Sevilla, del 5 al 8 de abril de 2011 Seville, from 5 to 8 April 2011

# IntroducciónIntroduction

En el estudio de superficies en 3-variedades aparecen técnicas importantes de cálculo variacional, variable compleja, EDPs elípticas o teoría geométrica de la medida, entre otras. En particular, algunas de las ramas clásicas de la teoría (como superficies mínimas, superficies de curvatura media constante, o EDPs geométricas) son un ejemplo especialmente interesante de dicha interacción.

Este congreso tendrá un énfasis en los aspectos más importantes de la teoría global de superficies mínimas y de curvatura media constante, así como en EDPs geométricas de especial relevancia. También se tratarán otros tipos de condiciones de curvatura (como superficies de curvatura constante), así como otras condiciones geométricas naturales (como por ejemplo, convexidad local).

Este congreso forma parte de las actividades del doc-course 2011 del Instituto de Matemáticas de la Universidad de Sevilla (IMUS).

The study of surfaces in 3-manifolds is a meeting point for different techniques from fields like variational calculus, complex analysis, elliptic PDEs or geometric measure theory, among others. In particular, some of the classic subjects in the theory (like minimal surfaces, constant mean curvature surfaces, or geometric PDEs) are interesting examples of this interaction.

This conference will have an emphasis in the most important facts of the global theory of minimal and constant mean curvature surfaces, as well as other specially relevant geometric PDEs. It will also be dealing with other types of curvature conditions (such as constant curvature surfaces) and other natural geometric conditions (as for example, local convexity).

This conference is part of the program for the doc-course 2011 by the Institute of Mathematics of the University of Seville (IMUS).

Hacer click en la siguiente imagen para descargarla:Click on the following image if you want to download it:

# ProgramaProgram

 Martes 5Tuesday 5 Miércoles 6Wednesday 6 Jueves 7Thursday 7 Viernes 8Friday 8 845 - 900 InscripciónRegistration 900 - 950 A. Ros H. Rosenberg F. Martín B. White 950 - 1040 J. Dorfmeister J. Espinar G. Smith B. Daniel Descanso y CaféCoffee Break 1110 - 1200 S. Cartier K. Grosse-Brauckmann S. Min B. Coskunuzer 1200 - 1250 M. Ritoré X. Cabré W. Meeks M. Schneider ComidaLunch 1530 - 1620 A. Alarcón [1915] Visit to the Alcázar[2045]Social dinner[1915]Visita al Alcázar[2045]Cena F. Pacard L. Hauswirth Descanso y CaféCoffee Break Descanso y CaféCoffee Break 1650 - 1740 M. Reiris L. Mazet P. Sicbaldi 1740 - 1830 F. Urbano D. Hoffman N. Nadirashvili
Conformal structure of minimal surfaces in $\mathbb{R}^3$

We show a technique for constructing minimal surfaces in Euclidean 3-space $\mathbb{R}^3$ of arbitrary conformal structure. Among other applications we prove that any open Riemann surface is the conformal structure of a minimal surface in $\mathbb{R}^3$ properly projecting into a plane. This solves a problem posed by Schoen and Yau. We also show that any convex domain of Complex 3-space $\mathbb{C}^3$ admits complete properly immersed null holomorphic curves.

Xavier Cabré Icrea - Universitat Politècnica de Catalunya
Uniqueness and stability of saddle-shaped solutions to the Allen-Cahn equation

We establish the uniqueness of a saddle-shaped solution to the diffusion equation $-\Delta u = f(u)$ in all of $\mathbb{R}^{2m}$, where $f$ is of bistable type, in every even dimension $2m \geq 2$. In addition, we prove its stability whenever $2m \geq 14$.

Saddle-shaped solutions are odd with respect to the Simons cone $\mathcal{C}=\{(x^1,x^2)\in\mathbb{R}^m\times\mathbb{R}^m:|x^1|=|x^2|\}$ and exist in all even dimensions. Their uniqueness was only known when $2m=2$. On the other hand, they are known to be unstable in dimensions 2, 4, and 6. Their stability in dimensions 8, 10, and 12 remains an open question. In addition, since the Simons cone minimizes area when $2m \geq 8$, saddle-shaped solutions are expected to be global minimizers when $2m \geq 8$, or at least in higher dimensions. This is a property stronger than stability which is not yet established in any dimension.

Sébastien Cartier Université Paris-Est Créteil Val-de-Marne
Constant mean curvature $1/2$ surfaces in $\mathbb{H}^2\times\mathbb{R}$ with vertical ends

We study surfaces with constant mean curvature (CMC) $1/2$ in $\mathbb{H}^2 \times \mathbb{R}$ with vertical ends, which admit a compactification of the mean curvature operator.

We construct CMC-$1/2$ entire graphs which are not asymptotic to rotational examples, with a control of their asymptotic behaviour.

The method adapts for annuli so that we are able to show existence of CMC-$1/2$ annuli with vertical ends, which are not asymptotic to rotational examples. Moreover we construct vertical CMC-$1/2$ annuli without axis, i.e. with non aligned asymptotically rotational ends."

Baris Coskunuzer Koc University
Generic uniqueness of area minimizing disks for extreme curves

In this talk, we will start with an overview of the Plateau problem in 3-manifolds. Then, we will give a sketch of the proof of the following statement: For a generic nullhomotopic simple closed curve $C$ in the boundary of a compact, orientable, mean convex 3-manifold $M$ with trivial second homology, there is a unique area minimizing disk $D$ embedded in $M$ where the boundary of $D$ is $C$. The same statement is also true for absolutely area minimizing surfaces, too.

Benoît Daniel Université Paris-Est Créteil Val-de-Marne
CMC surfaces in homogeneous 3-manifolds

We will talk about some recent results on constant mean curvature surfaces in homogeneous Riemannian $3$-manifolds, in particular in $\mathbb{H}^2\times\mathbb{R}$, the Heisenberg group $\mathrm{Nil}_3$ and the universal cover of $\mathrm{PSL}_2(\mathbb{R})$.

Josef Dorfmeister Technische Universität München
Constant mean curvature surfaces in hyperbolic 3-space

In recent years, many classes of surfaces have been investigated using loop group methods. Typical for this approach is an equivalent characterization of surfaces of a certain class by the harmonicity of some Gauss type map into a symmetric space. (It has been shown by Kobayashi that there are exactly seven different surface classes that can be described this way involving symmetric spaces of $\mathrm{Sl}(2,\mathbb{C})$).

The surfaces of constant mean curvature $|H|\gt 1$ fall into this category, as also follows from the Lawson correspondence. If $|H|\lt 1$, however, a (somewhat) different approach is needed, in particular=, since the natural Gauss type map has values in a $4$-symmetric space.

In this talk we will present ( joint work with J. Inoguchi and S. Kobayashi) the loop group method for CMC surfaces in $\mathbb{H}^3$ with $|H|\lt 1$.Time permitting, we will also address some features of surfaces spreading (singularly) across part of the boundary of the hyperbolic open ball.

Stable surfaces in Homogeneous 3-manifolds

We consider operators $L$ acting on functions on a Riemannian surface, $\Sigma$, of the form $L = \Delta + V -a K,$ where $\Delta$ is the Laplacian of $\Sigma$, $K$ the Gaussian curvature, $a$ is a positive constant and $V \in C^{\infty}(\Sigma)$. Such operators $L$ arise as the stability operator of $\Sigma$ immersed in a Riemannian $3-$manifold with constant mean curvature (for particular choices of $V$ and $a$). We assume $L$ is non positive acting on functions compactly supported on $\Sigma$. If the potential, $V:= c + P$ with $c$ a nonnegative constant, verifies either a integrability condition, i.e. $P \in L^1(\Sigma)$ and $P$ is non positive, or a decay condition with respect to a point $p_0 \in \Sigma$, i.e. $|P(q)|\leq M/d(p_0,q)$ (where $d$ is the distance function in $\Sigma$), we control the topology and conformal type of $\Sigma$. Moreover, we establish a Distance Lemma.

We apply such results to complete oriented stable $H-$surfaces immersed in a Killing submersion. In particular, for stable $H-$surfaces in a simply-connected homogeneous space with $4-$dimensional isometry group, we obtain:

• There are no complete, oriented, stable $H-$surfaces, $H>1/2$, so that either $K_e^+:={\rm max}\{0,K_e\} \in L^1 (\Sigma)$ or there exist a point $p_0 \in \Sigma$ and a constant $M$ so that $|K_e(q)| \leq M/d(p_0,q)$, here $K_e$ denotes the extrinsic curvature and $M$ is a constant.
• Let $\Sigma \subset \mathbb{E}^3(\kappa,\tau)$, $\tau \neq 0$, be an oriented complete stable $H-$surface so that either $\nu^2 \in L^1 (\Sigma)$ and $4H^2 +\kappa \geq 0$, or there exist a point $p_0 \in \Sigma$ and a constant $M$ so that $|\nu (p)|^2 \leq M/d(p_0,q)$ and $4H^2 +\kappa > 0$. Then:
• In $\mathbb{S}^3_{Berger}$, there are no such a stable $H-$surface.
• In ${\rm Nil}_3$, $H=0$ and $\Sigma$ is either a vertical plane (i.e. a vertical cylinder over a straight line in $\mathbb{R}^2$) or an entire vertical graph.
• In $\widetilde{{\rm PSL}(2,\mathbb{R})}$, $H=\sqrt{-\kappa}/2$ and $\Sigma$ is either a vertical horocylinder (i.e. a vertical cylinder over a horocycle in $\mathbb{H}^2 (\kappa)$) or an entire graph.
Two examples of minimal surfaces and their sisters

I will present two results obtained in PhD theses. Yong He constructed a family of deformations of the helicoid in $\mathbb{R}^3$, that is, a family of minimal immersions containing the helicoid. Their cousins give mean-curvature-1 surfaces in hyperbolic $3$-space which deform the catenoids. Julia Plehnert constructed certain dihedrally symmetric $k$-noids of genus $1$ in product spaces $\Sigma(\kappa)\times\mathbb{R}$ as sister surfaces.

Laurent Hauswirth Université de Marne-la-Vallée
On the geometry of minimal annuli in $\mathbb{S}^2\times\mathbb{R}$
David Hoffman Stanford University
Helicoidal surfaces in $\mathbb{S}^2\times\mathbb{R}$
Minimal planar domains in $\mathbb{H}^2\times\mathbb{R}$

We prove that any planar domain can be properly and minimally embedded in $\mathbb{H}^2\times\mathbb{R}$. The examples that we produce are vertical bi-graphs, and they are obtained from the conjugate surface of a Jenkins-Serrin graph. This is a joint work with M. Magdalena Rodríguez.

Laurent Mazet Université Paris 12
A general halfspace theorem for constant mean curvature surfaces

In this talk, we will present a general halfspace theorem for constant mean curvature surfaces. This result gives a common background for several halfspace results that were proved by several authors in recent years.

William H. Meeks III University of Massachusetts, Amherst
Constant mean curvature spheres in homogeneous 3-manifolds

Using the classical holomorphic quadratic Hopf differential, Hopf proved that a constant mean curvature $H>0$ sphere in $3$-dimensional Euclidean space is a round sphere of radius $\frac{1}{H}$. In particular, the moduli space of such spheres up to congruence is parametrized by the mean curvatures that lie in the interval $(0,\infty)$ and every such sphere has index one for the stability operator. In recent years, this result of Hopf has been generalized to other simply connected homogeneous $3$-manifolds $X$ such as the Riemannian product of a round sphere with the real number line $\mathbb{R}$ (however, minimal spheres in this case have index zero). I will discuss the classification theorem for the moduli space in a general $X$ due to Meeks, Mira, Perez and Ros; especially I will focus on the case where $X$ is a metric Lie group (a Lie group with a left invariant metric). In certain cases, depending on $X$ and $H$, we give show that a constant mean curvature $H$ sphere must be embedded; for instance, minimal spheres in $X$ are always embedded and if $X$ is a metric Lie group that is isomorphic to a non-unimodular Lie group with Milnor $D$ invariant less than or equal to one, then every constant mean curvature sphere in $X$ is embedded. One consequence of this classification result is that when $X$ is homeomorphic to the $3$-sphere, then it admits for every $H$ greater than or equal to $0$, a unique sphere $S(H)$ of constant mean curvature $H$, and this sphere has index one and it is Alexandrov embedded (in general when $H$ is not equal to $0$, $S(H)$ need not be embedded for certain homogeneous metrics).

Sung-Hong Min Korea Institute for Advanced Study
Total curvature of a polygon and embeddedness of minimal surfaces

In this talk, first we will focus on the total curvature of a polygon in $n$-dimensional Euclidean space. The sharp upper bound of the total curvature of a polygon with $2m+1$ vertices is $2m\pi$, where $m>1$.

And then, we will prove the following: Let $\Gamma_5$ be a piecewise geodesic Jordan curve in $\mathbb{H}^n$ or $\mathbb{S}^n_+$ with $5$ vertices. Then any minimal surface $\Sigma$ bounded by $\Gamma_5$ is embedded. As a consequence, $\Gamma_5$ is an unknot in $\mathbb{H}^3$ or $\mathbb{S}^3_+$.

Singularities of special Lagrangian graphs
Frank Pacard Université Paris Est-Créteil
Genus m-nodoids
Martin Reiris Max-Planck-Institut für Gravitationsphysik
Theorems, intuitions and applications of minimal surfaces in Geometry and Gravitation

We will recall old and new well established results on initial data sets in General Relativity (including $U(1)$-symmetric states) whose analysis requires the use of minimal surface theory and that are theoretically linked to the rest of the talk.

We will then move forward to briefly discuss the widely open problem of the dynamics of the gravitational field (as a hyperbolic geometric flow). In this context we will point out a series of theorems, intuitions and conjectures on the $L^{p}$-Cheeger-Gromov theory ($p>3/2$) of Riemannian three-manifolds with scalar curvature uniformly bounded below. These elaborations (if valid) should help to a deeper understanding of the problem of singularity formation in the gravitational field. They could find use in Riemannian variational problems as well.

We will finally explain how a detailed understanding of 'size relations' (of isoperimetric nature) of stable minimal surfaces (with or without boundary) on Riemannian three-manifolds with a priori bounded scalar curvature serves as a very refined tool to attack such problems. As an interesting by product we will mention how the they lead to a proof of a problem posed by Fischer-Colbrie and Schoen in 1980 on the flatness of complete stable cylinders when the ambient scalar curvature is non-negative.

Existence of isoperimetric regions in contact sub-Riemannian manifolds

We prove existence of isoperimetric regions in contact sub-Riemannian manifolds with compact quotient under the action of the contact isometry group. This is joint work with Matteo Galli.

Stable minimal surfaces and area minimizing surfaces in flat 3-manifolds

It was proved by Fischer-Colbrie and Schoen, Do Carmo and Peng, and Pogorelov that complete stable two-sided surfaces in flat $3$-manifolds are always planar. The behaviour of one-sided stable minimal surfaces is quite different. For instance, certain nonorientable quotients of the classic Schwarz $P$ and $D$ periodic minimal surfaces are stable in their ambient $3$-tori (Ross). A related question in classical minimal surface theory is to classify properly embedded area minimizing surfaces (mod $2$) in flat ambient spaces. We will review some results about these problems and, in particular, we will prove that area minimizing surfaces in $3$-tori and other compact quotients of $\mathbb{R}^3$ are planar.

Harold Rosenberg Instituto Nacional de Matemática Pura e Aplicada
An integer valued degree theory for hyper-surfaces of prescribed curvature

Consider immersions of a compact manifold $S$ into a compact manifold $M$, of codimension one. Let $K$ be an elliptic curvature function on the immersions (mean curvature, positive extrinsic curvature,...). We let $f$ be a smooth function on $M$ and we want to count the number of immersions of $S$ into $M$ whose $K$-curvature is $f$. When the space of such immersions is compact, we obtain an integer valued degree theory for generic prescribed functions $f$.

I will discuss this degree theory and some applications. This is joint work with Graham Smith.

Matthias Schneider Ruprecht Karls-Universität Heidelberg
Closed magnetic geodesics

We give new existence results for closed magnetic geodesics on surfaces. Magnetic geodesics correspond to curves with prescribed geodesic curvature. In case of the two sphere, a closed (embedded) magnetic geodesic leads to an (embedded) Hopf torus of prescribed mean curvature in the three sphere.

Pieralberto Sicbaldi Université Aix-Marselle 3
Bifurcating extremal domains for the first eigenvalue of the Laplacian

We show the existence of a smooth one-parameter family of domains that are critical points for the first eigenvalue of the Laplacian in flat tori. Such domains solve a special overdetermined elliptic problem and their existence provides a family of counterexemples to a conjecture of Berestycki-Caffarelli-Nirenberg. We will describe also some geometrical properties of such domains, whose boundaries share many similarities with Delaunay surfaces.

Graham Smith Centre de Reserca Matemàtica
Constant Curvature Immersed Hypersurfaces and the Euler Characteristic

We show how in various cases the integer valued degree described by H. Rosenberg in the preceeding talk "An integer valued degree theory for hyper-surfaces of prescribed curvature" can be shown to be equal to the Euler Characteristic of the ambient manifold. We also prove the prerequisite properness in a simple case. This is joint work with Harold Rosenberg.

Second variation of one-sided minimal surfaces

The study of the second variation of the area of minimal surfaces into Riemannian $3$-manifolds can be considered as a classical problem in differential geometry. In fact, the operator of the second variation (the Jacobi operator) carries the information about the stability properties of the surface when it is thought as a stationary point for the area functional. We study the second variation of the one-sided complete minimal surfaces of some $3$-manifolds with positive scalar curvature: the sphere, the real projective space, $\mathbb{S}^2\times\mathbb{R}$ and $\mathbb{R}P^2\times\mathbb{R}$.

Brian White Stanford University
Examples of curvature blow-up in embedded minimal surfaces

Nota importante

Important information

• Visit to the Alcázar will start at Puerta del Apeadero (Patio de Banderas).
• Dinner will take place at Restaurante Los Seises (Calle Don Remondo no.2). If you have any special need (like for example a vegetarian menu) please write to registration@sevilla.es.
• La visita al Alcázar comenzará en la Puerta del Apeadero (Patio de Banderas).
• La cena tendrá lugar en el Restaurante Los Seises (calle Don Remondo, 2). Para cualquier necesidad especial (por ejemplo, para pedir un menú vegetariano), escribir a registration@sevilla.es.

# InscripciónRegistration

Para inscribirse en el congreso, pinche en el siguiente enlace.

La fecha límite para la inscripción es el 25 de febrero de 2011.

The deadline for online registration is February 25th, 2011.

# Becas y ayudasGrants

Este congreso pertenece al módulo "Submanifold theory and applications" (28 Marzo-8 Abril), dentro de la programación del DOC-COURSE IMUS del Instituto de Matemáticas de la Universidad de Sevilla (IMUS). Se ofertan becas de alojamiento para los estudiantes que asistan a dicha escuela.

This conference is part of the module "Submanifold theory and applications" (28 March-8 April), an advanced school organized by the Institute of Mathematics of the University of Sevilla (IMUS). We offer accomodation grants for the students attending to the school, more information here.

## Direcciones del hotel y la residencia. Sedes del curso y el congresoAccommodation addresses. Conference and doc-course venue

1. Hotel Pasarela 4*
Avenida de la Borbolla, 11.
Está situado cerca del centro de la ciudad, a espaldas del Parque de María Luisa y la Plaza de España.
2. Lugar del congreso
Pabellón de México.
Paseo de la Palmera, esquina con Avenida de Eritaña. Está muy cerca del Parque de María Luisa.
3. Lugar del curso
Escuela Técnica y Superior de Ingeniería Informática (segunda planta, aula A.2.11). Avda. Reina Mercedes.
4. Residencia Universitaria Estanislao del Campo
Calle Guadalbullón, esquina con Carretera Su Eminencia).
Se encuentra enfrente del estadio de fútbol Benito Villamarín, en el barrio sevillano Heliopolis, cerca del campus Reina Mercedes.
1. Hotel Pasarela 4*
Avenida de la Borbolla, 11.
It’s located close to the city center, behind Parque de María Luisa and Plaza de España.
2. Conference Venue
Pabellón de México.
Paseo de la Palmera, corner with Avenida de Eritaña. It is very close to Parque de María Luisa.
3. Courses Venue
Escuela Técnica y Superior de Ingeniería Informática (second floor, room A.2.11). Avda. Reina Mercedes.
4. Residence Hall Residencia Universitaria Estanislao del Campo
Calle Guadalbullón (corner with Carretera Su Eminencia).
It’s located in front of the football stadium Benito Villamarín, in the sevillian neighbourhood called Heliopolis, and near Reina Mercedes Campus.

## Cómo llegar desde el aeropuerto o la estación de tren How to get from Airport/Train Station

Del aeropuerto a la residencia o al hotel

Ir en taxi desde el aeropuerto a cualquier punto de Sevilla cuesta alrededor de 27 euros (tarifa fija). También se puede tomar un autobús especial desde el aeropuerto hasta Prado de San Sebastián (última parada de este autobús), con un precio de 2,40 euros. Una vez allí, se puede tomar la línea 1 (Polígono Norte-Glorieta Plus Ultra), o la línea 37 (Prado-Bellavista). En ambos casos, para ir al hotel Pasarela hay que bajarse en la primera parada, mientras que para ir a la residencia Estanislao del Campo, hay que hacerlo en la octava. El precio del autobús urbano es de 1,30 euros.

From Airport to Residence Hall/Hotel

The taxi costs around 27 euros (fixed fee) from the airport to anywhere in Sevilla city. There is also a special bus from the airport to Prado de San Sebastián (last stop of this bus). This costs 2,40 euros. Then you can take line 1 (Polígono Norte-Glorieta Plus Ultra), or line 37 (Prado-Bellavista). In both cases, the hotel is at the first stop, and the Residence Hall is at the eighth stop. This costs 1,30 euros.

De la estación de tren a la residencia o al hotel

Se puede tomar un taxi o el autobús línea C1 (Isla de la Cartuja-Prado), en cuyo caso hay que bajarse en la última parada (Prado de San Sebastian). Entonces, se puede tomar la línea 1 del autobús urbano (Polígono Norte-Glorieta Plus Ultra), o la línea 37 (Prado-Bellavista). En ambos casos, para ir al hotel Pasarela hay que bajarse en la primera parada, mientras que para ir a la residencia Estanislao del Campo, hay que hacerlo en la octava. El precio del autobús urbano es de 1,30 euros.

From Train Station to Residence Hall/Hotel

You can take a taxi, or take bus line C1 (Isla de la Cartuja-Prado), get off at the last stop (Prado de San Sebastian). Then you can take line 1 (Polígono Norte-Glorieta Plus Ultra), or line 37 (Prado-Bellavista). In both cases, the hotel is at the first stop, and the Residence Hall is at the eighth stop. Each trip costs 1,30 euros.

## Cómo llegar a la sede del congreso How to get to the venue of the Conference

Del hotel Pasarela a la sede del congreso

Se puede ir a pie, atravesando la Avenida de la Borbolla y el Parque de María Luisa hasta alcanzar el Paseo de las Delicias. Una vez allí, se puede girar a la izquierda hasta llegar al Pabellón de México. También se puede seguir por la Avenida de la Borbolla, girar a la derecha para llegar a la Avenida Eritaña, donde podrá encontrarse el Pabellón de México haciendo esquina con el Paseo de la Palmera. La distancia total es de un kilómetro aproximadamente.

En caso de querer tomar un autobús, las líneas 1, 37, 38 paran cerca de la sede del congreso.

From Hotel Pasarela to the venue of the Conference

Walk along Avenida de la Borbolla, cross the Parque de María Luisa until reaching Paseo de las Delicias, and turn left until reaching the Pabellón de México at the same side. You can also continue Avenida de la Borbolla, turn right in order to take Avenida Eritaña, and you will find the Pabellón de México in the corner with Paseo de la Palmera. Total distance is about one kilometer.

In case you want to catch a bus, lines 1, 37, 38 will take you closer to the venue.

De la residencia Estanislao del Campo a la sede del congreso

También se puede ir a pie, yendo al Paseo de la Palmera y, girando a la derecha, después de un kilómetro y medio aproximadamente, se encuentra el pabellón de México a la derecha.

En caso de querer tomar un autobús, una buena elección es subirse en Avda. Manuel Siurot (prolongación de la Calle Guadalbullón, en frente de la residencia) a la línea 6 (San Lázaro-Heliópolis), y bajándose en la séptima parada.

From Residence Hall Estanislao del Campo to the venue of the Conference

Go to Paseo de la Palmera, turn right and after one kilometer and a half, approximately, you will find the Pabellón de México on your right.

If you want to catch a bus, you have to take line 6 (San Lázaro-Heliópolis) at Avda Manuel Siurot (prolongation of Calle Guadalbullón, in front of the Residence Hall), and getting off at the seventh stop.

## Cómo llegar a la sede del curso How to get to the venue of the Doc-course

De la residencia Estanislao del Campo a la sede del curso

Ir al Paseo de la Palmera, girar a la derecha y a la izquierda rodeando el estadio de fútbol, tomar la Avenida del Padre García Tejero hasta llegar a una rotonda, y después girar a la derecha para coger la Avenida Reina Mercedes. La Escuela de Ingeniería Informática se encuentra al lado izquierdo después de 100 metros aproximadamente. El Doc-Course tendrá lugar en el aula A.2.11 de la Escuela de Ingeniería Informática (segunda planta).

From Residence Hall Estanislao del Campo to the venue of the Doc-Course

Go to Paseo de la Palmera, turn right and left surrounding the football stadium, take Avenida del Padre García Tejero until reaching a traffic circle, and then turn right in order to take Avenida Reina Mercedes. You will find the Escuela de Ingeniería Informática on the left side after 100 meters approximately. The Doc-Course will take place at room A.2.11 in the Escuela de Ingeniería Informática (second floor).

Del hotel Pasarela a la sede del curso

Ir caminando al Prado de San Sebastián y tomar la línea de autobús urbano número 34, que para enfrente de la sede del curso.

From Hotel Pasarela to the venue of the Doc-Course

Walk to Prado de San Sebastián and take bus line 34, it stops in front of the doc-course venue.

## Lugares turísticos Touristic Visits

Sevilla has a lot of places worth visting. Here are some of the most popular ones:

• Cathedral, Giralda
• Alcázar
• Plaza de España and Parque de Maria Luisa
• Barrio de Santa Cruz (the oldest and most traditional district in the city)
• Torre del Oro
• Calle Betis (next to the river, full of bars)
• Calle Sierpes (shopping street)
• Alameda de Hércules (full of bars and pubs)

From Hotel Pasarela

The hotel is located behind Plaza de España, one of the most famous squares in Sevilla. The rest of important places in the city are in a walking distance from the hotel, but you can also take the light train at Prado de San Sebastián. This light train stops at the Cathedral (second stop) and City Hall (third stop).

From Residence Hall Estanislao del Campo

By taking line 34 (Los Bermejales-Prado) along Avenida Reina Mercedes (where it is ubicated the venue of the Doc-Course), you will get close to the city center (last stop, at Prado de San Sebastián). From there you can go walking to most of the important places in the city, but you can also take the light train at Prado de San Sebastián, it stops at the Cathedral (second stop) and City Hall (third stop).

By taking line 6 at Avenida Manuel Siurot (in front of the Residence Hall), or along Avenida Reina Mercedes (direction San Lázaro), you will go to Calle Betis and Alameda de Hércules.

Sevilla tiene muchos sitios que merece la pena ver. Aquí dejamos algunos de los más conocidos:

• La Catedral y la Giralda
• El Alcázar
• Plaza de España y Parque de Maria Luisa
• El Barrio de Santa Cruz (la parte más antigua y tradicional de la ciudad)
• La Torre del Oro
• La Calle Betis (cerca del río y llena de bars)
• La Calle Sierpes (en el centro comercial)
• La Alameda de Hércules (repleta de bares y pubs)

Desde el hotel Pasarela

El hotel está situado detrás de la Plaza de España, una de las plazas más famosas de Sevilla. El resto de lugares de interés turístico están a una distancia razonable a pie del hotel, pero también se puede tomar el tranvía en Prado de San Sebastián, que para en la Catedral (segunda parada) y en el ayuntamiento (tercera parada).

Desde la residencia Estanislao del Campo

Tomando la línea 34 de autobús urbano (Los Bermejales-Prado) a lo largo de Avenida Reina Mercedes (donde se encuentra la sede del curso), se llega muy cerca del centor de la ciudad (en la última parada, en Prado de San Sebastián). Desde allé se puede ir andando a muchos de los sitios de interés de la ciudad, pero también se puede tomar el tranvía en Prado de San Sebastián, que para en la caterdral (segunda parada) y en el ayuntamiento (tercera parada).

Tomando la línea 6 de autobús ubano en la Avenida Manuel Siurot (enfrente de la residencia), o a lo largo de la Avenida Reina Mercedes (dirección San Lázaro), se encuentra la Calle Betis y la Alameda de Hércules.

## Sistema de alquiler de bicicletas Rented bikes system (SEVICI)

Sevilla es una ciudad muy llana y tiene un sistema bastante extendido de carril bici conectando distintos puntos de la ciudad, lo que hace de la bicicleta un buen medio para disfrutar de la ciudad.

SEVICI es un sistema de alquiler de bicicletas, que dispone de muchos puntos donde pueden cogerse o dejarse las bicicletas. Un mapa detallado de las estaciones puede encontrarse en este enlace. Tienen el siguiente aspecto.

Sevilla is very flat, and it has a wide system of bike lines connecting the city, that makes the bike a good option to enjoy the city.

SEVICI is a system for renting a bike, it has many bike points where you can take or drop the bikes. A detailed map of the stations can be found at www.sevici.es. They look like this:

Se puede comprar una tarjeta para una semana por 10 euros en las máquinas que se encuentran al lado de las bicicletas (sólo es necesaria una tarjeta de crédito). Los primeros 30 minutos son gratuitos y, después de éstos, la primera hora cuesta 1 euro y las siguientes 2 euros, pero siempre se puede dejar la bicicleta a los 30 minutos y cogerla de nuevo, de forma que vuelve a ser gratuita.

Nota: cuando se deja una bicicleta, comprueba que se ha depositado correctamente o ¡el sistema creerá que todavía la tienes!

You can buy a card for one week for 10 euros at the machines in these points (you only need a credit card). The first 30 minutes are free, and after them the first hour is 1 euro and the next ones 2 euros, but you can always drop the bike before 30 minutes and take it again, so it will be free again.

Note: when dropping a bike, check that it is correctly returned, otherwise the system will think you still have it!