Harald Bohr Lecture: Stanislav Smirnov

Title: Complex analysis and 2D statistical physics

Speaker: Stanislav Smirnov (Professor at Université de Genève and Skolkovo Institute
of Science and Technology)

Abstract: Over the last decades, there was much progress in understanding 2D lattice models of critical phenomena. It started with several theories, developed by physicists. Most notably, Conformal Field Theory led to spectacular predictions for 2D lattice models: e.g., critical percolation cluster almost surely has Hausdorff dimension 91/48, while the number of self-avoiding length N walks on the hexagonal lattice grows like $(\sqrt{2+√2})^N N^{11/32}$. While the algebraic framework of CFT is rather solid, rigorous arguments relating it to lattice models were lacking.

More recently, mathematical approaches were developed, allowing not only for rigorous proofs of many such results, but also for new physical intuition. We will discuss some of the applications of complex analysis to the study of 2D lattice models.

Smirnov has been awarded the Fields Medal in 2010 for the proof of conformal invariance of percolation and the planar Ising model in statistical physics. His research involves complex analysis, dynamical systems and probability theory.