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Riemannian Convergence Theory: November 9 – 13, 2015

Organized by Simon Donaldson, Kenji Fukaya, Hans-Joachim Hein, Song Sun

Dates: November 9 – 13, 2015

Attendee ListDownload Talk ScheduleView Videos

The subject of the workshop is the Gromov-Hausdorff convergence of sequences of Riemannian manifolds under a variety of curvature and other natural geometric bounds. Such Gromov-Hausdorff limits are typically highly singu- lar metric spaces. By studying their regularity properties, one obtains uniform structural results for the class of all Riemannian manifolds satisfying a given col- lection of geometric bounds. The Gromov-Hausdorff convergence and regularity theory provides much of the technical underpinning of the more differential- geometric side of the 3 month SCGP program Moduli spaces and singularities in algebraic and Riemannian geometry which this workshop is a part of. It has a long and rich history (work of Cheeger, Fukaya and Gromov on sectional curva- ture bounds and of Cheeger and Colding on Ricci curvature bounds), with spec- tacular recent developments such as the proof of the codimension-4 conjecture for Ricci limit spaces by Cheeger and Naber. On the other hand, applications to algebraic geometry such as the ones that the SCGP program will focus on (in particular those related to the “collapsing” of Calabi-Yau manifolds) will require significant further development of the Riemannian theory. While the importance of this Riemannian convergence theory, and some of its main results, are now widely appreciated the more technical aspects of the theory are much less well-known. One purpose of the workshop is to gather together some of the main experts on Riemannian convergence theory to review recent progress in the area, learn about new challenges from the algebraic geom- etry side, and interact with the other participants of the 3-month programme coming from a variety of different backgrounds. The topics discussed will in- clude both the more traditional convergence theory (Riemannian manifolds of bounded sectional or Ricci curvature) and on more recent, less-developed, aspects of the subject such as Kahler metrics of constant scalar curvature and limits of geometric flows.

Talk Schedule


Time Title Presenter Location
10:00 am  Integral pinched curvature and the topology of some 3-manifolds Gilles Carron SCGP 102
11:00 am Coffee Break N/A  SCGP Lobby
12:30 pm Lunch N/A  SCGP Cafe
2:30 pm On the moduli space of critical metrics on connected sums of Einstein four-manifolds Jeff Viaclovsky  SCGP 102
3:30 pm Tea Time N/A  SCGP Lobby

Time Title Presenter Location
10:00 am Part 1: Quantitative Nilpotent Structure and Regularity of Collapsed Einstein Manifolds Ruobing Zhang SCGP 102
11:00 am Part 2: Quantitative Nilpotent Structure and Regularity of Collapsed Einstein Manifolds Ruobing Zhang SCGP 102
12:00 pm Lunch  N/A SCGP Cafe
1:00 pm SCGP Weekly Talk: Riemannian convergence theory Hans-Joachim Hein SCGP 102
3:30 pm Tea Time N/A SCGP Lobby


Time Title Presenter Location
10:00 am The nonuniqueness of the tangent cone at infinity of Ricci-flat manifolds Kota Hattori  SCGP 102
11:00 am Coffee Break N/A  SCGP Lobby
11:30 am Regularity and Convergence on certain Toric 4-manifolds without Ricci Curvature Conditions Brian Weber  SCGP 102
12:30 pm Lunch N/A  SCGP Cafe
4:00 pm Almost flat Calabi-Yau surface. Gao Chen  SCGP 102
3:30 pm Tea Time N/A  SCGP Lobby


Time Title Presenter Location
10:00 am Part 1: Regularity of Manifolds of Bounded Ricci Curvature and the Codimension 4 Conjecture Jeff Cheeger SCGP 102
11:00 am Coffee Break N/A SCGP Lobby
11:30 am Part 2: Regularity of Manifolds of Bounded Ricci Curvature and the Codimension 4 Conjecture Jeff Cheeger SCGP 102
12:30 pm Lunch N/A SCGP Cafe
2:30 pm Regularity scale and convergence of the Calabi flow. Bing Wang SCGP 102
3:30 pm Tea Time N/A SCGP Lobby


Time Title Presenter Location
10:00 am Co-associative fibrations of G2 manifolds Simon Donaldson SCGP 102
11:00 am Coffe Break N/A SCGP Lobby
11:30 am Degenerations of G2-manifolds and vanishing associatives Thomas Walpuski SCGP 102
12:30 pm Lunch N/A SCGP Cafe
2:30 pm Limits of the Kahler-Ricci flow Xiuxiong Chen SCGP 102
3:30 pm Tea Time N/A SCGP Lobby

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