Symmetry and convexity in geometric inequalities
May 20 to May 24, 2019
at the
American Institute of Mathematics,
San Jose, California
organized by
Karoly Boroczky,
Galyna Livshyts,
and Elisabeth Werner
Original Announcement
This workshop 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
Material from the workshop
A list of participants.
The workshop schedule.
A report on the workshop activities.
A list of open problems.
