in 3-dim is much harder. In 1982, Hamilton introduced Ricci flow, which deforms initial metric on manifolds to canonical metric by parabolic method, and shed light to Poincare's old conjecture. However, the thorough understanding of singularity during Ricci flow is the essential obstacle to finish this program. The key analysis of singularity was achieved by Perelman by introducing several new concepts and tools, which had great impact on geometry and analysis.
We will focus on introducing the intuitive ideas of this program, and basic geometry and PDE knowledge is enough to understand most part of the talk.
Biography: Guoyi Xu is an assistant professor in Mathematical Sciences Center at Tsinghua University since September 2013. He got Ph.D degree in mathematics in May 2010 from University of Minnesota under the supervision of Robert Gulliver. He had hold visiting assistant professorship in University of California, Irvine, where his mentor was Peter Li. His interest in math are geometric flows and its application in geometry and topology.