| Abstract | The kissing number K(d) is the maximum number of non-overlapping unit balls in the Euclidean space R^d that can touch a given unit ball. Determining or estimating the number K(d) has a long history, with the value of K(3) being the subject of a famous discussion between Newton and Gregory in 1694. We will discuss recent work on this topic and sketch a proof of an improvement we obtained on the lower bound of K(d). Our proof is based on the hard-core sphere model of an appropriate fugacity. Similar improvements in lower bounds are also obtained for general spherical codes, as well as for the expected density of random sphere packings in R^d.
This is joint work with Irene Gil Fernández, Jaehoon Kim and Oleg Pikhurko. |
