Public defence in the field of Mathematics and Statistics, M.Sc. David Adame Carrillo

Title of the thesis: Lattice models and conformal field theory

Doctoral student: David Adame Carrillo
Opponent: Professor Alessandro Giuliani, Universita degli Studi Roma Tre, Italy
Custos: Professor Kalle Kytölä, Aalto University School of Science, Department of Mathematics and Systems Analysis

Statistical mechanics is the classical branch of Physics and Mathematics that studies ensembles of a large number of microscopic entities. The purpose of statistical mechanics is the inference of macroscopic properties of a model from its microscopic degrees of freedom by conceiving the system probabilistically.

Since the 1980s, it has been known to physicists that the macroscopic properties of statistical models at a critical point can be described by quantum field theories with conformal symmetries, nowadays known as conformal field theories.

The object of this thesis is the mathematical description of the connection between statistical mechanics and conformal field theories in two dimensions. The key insight underpinning the results of this thesis is that, by carving the appropriate discrete complex analysis tools, one can conceive a critical lattice model as a discrete version of a conformal field theory.

Keywords: mathematical physics, statistical mechanics, conformal field theory

Thesis available for public display 10 days prior to the defence at: https://aaltodoc.aalto.fi/doc_public/eonly/riiputus/ 

Doctoral theses at the School of Science: https://aaltodoc.aalto.fi/handle/123456789/52