Dear Colleagues,

We are pleased to invite you to the following SPASS seminar https://sites.google.com/unipi.it/spass/seminars?authuser=0 (jointly organised by UniPi, SNS, UniFi and UniSi):

Speaker: Matteo Palmieri (Max Planck Institute, Leipzig, Germany)

Title: A geometrically linear approximation of min-max optimal matching

Date and time: Tuesday, September 22th at 14:00 CET

Place: Aula Bianchi Scienze, Palazzo della Carovana, Scuola Normale Superiore, Pisa

Abstract: In this talk, I will present a connection between min-max optimal matching and a certain isoperimetric problem with a random volume term with white-noise character. The former is the discrete combinatorial optimization task of finding the matching between two random point clouds, which is optimal in the sense that it minimizes the maximum distance between coupled points. The latter, in its additive form, can be interpreted as an isotropic version of the random-field Ising model at zero temperature. Both problems are critical in two dimensions and scale like the power 3/4 of the number of exponential scales involved. Relying on ideas from the regularity theory of minimal surfaces, in the second problem one may replace the perimeter by the Dirichlet energy. This defines a geometrically linearized, simpler, (1+1)-dimensional action, which enjoys an additional scaling invariance and allows us to identify the leading-order constant of the two optimal values. 

This is based on joint work with Xiaopeng Cheng, Felix Otto, Arthur Wachtel and Christian Wagner.

Link for online meeting: https://teams.microsoft.com/meet/390074246582827?p=Xp6u4MkqCTuuHNvlpl

On behalf of the organisers,

                                      Lorenzo Marino