Combinatorial covering properties of topological groups.

‎‎‎The study of combinatorial properties of uniform covers of topological groups was initiated about 30 years ago by C. Hernandez and M. Tkachenko, who studied o-bounded topological groups defined by Okunev. It was soon noticed by L. Babinkostova, M. Scheepers, and others that this is a uniform analogue of the classical Menger covering property, which is why these groups are now called M-bounded.

‎‎‎The minicourse will be devoted to the preservation of M-bounded groups under products and squares, characterizations of free M-bounded groups, and games related to M-boundedness. I will also address the uniform counterparts of other combinatorial covering properties in the realm of topological groups.