Colloquium: Quasirandomness in Permutations and Tournaments

Jonathan Noel from the University of Warwick will be giving a Colloquium talk "Quasirandomness in Permutations and Tournaments" on Thursday, February 27th at 3:30pm in Engineering/Computer Science (ECS) 125.

Abstract: Informally, a combinatorial object is "quasirandom" if its global structure resembles that of a random object of the same type. In this talk, we will discuss two problems in which quasirandomness plays a key role. First, we provide several new characterizations of quasirandom permutations which have both practical and theoretical applications. We then turn our attention to an extremal problem on cycles in tournaments in which quasirandom structure appears in the tight examples. Our proofs involve a blend of combinatorial arguments and methods from semi-definite programming and spectral theory. This talk contains joint work with Timothy Chan, Andrzej Grzesik, Daniel Kral, Yanitsa Pehova, Maryam Sharifzadeh and Jan Volec.