In this talk, I will first introduce some basic concepts in the focusing Nonlinear Schrodinger (fNLS) soliton gas theory within a framework developed by El and Tovbis in 2020. Then we will discuss some new results on the spectral theory for fNLS soliton gases. Specifically, I will show how to compute the averaged conserved quantatites for the fNLS gases. Lastly, we will also briefly touch another method within the soliton gas theory—the primitive potential method developed by Zakharov. Some related recent work will be metioned as well.

11.30.pdf