Abstract: Let T be a subset of R^d, such as a ball, a cube or a cylinder, and consider all possibilities for packing translates of T, perhaps with its rotations, in some bounded domain in R^d. What does a typical packing of this sort look like? One mathematical formalization of this question is to fix the density of the packing and sample uniformly among all possible packings with this density. Discrete versions of the question may be formulated on lattice graphs.

The question arises naturally in the sciences, where T may be thought of as a molecule and its packing is related to the spatial arrangement of molecules of a material under given conditions. In some cases, the material forms a liquid crystal - states of matter which are, in a sense, between liquids and crystals.

I will give a gentle review of ideas from this topic (with many pictures!), mentioning some of the predictions and the mathematical progress. I will then elaborate on a recent result, joint with Daniel Hadas, on the structure of high-density packings of 2x2 squares with centers on the square lattice.

Bio Paragraph: Ron Peled is a professor at Tel Aviv University. He received his Ph.D. from UC Berkeley in 2008 under the guidance of Steven N. Evans and Yuval Peres, and was a Courant Instructor at the Courant Institute of New York University prior to taking up his current position.

He is the author of more than 60 papers on topics in Probability Theory, Statistical Physics, Discrete Mathematics and Analysis. His research has been recognized by the European Research Council's Starting and Consolidator grants while his teaching has been recognized by the Rector's Distinguished Teacher Award of Tel Aviv University. He has supervised many graduate students and post-doctoral scholars. 

This year he is a visiting fellow at Princeton University and a visitor at the Institute for Advanced Study.

He is happy to give a mini-course and colloquium at BICMR, together with his students Michal Bassan and Daniel Hadas, and hopes to make the talks accessible and fun to all :)