Abstract: In this first talk of the lecture series, I will go over the (non-)construction of the focusing Gibbs measures on the one-dimensional torus. This study was initiated by Lebowitz, Rose, and Speer (1988) and continued by Bourgain (1994) and Carlen-Fr\"ohlich-Lebowitz (2016). In the mass-critical case, a critical mass threshold is given by the mass of the ground state on the real line. I first present an argument, showing the optimality of this critical mass threshold. Then, I will show that the Gibbs measure is indeed normalizable at the optimal mass threshold, which answers an open question posed by Lebowitz, Rose, and Speer (1988). This first talk is based on a joint work with Philippe Sosoe (Cornell) and Leonardo Tolomeo (Bonn).
Zoom Information:
https://zoom.us/j/86389621617?pwd=WFlOeWdsaDZlYW9RSUlpa3ZBYTBBZz09
Conference Number：863 8962 1617
Password：079095
