Selected topics in geometric analysis Ⅲ
This course is on Hamilton-Perelman’s theory of Ricci flow and a complete proof of the Poincaré conjecture.
Lecturer
Date
24th March ~ 18th June, 2025
Location
| Weekday | Time | Venue | Online | ID | Password |
|---|---|---|---|---|---|
| Monday,Wednesday | 15:20 - 16:55 | A7-301 | ZOOM 05 | 293 812 9202 | BIMSA |
Prerequisite
Real analysis, Riemannian geometry.
Syllabus
1. Hamilton’s Ricci flow
2. Perelman’s reduced volume and its applications
3. Completion of the proof of the Poincaré conjecture
2. Perelman’s reduced volume and its applications
3. Completion of the proof of the Poincaré conjecture
Reference
[1] H. D. Cao, X. P. Zhu, A complete proof of the Poincaré and geometrization conjectures-application of the Hamilton-Perelman theory of the Ricci flow, Asian J. Math. 10(2) (2006) 165-492.
[2] R. S. Hamilton, Three manifolds with positive Ricci curvature, J. Differential Geom., 17 (1982) 255-306.
[3] R. S. Hamilton, Four-manifolds with positive curvature operator, J. Differential Geom. 24 (1986) 153-179.
[4] R. S. Hamilton, The Ricci flow on surfaces, Contemporary Mathematics, 71 (1988) 237-261.
[5] R. S. Hamilton, The Harnack estimate for the Ricci flow, J. Differential Geom., 37 (1993) 225-243.
[6] R. S. Hamilton, A compactness property for solution of the Ricci flow, Amer. J. Math., 117 (1995) 545–572.
[7] R. S. Hamilton, The formation of singularities in the Ricci flow, Surveys in Differential Geometry, 2, pp 7-136, International Press, 1995.
[8] G. Perelman, The entropy formula for the Ricci flow and its geometric applications, arXiv:math.DG/0211159.
[9] G. Perelman, Ricci flow with surgery on three-manifolds, arXiv:math.DG/0303109.
[10] G. Perelman, Finite extinction time for the solutions to the Ricci flow on certain three-manifolds, arXiv:math.DG/0307245.
[2] R. S. Hamilton, Three manifolds with positive Ricci curvature, J. Differential Geom., 17 (1982) 255-306.
[3] R. S. Hamilton, Four-manifolds with positive curvature operator, J. Differential Geom. 24 (1986) 153-179.
[4] R. S. Hamilton, The Ricci flow on surfaces, Contemporary Mathematics, 71 (1988) 237-261.
[5] R. S. Hamilton, The Harnack estimate for the Ricci flow, J. Differential Geom., 37 (1993) 225-243.
[6] R. S. Hamilton, A compactness property for solution of the Ricci flow, Amer. J. Math., 117 (1995) 545–572.
[7] R. S. Hamilton, The formation of singularities in the Ricci flow, Surveys in Differential Geometry, 2, pp 7-136, International Press, 1995.
[8] G. Perelman, The entropy formula for the Ricci flow and its geometric applications, arXiv:math.DG/0211159.
[9] G. Perelman, Ricci flow with surgery on three-manifolds, arXiv:math.DG/0303109.
[10] G. Perelman, Finite extinction time for the solutions to the Ricci flow on certain three-manifolds, arXiv:math.DG/0307245.
Audience
Graduate
Video Public
No
Notes Public
Yes
Language
Chinese
Lecturer Intro
Liangdi Zhang received his Ph.D. degree from Zhejiang University in June 2021. He worked as a postdoc at Beijing Institute of Mathematical Sciences and Applications (BIMSA) and Tsinghua University from August 2021 to August 2023. He is currently an assistant professor at BIMSA. His research interests include differential geometry and geometric analysis.