Sumários

Linear Algebra. Exponential of a Matrix.

2 Março 2022, 11:00 • Orlando Manuel Bartolomeu Neto

Normal form of a Symmestric matrix and generalizations.
Exponential of a Matrix.

Seminar

25 Fevereiro 2022, 11:00 • Orlando Manuel Bartolomeu Neto

Initial topology. Final topology.
Free objects: vector spaces, rings of polynomials, free modules, free abelian groups, free groups.
Finitely presented groups.

Representations of Finitely presented groups.

Fundamental Group of a topological space.

$\pi_1(\mathbb S^1)$.

Torus decomposition of $\mathbb S^3$.

Linear Algebra Review

23 Fevereiro 2022, 11:00 • Orlando Manuel Bartolomeu Neto

Normal Forms of Matrices Normal forms for symmetric matrices and generalizations,Jordan normal form,

Trace of a Matrix, Inner products.

HALL Appendix

Jordan Blocks and powers of the (complex) logarithm.

Apresentação

22 Fevereiro 2022, 09:30 • Orlando Manuel Bartolomeu Neto

Presentation of the course.
There will be some classes in seminar style where relevant but not central themes will be presented with less detail.
This will be also the space where the PhD students will present their additional work,
Evaluation: Final Exam or to participate actively and regularly in the course:Present the solutions of two nontrivial exercises per week, make small presentations, solve exercises in the classroom, to participate in the discussions...
Main Bibliography: Brian C. Hall Lie Groups, Lie Algebras, and Representations. [HALL]
Topologic Groups. Homogeneous Spaces.
See pdf.