（I）On Shalev's conjecture for linear and unitary groups
讲座题目：On Shalev's conjecture for linear and unitary groups
主 讲 人：Galt Alexey 研究员
We consider images of finite simple linear and unitary groups under power words. In particular, we improve the bound in Shalev's conjecture in this case.
（II）On recognition of symmetric and alternating groups by sets of integers
讲座题目：On recognition of symmetric and alternating groups by sets of integers
主 讲 人：Alexey Staroletov 教授
This set defines so-called prime graph Γ(G). Denote by S_n (A_n ) the symmetric (alternating) group of degree n. In this talk we discuss the following recognition problems: what can we say about ? finite group G such that the spectrum of G coincides with that of S n (A_n ) for some n ≥ 5? Similar questions arise for G such that Γ(G) = Γ(S_n ) (Γ(A_n )). Also we mention some results about other recognition sets.