Upper bounds on the Shannon capacity

The problem of error-free information transmission in presence of noise naturally leads to a graph parameter, called Shannon capacity. Despite sixty years of research, very little is known about this parameter. The reason is that only two upper bounds for Shannon capacity are known. In this talk, we review these bounds, and bring to light a new upper bound by Blasiak. We show that it is sometimes stronger than both of the existing bounds and that it is multiplicative. Joint workwith Chris Cox.