Will Wylie's research

My research is in geometry and topology. Specifically I am interested in Ricci curvature, its applications, and its generalizations. Even more specifically I have recently been studying Ricci flow, Ricci solitons, quasi-Einstein metrics, Ricci curvature on metric measure spaces, and the topology of manifolds with non-negative Ricci curvature.

Prior to 2008-2009 I was a VIGRE post-doc at UCLA and was a post-doc at MSRI with the program on geometric evolution equations during the Fall of 2006.

I did my Phd at UC Santa Barbara and my thesis advisor was Guofang Wei.

Preprints/Publications:

(with P. Petersen) On the classification of gradient Ricci solitons. arXiv.

(with G. Wei) Comparison Geometry for the Bakry-Emery Tensor. To appear in J. of Diff. Geom. arXiv.

(with P. Petersen) Rigidity of gradient Ricci solitons. Pacific J. of Math. 241 (2):329-345, 2009. available online. arXiv.

(with P. Petersen) On gradient Ricci solitons with symmetry. Proc. Amer. Math. Soc.,137:2085-2092, 2009. available online. arXiv.

Shrinking Ricci solitons have finite fundamental group. Proc. Amer. Math. Soc.,136(5):1803-1806, 2008. available online.

(with G. Wei) Comparison Geometry for smooth metric measure spaces. Proc. of the 4th ICCM , Hangzhou, China, Vol. II 191-202, 2007. pdf file.

Noncompact manifolds with non-negative Ricci curvature. J. of Geometric Analysis, 16(3) 535-550, 2006. available online.

William Wylie

Lecturer in Mathematics

University of Pennsylvania

Preprints/Publications: