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Geometric Analysis Reading Group

Fall 2025 • Wednesdays 3PM • 2-361

Collapsing Riemannian metrics: old and new

Week Date Topic Reading Presenter
1 09-17 Introduction - Cosmin Manea
2 09-24 Almost flat manifolds [BuKa1] Jacob Reznikov
3 10-1
4 10-8 Fibrations, F-structures, & Anderson examples [ChGr1], [ChGr2], [Fuk1], [And1] Benjy Firester
5 10-15 Fibrations, F-structures, & Anderson examples [ChGr1], [ChGr2], [Fuk1], [And1] Benjy Firester
6 10-22 Mike Law
7 10-29
8 11-5 Dongyeong Ko
9 11-12
10 11-19 Shrey Aryan
11 11-26
12 12-3
13 12-10

Bibliography

  1. [And1] Michael T. Anderson, “Hausdorff perturbations of Ricci-flat manifolds and the splitting theorem,” October 1992.
  2. [BuKa1] Peter Buser and Hermann Karcher, “Gromov’s almost flat manifolds,” Astérisque, tome 81 (1981). <http://www.numdam.org/item?id=AST_1981__81__1_0>
  3. [ChGr1] Jeff Cheeger and Mikhael Gromov, Collapsing Riemannian manifolds while keeping their curvature bounded. I.
  4. [ChGr2] Jeff Cheeger and Mikhael Gromov, Collapsing Riemannian manifolds while keeping their curvature bounded. II.
  5. [Fuk1] Kenji Fukaya, “Collapsing Riemannian manifolds to ones of lower dimensions,” 1987.
  6. [Fuk2] Kenji Fukaya, “Collapsing of Riemannian manifolds and eigenvalues of Laplace operator,” Invent. Math. 87 (1987), 517–547.
  7. [Kar1] Hermann Karcher, “Report on M. Gromov’s almost flat manifolds,” Séminaire N. Bourbaki, 1980, exp. no. 526, pp. 21–35.