Brown University, Providence, RI/USA
The prototypical emergent phenomena are the bulk 'phases' of large collections of molecules, such as the fluid and solid phases. The solid phase is understood to emerge from an energy minimizing ideal crystal by the addition of random defects as energy increases from its minimum, the crucial/amazing fact being that the phase preserves something from the ideal crystal that unambiguously distinguishes it from the fluid phase. In this workshop we will focus on two significant variants of this classic picture: quasicrystals, and complex networks/random graphs. The analogue of energy minimizing crystals for quasicrystals are aperiodic tilings, such as the kite and dart tilings of Penrose, and for complex networks the analogue of energy minimizing crystals are (multi-partite) extremal graphs, graphs which minimize the number of subgraphs of some type. The workshop will focus on extremal graphs and aperiodic tilings and on the 'solid' phases they are believed to yield when random defects are introduced. It is hoped that progress can be made by pooling the expertise of researchers interested in the various aspects of these subjects.