Every participant is encouraged to submit an abstract for this meeting, presenting either their own work or giving some insight into a topic of interest to them. Selected talks among the submitted abstracts shall be communicated to the participants before June 1st.

The meeting is open to non-spanish based topologists as well. Please bear in mind that although topologists, attendees will be working in different branches of the field. As such, talks should aim to be understandable on an overview level by non-specialists. We have blackboards, and computers for slide shows are available. Please let us know if you need anything special.

You can find the abstracts here.

Besides presentations given by the participants, there shall be two mini-courses consisting of three lectures each. The 2015 invited lecturers are:

**José M. Montesinos**(Universidad Complutense de Madrid)

Title: **Branched Coverings**

- Examples of branched coverings. 2-bridge knots and lens spaces.
- 3-Manifolds as branched coverings over knots.
- Universal groups and 3-manifolds: hyperbolic manifolds.
- Open manifolds, wild knots and branched coverings.

- Ordinary coverings Theory: Masseyś book. Absolutely necessary.
- Elementary algebraic Topology (fundamental group and homology theory): Massey again or Greenberg.
- Simplicial complexes and polyhedra: just the definitions and some of the elementary topological properties.
- Concept of triangulated and combinatorial manifolds: just to know the concepts.
- General Topology: Kelley
- Manifolds: definition and elementary topological properties (Spivak).
- Orbifolds: definitions and elementary properties. (Montesinos: Classical Tessellations and three manifolds; Thurston. Notes, Princeton. Matsumoto-Montesinos paper on Thurston’s uniformization theorem: just the first initial sections).
- Hyperbolic geometry from linear algebra point of view: Beltrami-Klein model (Santaló).
- Knot theory. Presentation of a knot group. (Burde-Zieschang)
- Ordinary combinatorial group theory: group presentations (Magnus-Karrass-Solitar book and Crowell and Fox book on Knot Theory)
- 3-manifolds: Heegaard splittings and Dehn-surgery (Hempel book on 3-manifolds or original paper by Lickorish in Annals of Mathematics)

**Aniceto Murillo**(Universidad de Málaga)

Title: **Some Applications of Algebraic Topology**

Topics:

- Topological complexity.
- Rational topological complexity.
- Persistent homology.

Background:

This minicourse is directed to an audience with a basic knowledge in algebraic topology in general, and homotopy theory, in particular. Apart from some recent develepments, which will also be presented, and results of a somewhat general nature, most of the content can be found in these two standard references:

- M. Farber, Invitations to Topological Robotics, Zurich Lectures in Advances Mathematics, European Mathematical SOciety, 2008. (chapter 4).
- H. Edelsbrunner and J. Harer, Computational Topology: An Introduction, American Mathematicas Society, 2010. (chapter VII).