Many models of statistical physics exhibit phase transitions: a drastic change in behaviour as a parameter is varied across a critical point. Their critical behaviour is remarkably rich, marked by strong correlations, scale and rotational invariance, and independence on microscopic details. In the '80s, the physicists Belavin, Polyakov, and Zamalodchikov conjectured that many planar models exhibit a more dramatic type of emergent symmetry: conformal invariance. Mathematicians have made remarkable progress in establishing conformal invariance of certain planar models in the past two decades, but we are very far from the full picture. I will give you a glimpse at some of the highlights.
This talk is aimed at SN Bhatt students. PhD students are welcome to attend.