L6

The West Antarctic Ice Sheet is a marine ice sheet that rests on a bed below sea level. The stability of a marine ice sheet and its contribution to future sea level rise are controlled by the dynamics of the grounding line, where the grounded ice sheet transitions into a floating ice shelf. Recent observations suggest that Antarctic ice shelves experience widespread thinning due to contact with warming ocean waters, but quantifying the effect of these changes on marine ice sheet stability and extent remains a major challenge for both observational and modelling studies. In this talk, I show that grounding line stability of laterally confined marine ice sheets and outlet glaciers is governed by ice shelf dynamics, in particular calving front and melting conditions. I will discuss the implications of this dependence for projections of the future evolution of the West Antarctic Ice Sheet.

We analyze the asymptotic relative size of the largest independent set of a random d-regular graph on n → ∞ vertices. This problem is very different depending on d because of a surprising phase transition. This is somewhat similar to finding the density of ``water'' above and below its freezing point. These phase transitions are related to algorithmic thresholds, mixing properties, counting, graph reconstruction, graph limits and other questions. We are still far from a complete understanding of all these questions. Our tools are partially coming from statistical physics.