Job applications involve a lot of work and can be overwhelming. Join us for a workshop and Q+A session focused on breaking down academic applications: we’ll talk about approaching reference letter writers, writing research statements, and discussing what makes a great CV and covering letter.

How do you make the most of graduate supervisions?  Whether you are a first year graduate wanting to learn about how to manage meetings with your supervisor, or a later year DPhil student, postdoc or faculty member willing to share their experiences and give advice, please come along to this informal discussion led by DPhil students for the first Fridays@4 session of the term.  You can also continue the conversation and learn more about graduate student life at Oxford at Happy Hour afterwards.

Complex networks have become the main paradigm for modeling the dynamics of interacting systems. However, networks are intrinsically limited to describing pairwise interactions, whereas real-world systems are often characterized by interactions involving groups of three or more units. In this talk, I will consider social systems as a natural testing ground for higher-order network approaches (hypergraphs and simplicial complexes). I will briefly introduce models of social contagion and norm evolution on hypergraphs to show how the inclusion of higher-order mechanisms can lead to the emergence of novel phenomena such as discontinuous transitions and critical mass effects. I will then present some recent results on the role that structural features play on the emergent dynamics, and introduce a measure of hyper-coreness to characterize the centrality of nodes and inform seeding strategies. Finally, I will delve into the microscopic dynamics of empirical higher-order structures. I will study the mechanisms governing their temporal dynamics both at the node and group level, characterizing how individuals navigate groups and how groups form and dismantle. I will conclude by proposing a dynamical hypergraph model that closely reproduces the empirical observations.
 

We give a strongly polynomial algorithm for minimum cost generalized flow, and as a consequence, for all linear programs with at most two nonzero entries per row, or at most two nonzero entries per column. While strongly polynomial algorithms for the primal and dual feasibility problems have been known for a long time, various combinatorial approaches used for those problems did not seem to carry over to the minimum-cost variant.

Our approach is to show that the ‘subspace layered least squares’ interior point method, an earlier joint work with Allamigeon, Dadush, Loho and Natura requires only a strongly polynomial number of iterations for minimum cost generalized flow. We achieve this by bounding the straight line complexity, introduced in the same paper. The talk will give an overview of the interior point method as well as the combinatorial straight-line complexity analysis for the particular setting. This is joint work with Daniel Dadush, Zhuan Khye Koh, Bento Natura, and Neil Olver.