Several spinor models were proposed several decades ago in the efforts to explain the nature of strong interactions, see . These are
• Nambu--Jona-Lasinio--Vaks--Larkin models (1961), related to SU(n)
• Gross–Neveu models (1974), related to SP(2n).
• Zakharov– Mikhailov spinor models (1980) related to SO(n).
Following  we will analyze their reductions to two-dimensional space-time and will explain how they could be integrated explicitly. We will start by constructing their Lax representations. Then the spectral properties of their Lax operators will be outlined. Using the dressing Zakharov-Shabat method we will construct their soliton solutions. Other integrable deformations of these models will be formulated following .
The lectures will take place each Tuesday, 18:30 EET. For participants residing in Sofia it is good to attend the lectures in person at Sofia Tech Park, Laboratory complex. The online participation is at https://meet.iaps.institute/integrable-spinor-models.
 V. E. Zakharov and A. V. Mikhailov. On the Integrability of Classical Spinor Models in Two- Dimensional Space-Time. Commun. Math. Phys. 74, 2140 (1980).
 V. S. Gerdjikov. Z2-reductions of spinor models in two dimensions. arXiv:1210.3722v1 [nlin.SI]
 В. Е. Захаров, А. Б. Шабат, “Интегрирование нелинейных уравнений математической физики методом обратной задачи рассеяния. II”, Функц. анализ и его прил., 13:3 (1979), 13–22; Funct. Anal. Appl., 13:3 (1979), 166–174
Lecture 1. July 26th, 2022. Lax representation and Nambu-Jona-Lasinio-Vaks-Larkin, Gross-Neveu and Zakharov-Mikhailov models, slides, video (damaged recording; change the video player if interruptions occur)
Институт за съвременни физически изследвания и Квантерал