We show a (3/2-\epsilon)-approximation algorithm for the graphical traveling salesman problem where the goal is to find a shortest tour in an unweighted graph G. This is a special case of the metric traveling salesman problem when the underlying metric is defined by shortest path distances in G. The result improves on the 3/2-approximation algorithm due to Christofides for the case of graphical TSP.
Artist Paul Hodgson was a Director's Visitor at the Institute in 2010. In a Friends Forum, he discussed the "difficulties in making a judgement and dubtfulness in choosing one thing over another," that underlie his current practice and emerge "both in the way that I fabricate the work, and the images that I choose to present."
Let G be a connected reductive group over Q such that G(R) has discrete series representations. I will report on some statistical results on the Satake parameters (w.r.t. Sato-Tate distributions) and low-lying zeros of L-functions for families of automorphic representations of G(A). This is a joint work with Nicolas Templier.
I will survey the development of modern infinite cardinal arithmetic, focusing mainly on S. Shelah's algebraic pcf theory, which was developed in the 1990s to provide upper bounds in infinite cardinal arithmetic and turned out to have applications in other fields.
This modern phase of the theory is marked by absolute theorems and rigid asymptotic structure, in contrast to the era following P. Cohen's discovery of forcing in 1963, during which infinite cardinal arithmetic was almost entirely composed of independence results.