MIT Combinatorics Seminar Combinatorial Aspects of Covers of Groups by Cosets or Subgroups Zhi-Wei Sun (Nanjing University) Friday, Arpil 21, 2006   4:30 PM;   Building 2 Room 105;  ABSTRACT If a group $G$ is a union of finitely many left cosets $a_1G_1,\ldots,a_kG_k$ of subgroups $G_1,\ldots,G_k$, then the system $\{a_iG_i\}_{i=1}^k$ is said to be a cover of $G$. In this talk we give a survey of results on extremal problems concerning covers of groups, and introduce progress on the famous Herzog-Sch\"onheim conjecture which states that if $\{a_iG_i\}_{i=1}^k\ (1