Ramsey graphs and anti-concentration

Anti-concentration inequalities provide limits on the extent to which random variables can be concentrated: for example, they commonly give uniform upper bounds on the probability that a random variable takes any particular value. In this talk I'll discuss some of the many connections between anti-concentration and combinatorics, initially focusing on applications to Ramsey graphs but also touching on a few other topics such as the polynomial Littlewood-Offord problem and permanents of random matrices.