Dear Colleagues, We would like to invite you to the following SPASS seminar, jointly organized by UniPi, SNS, UniFi and UniSi: The free energy of (a box version of) the interacting Bose gas Prof. Wolfgang König, WIAS and TU Berlin (abstract below) The seminar will take place on 11 October at 11:30 in Aula Tricerri, Dipartimento di Matematica e Informatica “Ulisse Dini”, Firenze, and streamed online here <https://www.google.com/url?q=https://meet.google.com/gji-phwo-vbg&source=gmail-imap&ust=1665674787000000&usg=AOvVaw0huPd655tzoo6F6teM2bXi>. The organizers, A. Agazzi, G. Bet, A. Caraceni, F. Grotto, G. Zanco https://sites.google.com/unipi.it/spass <https://www.google.com/url?q=https://sites.google.com/unipi.it/spass&source=gmail-imap&ust=1665674787000000&usg=AOvVaw2APclf0Ax-wsIciF7N07SE> -------------------------------------------- Abstract: The interacting quantum Bose gas is a random ensemble of many Brownian bridges (cycles) of various lengths with interactions between any pair of legs of the cycles. It is one of the standard mathematical models in which a proof for the famous Bose–Einstein condensation phase transition is sought for. We introduce a simplified version of the model in $Z^d$ instead of $R^d$ and with an organisation of the particles in deterministic boxes in- stead of Brownian cycles as the marks of a reference Poisson point process. We derive an explicit and interpretable variational formula in the thermody- namic limit for the canonical ensemble for any value of the particle density. In this formula, each of the microscopic particles and the macroscopic part of the configuration are seen explicitly (if they exist); the latter receives the interpretation of the condensate. The methods comprises a two step large- deviation approach for marked Poisson point processes and an explicit dis- tinction into microscopic and macroscopic marks. We discuss the conden- sate phase transition in terms of existence of minimizer. (based on joint works with Adams/Collevecchio (2011) and Collin/Jahnel (preprint 2022).) ---------------------------------------------------------------------- Gianmarco Bet (he/him) Senior researcher https://gianmarco.bet Phone: (+39) 055 2751491 Department of Mathematics and Informatics "U. Dini" University of Florence Viale Morgagni, 65 50134 Firenze, Italy Office 64 ---------------------------------------------------------------------- ---------------------------------------------------------------------- Gianmarco Bet (he/him) Senior researcher https://gianmarco.bet Phone: (+39) 055 2751491 Department of Mathematics and Informatics "U. Dini" University of Florence Viale Morgagni, 65 50134 Firenze, Italy Office 64 ----------------------------------------------------------------------