Margulis inequalities - first introduced by Eskin-Margulis-Mozes during their work regarding quantitative Oppenheim conjecture, became an indispensable tool in dynamics, in particular regarding non-divergence questions and isolation theorems.

I plan to introduce the inequalities and their proofs, especially the so-called "key lemma" of Margulis, in three main examples - translates of K-orbits, stationary measures generated by random walks of "large subgroups" and translates of horospherical segments.

If time permits, I will describe some more advanced examples such as the Margulis inequality of Eskin-Mirzakhani-Mohammadi in the moduli spaces setting and the isolation theorem of Eskin-Lindenstrauss. Speaker(s): Asaf Katz (U Michigan)