# Lattice and sheaf theory

Course Code : | 1001WETTRA |

Study domain: | Mathematics |

Academic year: | 2017-2018 |

Semester: | 1st semester |

Sequentiality: | Min 8/20 for Groups and rings. |

Contact hours: | 60 |

Credits: | 6 |

Study load (hours): | 168 |

Contract restrictions: | No contract restriction |

Language of instruction: | Dutch |

Exam period: | exam in the 1st semester |

Lecturer(s) | Wendy Lowen |

### 1. Prerequisites *

specific prerequisites for this course

1BA and 2BA. More precisely the course makes use of the following courses: Linear algebra, Groups and commutative rings, Calculus and Set theory and Analytical topology and, to a lesser extent, Logic, Differential geometry, Fields and classical Galois theory, Banach and Hilbert spaces.

### 2. Learning outcomes *

### 3. Course contents *

PART1:

- partially ordered sets

- lattices, considered as algebraic objects

- distributive lattices as sublattices of power sets

- Boolean algebras

- frames as point free topological spaces

- modular lattices, length and Goldie dimension

- continuous and algebraïc dcpo's

PART2:

- sheaves on spaces in topology, differential geometry, algebraic geometry

- sheaves on frames in set theory

- sheafification

### 4 International dimension*

### 5. Teaching method and planned learning activities

Personal work

Project

Project

### 6. Assessment method and criteria

Written assignment

Presentation

### 7. Study material *

#### 7.1 Required reading

Course notes available.

**7.2 Optional reading**

The following study material can be studied voluntarily :Introduction to Lattices and Order, B.A. Daveay and H. A. Priestley, Cambridge

### 8. Contact information *

Wendy Lowen

wendy.lowen@ua.ac.be

Joris Mestdagh

mestdaghjoris@hotmail.com