Titles and Abstracts

In condensed matter physics, it is known that some topological properties of quantum systems are related to the topology of the Hamiltonian operator as a self-adjoint operator with a spectral gap. In particular, recent researches reveal that symmetries of quantum systems, such as time-reversal or particle-hole symmetries, provide a rich physical and mathematical theory. In this talk, we introduce relations between classification of non translation-invariant topological phases and the operator algebras in coarse topology. Classification of topological phases, a primary invariant called ‘index’ and the bulk-edge correspondence for these invariants are described in terms of twisted equivariant K-theory of coarse C*-algebras. It contains a new result on the bulk-edge correspondence for quasicrystals. Tianshu Liu Title. Towards the N=2 minimal models Abstract. Conformal field theory is an essential tool of modern mathematical physics with applications to string theory and to the critical behaviour of statistical lattice models. The symmetries of a conformal field theory include all angle-preserving transformations. In two dimensions, these transformations generate the Virasoro algebra, a powerful symmetry that allows one to calculate observable quantities analytically. The symmetries of a conformal field theory may be strictly larger than the Virasoro algebra. One possibility which is crucial importance to string theory applications is that of supersymmetry, where the Virasoro algebra is extended by a given number of fermionic fields. The talk aims to explain certain aspects of N=2 superconformal field theory using the arsenal of mathematical technology and physical insight that has been built up over the last five years. Conformal field theory is an essential tool of modern mathematical physics with applications to string theory and to the critical behaviour of statistical lattice models. The symmetries of a conformal field theory include all angle-preserving transformations. In two dimensions, these transformations generate the Virasoro algebra, a powerful symmetry that allows one to calculate observable quantities analytically. The symmetries of a conformal field theory may be strictly larger than the Virasoro algebra. One possibility which is crucial importance to string theory applications is that of supersymmetry, where the Virasoro algebra is extended by a given number of fermionic fields. The talk aims to explain certain aspects of N=2 superconformal field theory using the arsenal of mathematical technology and physical insight that has been built up over the last five years. Giuseppe de Nittis Title. Topological nature of the Fu-Kane-Mele invariants Abstract. Condensed matter electronic systems endowed with an odd time-reversal symmetry (TRS) (a.k.a. class AII topological insulators) show topologically protected phases which are described by an invariant known as Fu-Kane-Mele index. The construction of this invariant, in its original form, is specific for electrons in a periodic background and is not immediately generalizable to other interesting physical models where different forms of TRS also play a role. By exploiting the fact that system with an odd TRS (in absence of disorder) can be classified by Quaternionic vector bundles, we introduce a Quaternionic topological invariant, called FKMM-invariant, which generalizes and explains the topological nature of the Fu-Kane-Mele index. We show that the FKMM-invariant is a universal characteristic class which can be defined for Quaternionic vector bundles in full generality, independently of the particular nature of the base space. Moreover, it suffices to discriminate among different topological phases of system with an odd TRS in low dimension. As a particular application we describe the complete classification over a big class of low dimensional involutive spheres and tori. We also compare our classification with recent results concerning the description Condensed matter electronic systems endowed with an odd time-reversal symmetry (TRS) (a.k.a. class AII topological insulators) show topologically protected phases which are described by an invariant known as Fu-Kane-Mele index. The construction of this invariant, in its original form, is specific for electrons in a periodic background and is not immediately generalizable to other interesting physical models where different forms of TRS also play a role. By exploiting the fact that system with an odd TRS (in absence of disorder) can be classified by Quaternionic vector bundles, we introduce a Quaternionic topological invariant, called FKMM-invariant, which generalizes and explains the topological nature of the Fu-Kane-Mele index. We show that the FKMM-invariant is a universal characteristic class which can be defined for Quaternionic vector bundles in full generality, independently of the particular nature of the base space. Moreover, it suffices to discriminate among different topological phases of system with an odd TRS in low dimension. As a particular application we describe the complete classification over a big class of low dimensional involutive spheres and tori. We also compare our classification with recent results concerning the description