BEGIN:VCALENDAR VERSION:2.0 PRODID:-//Talks.cam//talks.cam.ac.uk// X-WR-CALNAME:Talks.cam BEGIN:VEVENT SUMMARY:Global Minimizers of a Large Class of Anisotropic Attractive-Repul sive Interaction Energies in 2D - Ruiwen Shu (University of Oxford) DTSTART:20220419T123000Z DTEND:20220419T131500Z UID:TALK171557@talks.cam.ac.uk DESCRIPTION:I will discuss my joint work with José\; Carrillo on a l arge family of Riesz-type singular interaction potentials with anisotropy in two dimensions. Their associated global energy minimizers are given by explicit formulas whose supports are determined by ellipses under certain assumptions. More precisely\, by parameterizing the strength of the anisot ropic part we characterize the sharp range in which these explicit ellipse -supported configurations are the global minimizers based on linear convex ity arguments. Moreover\, for certain anisotropic parts\, we prove that fo r large values of the parameter the global minimizer is only given by vert ically concentrated measures corresponding to one dimensional minimizers. We also show that these ellipse-supported configurations generically do no t collapse to a vertically concentrated measure at the critical value for convexity\, leading to an interesting gap of the parameters in between. In this intermediate range\, we conclude by infinitesimal concavity that any superlevel set of any local minimizer in a suitable sense does not have i nterior points. Furthermore\, for certain anisotropic parts\, their suppor t cannot contain any vertical segment for a restricted range of parameters \, and moreover the global minimizers are expected to exhibit a zigzag beh avior. All these results hold for the limiting case of the logarithmic rep ulsive potential\, extending and generalizing previous results in the lite rature. \; LOCATION:Seminar Room 2\, Newton Institute END:VEVENT END:VCALENDAR