Given a (finite) family of structures, is it possible to choose an element from each structure to form a new structure of the same kind? This new structure is poetically called rainbow for we can think of each given structure is in a different color. Some longstanding combinatorial problems, such as transversals in a Latin square and the Caccetta--Haggkvist conjecture, are rainbow in nature. In this talk, we will discuss a line of attacks to such problems via algebraic topology.

海报