Confirmed Invited Speakers:
Title: Layered H-partitions with applications
Abstract: We introduce a new structural tool called layered H-partitions, and prove that every planar graph has such a partition of bounded layered width in which H has bounded treewidth. These results generalise for graphs that exclude an apex graph as a minor. With the help of this tool we settle two long-standing problems, one on queue-number of planar graphs of Heath, Leighton and Rosenberg from 1992 and one on the non-repetitive chromatic number of planar graphs by Alon, Grytczuk, Haluszczak and Riordan from 2002.
Title: The Awesome Diversity of the Clique Graph Operator Dynamics
Title: Small maximal independent sets
Abstract: We study random constructions in incidence structures using a general theorem on independent sets in (hyper)graphs. Our main result applies to a wide variety of well-studied problems in finite geometry to give almost tight bounds on the sizes of various substructures. This is joint work with Michael Tait (Carnegie Mellon) and Jacques Verstraete (UCSD).
Title: Graphs as curves and special points on them
Abstract: Graphs share many properties with algebraic curves. Recently, a series of classical results valid for curves have been given analogs for graphs, such as the Riemann-Roch Theorem and the Riemann-Hurwitz Theorem. These results imply for example that every vertex has associated a certain finite sequence of positive integers called gap sequence, in analogy with the concept of Weierstrass gaps of an algebraic curve. The analysis of these sequences of gaps involves techniques such as chip-firing, cohomology, graph covers and representation theory.