Speaker: Edinah K. Gnang (JHU)
Title: On the Kotzig-Ringel-Rosa conjecture
In this talk we describe and motivate the K.R.R. conjecture and describe a functional graph theoretic approach enabling us to tackle the K.R.R. conjecture via a composition lemma.
Speaker: Daniel Kalmanovich (HUJI)
Title: Cubical polytopes
Convex polytopes have fascinated people for ages, and questions about their combinatorics and their geometry have been widely studied.
Speaker: Xinyu Wu (CMU)
Title: Explicit near-fully X-Ramanujan graphs
In this talk I will introduce constructions of finite graphs which resemble some given infinite graph both in terms of their local neighborhoods, and also their spectrum.
Abstract: I will discuss a quantitative equidistribution result for the random walk on a torus arising from the action of the group of affine transformations. This is a joint work with Weikun He and Elon Lindenstrauss.
Abstract: I will report on recent results on sharp error rates in the local limit theorem for the Sinai billiard map (one and two dimensional) with infinite horizon. This is joint work with F. Pene. This result allows to also obtain higher order terms and thus, sharp mixing rates in the speed of mixing of dynamically Hölder observables for the planar and tubular infinite horizon Lorentz gases in the map (discrete time) case.
Abstract: We construct a set which is dense in the Bohr topology on the group of integers and which is not a set of measurable recurrence, answering a question asked by Bergelson, Hegyvári, Ruzsa, and the author, in various combinations. This talk will provide a broad overview and explain details of the construction. We will see similarities to many other examples in additive combinatorics and ergodic theory, such as Igor Kriz's construction showing topological recurrence does not imply measurable recurrence, and Ruzsa's niveau sets.
Abstract: Quantitative equidistribution for linear random walks on the torus was first obtained by Bourgain, Furman, Lindenstrauss and Mozes. In this talk I will present a recent progress where the proximality assumption in their result is relaxed. I will also discuss an application to expansion in groups. This is based on a joint work with Nicolas de Saxcé.
A matroid is a combinatorial object based on an abstraction of linear independence in vector spaces and forests in graphs. It is a classical question to determine whether a given matroid is representable as a vector configuration over a field. Such a matroid is called linear.