We consider a bond percolation on the hypercube in the supercritical regime. We derive vertex-expansion properties of the giant component. As a consequence we obtain upper bounds on the diameter of the giant component and the mixing time of the lazy random walk on the giant component. This talk is based on joint work with Joshua Erde and Michael Krivelevich.

What is curiosity? Is it an emotion? A behavior? A cognitive process? Curiosity seems to be an abstract concept—like love, perhaps, or justice—far from the realm of those bits of nature that mathematics can possibly address. However, contrary to intuition, it turns out that the leading theories of curiosity are surprisingly amenable to formalization in the mathematics of network science. In this talk, I will unpack some of those theories, and show how they can be formalized in the mathematics of networks. Then, I will describe relevant data from human behavior and linguistic corpora, and ask which theories that data supports. Throughout, I will make a case for the position that individual and collective curiosity are both network building processes, providing a connective counterpoint to the common acquisitional account of curiosity in humans.

We will discuss the pros and cons of targets vs quotas in increasing diversity in Mathematics.

We will be joined for lunch by the undergraduate society for women and non-binary students in Maths. Sign up here: https://forms.gle/q3uywCN3Dn78Kvkq6. Note: this event is only open to women and non-binary students.

We will be joined by Professor Kobi Kremnizer, who is a trained mental health first-aider, to discuss ways to protect your mental health this season.