EMENTA:

• Conjuntos e relações;
• Demonstrações por indução e contradição, exemplos;
• Números naturais. Cardinalidades finitas e infinitas, enumerabilidade;
• Números racionais e reais. Limites e convergência de sequências e séries numéricas;
• Topologia da reta: abertos, fechados, compactos, conexos, densos;
• Conjunto ternário de Cantor;
•  Funções contínuas: Teorema de Bolzano-Weierstrass, Teorema do Valor Intermediário, continuidade uniforme.

MAT1605/MAT2614
Turma 3ZB

• Introdução à Análise
• Tópicos de Análise I

EMENTA:

• Idea and examples of topological invariants of quantum nature.
• Topological and conformal quantum field theory.
• Alexander, Jones and HOMFLY-PT polynomials of knots and links.
• Vassiliev knot invariants and Kontsevich integral.
• Chern–Simons and Wess–Zumino–Novikov–Witten theories.
• Witten–Reshetikhin–Turaev invariants.
• Khovanov homology, categorification.
• Loops on surface: Goldman bracket and Turaev cobracket.
• Mapping class group, monodromy of Knizhnik–Zamolodchikov connection.

MAT2725

• Tópicos de Topologia
  Introdução à Topologia Quântica

EMENTA:

• Basics in gauge theory: bundles, connection and curvature.
• Anti-self-duality equations and instantons.
• Moment maps and symplectic reduction.
• Hyper-Kähler geometry and reduction.
• The ADHM equations.
• The moduli space of instantons and Donaldson’s theorems.
• The moduli space of Higgs bundles.
• Non-abelian Hodge correspondence.
• Hitchin integrable system.

MAT2425

• Tópicos de Física Matemática I
  

  Gauge Theory and moduli spaces: an introduction

EMENTA:

1. 1D spectral problem for the Schrödinger equation and WKB substitution
2. Representation near the turning points
3. Definition of the Maslov’s Canonical Operator in 1D case
4. 2D Cauchy problem for the surface linear wave propagation over non-uniform bottom
5. Pseudo-differential operators
6. Definition of the Maslov’s Canonical Operator in 2D case
7. Lagrangian manifold and elements of symplectic geometry
8. Asymptotic description of the 2D surface wave

MAT2615
Turma 3ZB

• Tópicos de Análise II
  

  Introduction into Semi-Classical Analysis

• Números e Funções Reais
• Geometria
• Matemática Discreta
• Aritmética
  

PMA 2021/MA 21

•  Resolução de Problemas