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Título: Statistical aspects in topological phase transitions

Resumo: Mathematically, the topology (number of holes) of any object in our daily life (chairs, tables, cups...) is given by the integration of the Gaussian curvature of its surface. In a similar manner, the integration of a certain curvature calculated from the quantum mechanical wave function of a solid determines the topology of the solid. I will demonstrate that at the topological phase transitions (when number of holes changes), the curvature generally diverges at certain momentum. Through this divergence, a number of aspects we are familiar with in statistical mechanics also manifest in topological phase transitions, including correlation function, critical exponents, scaling laws, universality class, and renormalization group, pointing to a unified picture for the topological phase transitions in any known solids.