Metric Geometry and Geometric Analysis Graduate Summer School

GRADUATE SUMMER SCHOOL METRIC GEOMETRY AND GEOMETRIC ANALYSIS

This graduate school will be held at The Mathematical Insitute, University of Oxford from 11 July 2022 to 22 July 2022.https://www.maths.ox.ac.uk/ 

Andrew Wiles Building

Accommodation will be at St Edmund Hall, Oxford.  https://www.seh.ox.ac.uk/

St Edmund hall

Organizers:  Cornelia Drutu (University of Oxford), Panos Papazoglou (University of Oxford)
The program is composed of four mini-courses, with lectures in the morning and problem sessions in the afternoon, and a number of research talks. Lecturers of the mini-courses:

Mladen Bestvina (University of Utah) https://www.math.utah.edu/~bestvina/

Bruce Kleiner (New York University, Courant Institute)  https://cims.nyu.edu/people/profiles/KLEINER_Bruce.html

Urs Lang (ETH Zurich) https://people.math.ethz.ch/~lang/

Regina Rotman (University of Toronto) http://www.math.toronto.edu/rina/

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.

Participation will be on a selective basis with a maximum of 40 students.

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:

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

Chapters 3, 8, 10, 11 of “Geometric Group Theory” by C. Drutu and M. Kapovich

The students who are 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.

To apply please send the following:

A cover letter explaining how the school will benefit your research. Please also state whether you need to apply for full or partial funding and if you can attend the school without funding. 

A CV, with details of your PhD, supervisor, and any results obtained and/or papers or preprints. Please also provide the name of a referee. 

The application should be sent to helen.mcgregor@maths.ox.ac.uk.  The reference should be sent separately by the referee to helen.mcgregor@maths.ox.ac.uk.  

The closing date for applications is 18 March 2022

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.)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 summer school is financially supported by:

The Mathematical Sciences Research Institute, Berkeley, California
The Clay Mathematical Institute
The Heilbronn Institute
The Mathematical Institute, University of Oxford
The Foundation Compositio
The Queen's College, Oxford