Marcio Jose Martins

• Abstract

  The main purpose of this research is to establish a new approach to uncover relevant exactly two-dimensional solved models by exploring a direct relationship with the theory of Algebraic Geometry. We intend to develop a systematic manner to solve a high number of polynomial equations derived from the Yang-Baxter equation by combining analytical techniques with computational algorithms u...

  Integrable sistems and algebraic geometry, AP.R

• Abstract

  This research project aims to investigate the mathematical and the physical properties of integrable systems that are based on super group symmetries. In particular we intend to study the physical properties of spin chains built up from mixing representations of the U_q[SL(12)] quantum superalgebra. We shall use the respective Bethe ansatz solution to extract the ground state behavior, ...

  Integrable lattice models based on super groups, AV.EXT

• Abstract

  This research proposal intends to investigate several aspects related to the Physical Mathematics of two-dimensional integrable models. We will consider the exact solution of vertex models of Statistical Mechanics based on the Uq[SU(2)] quantum group at roots of unity, on the classical exceptional Lie algebras and superalgebras, on the non-compact SL(2,R) algebra as well as extensions ...

  Physical mathematics of integrable systems, AP.TEM

(Only some records are available in English at this moment)

• Abstract

  The aim of this project is to unveil the algebraic invariants governing integrable classical vertex models of statistical mechanics whose number of states per edge bigger or equal to three. This problem is of central interest in the field of exactly solved models since it has direct connection with the unsolved issue of classification of solutions of the Yang-Baxter equation. We also in...

  Algebraic curves of integrable models: theory and applications, BP.DR

• Abstract

  We will make a systematic study of the applications of the group theory in the classic physics and quantum physics, with base in the book "Group Theory in Physics" of Wu-Ki Tung.

  Group theory in physics, BP.IC

• Abstract

  The reaserch project is concerned about the study of physical properties of integrable systems invariant by superalgebras. We plan to identify the universality classes of supersymmetric systems as well as the understanding of the phase transition of related physical systems.

  Criticality of integrable systems invariant by super algebras, BP.PD

(Only some records are available in English at this moment)