时间：2023年4月9日
地点：西湖大学云谷校区E10-405
1. 8:30-9:30
Speaker：周胜铉，北京大学
Title：Introduction to Milnor's Conjecture
Abstract：In this talk, we will review the history of Milnor's conjecture, such as the low-dimensional case, the almost nilpotent properties of fundamental groups and the finite generation of local fundamental groups, etc.
2. 9:50-10:50
Speaker：Aaron Naber，Northwestern University
Title：Ricci Curvature, Fundamental Group and the Milnor Conjecture
Abstract：It was conjectured by Milnor in 1968 that the fundamental group of a complete manifold with nonnegative Ricci curvature is finitely generated. The main result of this paper is a counterexample, which provides an example M^7 with Ric>= 0 such that \pi_1(M)=Q/Z is infinitely generated.
There are several new points behind the result. The first is a new topological construction for building manifolds with infinitely generated fundamental groups, which can be interpreted as a smooth version of the fractal snowflake. The ability to build such a fractal structure will rely on a very twisted gluing mechanism. Thus the other new point is a careful analysis of the mapping class group \pi_0Diff(S^3\times S^3) and its relationship to Ricci curvature. In particular, a key point will be to show that the action of \pi_0Diff(S^3\times S^3) on the standard metric g_{S^3\times S^3} lives in a path connected component of the space of metrics with Ric>0.
Tencent Meeting: 448 331 498
PASSCODE: 230409
3. 11:20-12:10
Speaker：王枫，浙江大学
Title：On the Kahler-Ricci flow on spherical Fano manifolds
Abstract：I will talk about the recent progress of the Kahler-Ricci flow on Fano manifolds. Especially, I will give some more precise results for spherical Fano manifolds.
