Quantum graphs—networks composed of vertices connected by edges on which quantum wave dynamics are defined—have emerged as a versatile model for exploring the interplay between geometry, topology, and ...

This lecture course is devoted to the study of random geometrical objects and structures. Among the most prominent models are random polytopes, random tessellations, particle processes and random ...

When the mathematicians Jeff Kahn and Gil Kalai first posed their “expectation threshold” conjecture in 2006, they didn’t believe it themselves. Their claim — a broad assertion about mathematical ...

We explore the asymptotic properties of strategic models of network formation in very large populations. Specifically, we focus on (undirected) exponential random graph models. We want to recover a ...

As mathematical abstractions go, graphs are among the simplest. Scatter a bunch of points in a plane. Connect some of them with lines. That’s all a graph is. And yet they are incredibly powerful. They ...