for this workshop
Symmetry and convexity in geometric inequalities
American Institute of Mathematics, San Jose, California
Karoly Boroczky, Galyna Livshyts, and Elisabeth Werner
This workshop, sponsored by AIM and the NSF, will be devoted to the study of the effects which symmetry has on the Brunn-Minkowski inequality, a corner stone of convex geometric analysis. It is well understood that many inequalities in analysis self-improve under additional symmetry assumptions, however, it is not clear how to effectively adapt some of the analytic tools to the study of the Brunn- Minkowski type inequalities to obtain meaningful geometric consequences. In recent years, a number of relevant conjectures have appeared, such as the Log-Brunn-Minkowski conjecture, the B-conjecture, the Gardner-Zvavitch dimensional Brunn-Minkowski conjecture, and others. These conjectured inequalities are intimately connected to certain Monge-Ampere type differential equations that are recent versions of the Minkowski problem. The aim of this workshop is to bring together experts working in convex and differential geometry, functional analysis, harmonic analysis and PDEs, geometric flows, complex analysis, in order to work together towards better understanding the role of symmetry in geometric inequalities.
The main topics for the workshop are
- Symmetry in Brunn-Minkowski type inequalities
- Uniqueness in certain Monge-Ampere type equations, arising in geometric flows
This event will be run as an AIM-style workshop. Participants will be invited to suggest open problems and questions before the workshop begins, and these will be posted on the workshop website. These include specific problems on which there is hope of making some progress during the workshop, as well as more ambitious problems which may influence the future activity of the field. Lectures at the workshop will be focused on familiarizing the participants with the background material leading up to specific problems, and the schedule will include discussion and parallel working sessions.
The deadline to apply for support to participate in this workshop has passed.
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