Recently, the techniques from calculus of variations have been extensively used to tackle isoperimetric-type inequalities in Euclidean space. In particular, progress was made on a number of newly emerged questions in geometric probability theory. Understanding these questions will shed light on how symmetry and structure influence various families of isoperimetric-type inequalities.
This circle of ideas has been used in Riemannian geometry for decades in the fields of geometry and probability such as hypercontractive inequalities and their interactions with curvature. Recently, these ideas have found new applications.
Conversely, questions motivated purely by differential geometry, such as mean curvature flow, are ameliorated by studying isoperimetric-type problems with respect to the Gaussian measure. This connection was evidenced by Huisken’s monotonicity formula and studies of singularities in mean curvature flow. The above isoperimetric-type questions have tight connections in theoretical computer science and social choice theory — appearing e.g. in the computational hardness for MAX-CUT and in the Majority is Stablest Theorem. The interplay of geometry and probability appears also in recent breakthrough developments on the KLS-conjecture, itself an isoperimetric-type problem for arbitrary Euclidean convex sets.
In summary, a few different communities of researchers have an interest in similar problems, perhaps without realizing the common intersection of interests. This conference proposes to bring together these disparate fields to discuss these related questions, and to share insights and problems.
This workshop will include a poster session; a request for posters will be sent to registered participants in advance of the workshop.
(University of Southern California (USC))
Alina Stancu (Concordia University)
Elisabeth Werner (Case Western Reserve University)