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Summer Graduate School

Metric Geometry and Geometric Analysis (Oxford, United Kingdom) July 11, 2022 - July 22, 2022
Parent Program: --
Location: University of Oxford, United Kingdom
Organizers LEAD Cornelia Drutu (University of Oxford), Panos Papazoglou (University of Oxford)

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Cornelia picture 2
Several geometric ideas in the context of a surface: hyperbolic metric, CAT(0) inequality, Gromov hyperbolicity/coarse median geometry, nonpositively-curved square tiling, Besikovitch inequality. (Picture by M. Hagen and A. Sisto.)

The purpose of the summer school is to introduce graduate students to key mainstream directions in the recent development of geometry, which sprang from Riemannian Geometry in an attempt to use its methods in various contexts of non-smooth geometry. This concerns recent developments in metric generalizations of the theory of nonpositively curved spaces and discretizations of methods in geometry, geometric measure theory and global analysis. The metric geometry perspective gave rise to new results and problems in Riemannian Geometry as well.


All these themes are intertwined and have developed either together or greatly influencing one another. The summer school will introduce some of the latest developments and the remaining open problems in these very modern areas, and will emphasize their synergy.

Suggested prerequisites

We anticipate that the participating students will come from diverse backgrounds in Geometric Group Theory, Riemannian Geometry and Geometric Analysis.

The following textbooks would give adequate preparation but we don’t expect students to have necessarily studied all of them:

  • Chapters 3, 8, 10, 11 of “Geometric Group Theory” by C. Drutu and M. Kapovich
  • First 4 chapters of "Riemannian Geometry" by M. P. Do Carmo and the first 2 chapters of "Morse Theory" by J. Milnor
  • Parts I.2, I.3, I.8, and II.1 of “Metric Spaces of Non-Positive Curvature” by Bridson-Haefliger

The students who have been selected to take part in the school will be sent a compilation of introductory texts extracted from the books above and other existing lecture notes, for study beforehand, by email and, if they so wish, a paper version by ordinary mail as well. A more definite and specific list of prerequisites will be given later on after consulting with the lecturers so that background material matches the specific topics they plan to cover in their lectures.

For eligibility and how to apply, see the Summer Graduate Schools homepage

Due to the small number of students supported by MSRI, only one student per institution will be funded by MSRI. You may must also apply directly with The Mathematical Insitute, University of Oxford, take a look at this page for more information.