The dynamics of differential operators, in the topological sense and also in the sense of measure, can be described by using methods of Functional Analysis and Operator Theory.

In addition, such dynamics can also be found for the solution of certain linear partial differential equations, by using the theory of stongly continuous semigroups. Some of these results can even be successfully applied in the nonlinear setting.

Recently, the tools used in this area have permitted to show phenomena such as chaos in any of its formulations (such as the one of Devaney or the one of distibutional chaos in the sense of Schweizer and Smítal), topologically mixing and weakly mixing properties, as long as ergodicity.

Besides, the description of "wandering" orbits in the phase space, and the frequency in which these orbits visit several regions have been also analyzed.In this session, we pretend to show the last advances in the study of the dynamics of operators and strongly continuous semigroups of operators, as long as the applications and particular models coming from linear PDE's and infinite systems of ODE's.

The singular characteristics of the plane topology-or more generally of the surfaces-- allow us to use specific techniques for analyzing dynamical problems. However, this dynamics is rich and complicated and some interesting problem on it appear. In this session our aim is to present some of the recent advances in discrete and continuous dynamical systems and on the relations between them.

Since the early's 70, optimal design of structures has been a very active research topic which is in the interface of Mathematics, Physics and Engineering. At the mathematical level, this topic includes, among others, ideas and methods coming from Calculus of Variations, Homogenization Theory of Partial Dierential Equations and Numerical Analysis.

This special session aims at presenting (some of) the most relevant contributions on this eld both on mathematical methods and industrial applications. In particular, an special emphasis will be paid on shape and topology optimization under uncertainties and the design of piezo-electric structures.

The list of invited speakers will include national researchers of the groups working on this eld as well as some of the most relevant international researchers in structural optimization.

The main objetive of this session is to offer a wide range of recent results on the asymptotic behavior of dynamical systems generated by ordinary and partial differential equations containing some nonautonomous or stochastic terms. Some topics fitting this session are: asymptotic dynamics of nonautonomous systems, in particular, those problems related to the existence and geometric properties of attractors, stability and stabilization problems, dynamics of systems modeled by equations with delay or memory, problems with nonuniqueness of solutions, analysis of stochastic models with applications to several phenomena from the applied sciences, etc.

Differential equations govern many phenomena that happen in the nature and play an important role in the progress of engineering and technology. Essentially all the fundamental equations are nonlinear, and, in general, such nonlinear equations are often very difficult to solve explicitly. Symmetry group techniques provide methods to obtain solutions of these equations. These methods have several applications, for example, in the study of nonlinear partial differential equations, that admit conservation laws which arise in many disciplines of the applied sciences.

We invite authors to present original research articles as well as review articles, in the following topics:

- Theoretical analysis in group analysis and differential equations, applications, and conservation laws.
- Numerical algorithms concerning the symmetry groups for partial differential equations.
- Direct methods to obtain exact explicit solutions for differential equations and applications.
- New applications to the sciences in engineering, physic, biology, financial, etc.

Control theory originated from the desire and the need of controlling the behaviour of dynamical systems which model a number real-world phenomena of interest in Physics, Chemistry, Biology, Economy, etc. The usual objective of control theory is to find out how to act on a system, usually modelled by Partial Differential Equations (PDEs), in order to minimize a cost or to drive the system from an initial state to a final desired one, or even both things at the same time.

It is therefore a very relevant topic in Applied Mathematics both for its applications and for the development of analytical and numerical methods that leads to. In particular, it includes several branches of Mathematics such as Optimization, Calculus of Variations, Functional Analysis and its applications to PDEs and, of course, Numerical Analysis.

Because of the similarity in the techniques which are used, it is usual to link Control Theory and Inverse Problems. In the latter case, some of the system input data are unknown but there are (partial) informations on the solution's behaviour which must be properly used in order to compute the unknown parameters of the system.

Both control theory and the study of inverse problems have a lot of applications. Among others, the control and stabilization of complex structures; the design and control of robots; the control of fluids, combustion systems, elastic and visco-elastic materials; the optimal design and identification of solids in elastic structures; the control oriented towards the determination of optimal therapies in Medecine, etc.

Control theory is a well consolidated area in SēMA, with a number of very active teams which are grouped in a network of excellence supported by the Economy and Competitiveness Ministry.

The main goal of this special session is to join these different groups together with several prestigious international researchers in order to present the main recent advances as well as the challenges that remain.

The special session will deal with the actual research in mathematical biology in its widest sense.

The topics that will be treat included but are not limited to: qualitive behaviour of solutions; stability and asymptoticity in mathematical models; modelization of biological processes and new methods for studying biological phenomena.

The objective is put together researchers with different interests in the setting of mathematical biology with the aim of discussing what are the new trends in the field and how to study them. The impact or application of theoretical results in the study of real world problems will be very wellcome.

Recently, a new generation of mathematical and computational models on cancer has emerged that have been built in close collaboration with experimentalists and are primarily aimed at understanding aspects of cancer progression and treatment. A key to making these models clinically relevant is that they must utilize patient specic data. The quality and quantity of this data varies wildly across tumor type and covers a wide range of spatial scales (e.g. molecular, histology, imaging, tissue, organ). To further complicate matters most cancers have multiple therapeutic options, some have even up to twenty or more. This produces a huge therapeutic parameter space with vast numbers of potential drugs, doses, and schedule combinations. Thus, a key challenge in further developing the field is how to best utilize limited patient data to produce clinically useful predictions that can aid both our understanding of this devastating disease and crucially allow us to treat it better.

On the other hand, from a theoretical point of view, the mathematical models can shed light on main aspects of the dynamics of cancer and to help us understand some processes and even reveal new ones. Quite often, the mathematical models provide a theoretical test bench for which one can compare their predictions with those observed in real life.

Therefore, the aim of this special session is to provide a suitable scenario for the presentation of a broad spectrum of frameworks on mathematical oncology: from the more theoretical approaches to those providing clinically relevant quantitative predictions and utilizing patient data of specic types of cancer. We hope that this special session will bring together experts from many elds that will contribute to the state of the art on mathematical oncology.

This session will focus on computational methods for studying dynamical systems, such as extracting invariant structures and analyzing bifurcations. In recent years there has been a significant development of numerical algorithms, and techniques for computer assisted proofs. Such techniques can be used to rigorously prove (using a computer) the existence of objects close to the ones produced numerically.

The aim of this session is to discuss the recent advances in numerical and rigourous computations in dynamical systems, and fostering new challenges for future research.

In the last years, the dynamical systems has experimented a big development, particaularly in their frontiers with other sciences.

This session will treat the interaction, in both senses, between dynamical systems with other banches of sciences. As a example we can state the dynamics of chemical reactions, the disign of spacial missions, the population dynamics or the neurosciences.

The industrial sector is important to the EU economy, and remains a driver of growth and employment. Industry 4.0 is a new term applied to a group of rapid transformations in the design, manufacture, operation and service of manufacturing systems and products.

The challenge is to move towards smart factories allowing, between other things, an increased flexibility in production, a reduction of the time between the design of a product and its delivery, or important improvements in product quality and significantly reduced error rates.

The aim of the proposal is to present the great potential of mathematical technologies, like key technology enabling to help to companies and administrations to advance in the challenges of Industry 4.0. The main idea will be to collect and present an overview of the capabilities of research groups, members of the Spanish Network for Mathematics and Industry (math-in), through their really industrial & societal success stories, highlighting, the benefits of transferring the involved mathematical technology for the firms or administrations customers.

In addition, a talk will be devoted to introduce the goals and strategies of the math-in network, with the objective of leveraging the impact of mathematics on innovations in key technologies, and to enhance communication and information exchange between involved stakeholders from industry and academia.

The problems arising in the field of quantitative finance require the use of a variety of mathematical, numerical and computational tools: for the modeling, the mathematical or the choice of numerical methods and their efficient implementation on the computer, using the more appropriate hardware and software tools. Among others, techniques of stochastic calculus, differential equations and stochastic partial differential, measure theory, statistics, optimization, numerical methods, Monte Carlo simulation are used. HPC tools are also used, when required by the computational cost.

As a result of the financial crisis in 2007, it has become necessary to review the existing models, which has given rise to new models. For example, volatility models more in line with the market reality, multicurve interest rate models, models that include counterparty risk in the valuation of derivatives, etc. In all cases it is necessary to calibrate models with market data, in changing conditions and practically in real time. This has led to new requirements in mathematics, numerical and computational techniques to solve them.

The objective of this session is to present some recent advances in this area, in order make them available to the community of applied mathematics.

**SS 13.**

This special session is devoted to the presentation and discussion of the recent results on the theory of discrete and continuous dynamical systems of low dimension with special emphasis on results on topological dynamics, difference equations and application of the development obtained which generate new models in the applied sciences.

Equally, it is considered of big interest the surveys or revisions which show the state of the art of the different fields and research lines.

**SS 25.**

Topology can be considered as one of the pillars that have been able to build the solid foundations of analysis and geometry as it is the standard structure used to describe concepts such as proximity, convergence and continuity. In recent years, as a result of intensive research, there has been a new incentive in their study because of their new applications in new fields such as economics, computer science, image processing, etc. Because of these interactions, new problems have emerged in the field of both theoretical and applied topology.

The goal of this session is to accommodate the latest developments in the applications of topology in its broadest sense as well as theoretical problems arising from these applications. Thus, it is considered of interest contributions on topics such as asymmetric topology, fuzzy topology, topology in computer science, digital topology, dynamical systems, topological methods in algebra and analysis, fractal dimension and self-similar sets, geometric topology, set theoretic topology, continuous theory, etc. and especially those that focus on applications.

When solving physical problems numerically, one must compute, as accurately as possible, objects associated with matrices, matrix pencils and matrix polynomials (e.g. eigenvalues, eigenvectors, singular values, invariants and canonical form for a particular equivalence relation, invariant subspaces). Moreover, one must be able to give a precise meaning to "as accurately as possible". For this, we need to study how eigenvalues, eigenvectors, etc, behave under perturbations of the matrix.

Often, some elements or symmetries in the matrices are xed by physical constraints (elasticity of a spring, viscosity of a liquid, symmetries under rotation or translation, etc.). Structured perturbation theory takes this physical reality into account by only considering perturbations which respect these constraints.

Hence the interest in working, for example, in: structured backward stability of algorithms to compute eigenvalues; structured conditioning of eigenvalues; change of invariants under low rank perturbations; structured perturbation of matrix canonical forms; perturbation bounds for roots of polynomials or for invariant subspaces; computation of singular values and structured pseudoespectra; structured distance to uncontrollability, and so on.

The aim of this session is to share recent advances in structured matrix perturbation theory, which appears in a natural way in problems related to algorithm stability and conditioning of numerical problems. Some specic problems that could be addressed in this session are, for example:

- structured backward errors of polynomial eigenvalue problems solved via linearizations;
- change of the conditioning of polynomial matrix eigenvalues when a Mobius transformation is applied on the polynomial;
- change of the multiplicities of matrix pencil eigenvalues when the pencil is perturbed with small rank perturbations;
- change of the Brunovsky structure of a controllable pair when a column of the control matrix is perturbed;
- distance from a given matrix polynomial to the nearest one with specied eigenvalues;
- condition numbers and structured pseudospectra for small perturbations;
- distance from a controllable equisingular switched system to an uncontrollable one;
- stabilization of linear systems.

Mathematical modelling of problems arising in engineering, physics, mechanics, etc. leads in many cases, directly or after a discretization process to solving systems of linear equations of finite dimension. Besides, other problems of Numerical Analysis, such as approximation, interpolation, nonlinear systems, computation of eigenvalues, etc., lead to the resolution of large systems. Thus, it is essential to develop efficient numerical methods to solve them. In this special session different works that intend to present efficient methods for solving such problems and applications from a multidisciplinary approach are presented.

In many areas of knowledge, it is needed to address the resolution of systems with high computational cost. For this purpose, scientists and engineers use the so-called high-performance computing. Other alternatives are based on the use of the structure of the matrix, either to reduce the computational cost or to build solutions that do not depend on the conditioning of the matrix (high relative accuracy). It also should be noted that in many industrial and scientific applications large, and frequently sparse, matrices appear suggesting the use of iterative methods versus direct methods for their resolution. In this context the use of preconditioners can accelerate the convergence of iterative methods.

Economics and Social Sciences are characterized by their complexity and conceptual flexibility. On the one hand, these sciences introduce new conceptual frameworks that help the other sciences to outline and formalize the problem and to suggest solutions to it. On the other hand, the economists make use of methodologies coming from other areas of knowledge in order to apply them on economic or social problems.

Thus, mathematics, stochastic mathematics or statistics, provide elements of great importance for the economy; in particular for the business economics or economics applied to industrial processes or economic magnitudes. In this sense, classical applications such as time-series analysis, diffusion problem analysis, or optimization problems, and more recent ones related to the estimation of risk, either for an asset or for the solvency of a firm, or to the extreme-value theory can be outlined. More recent proposals rely on adapting fuzzy methodologies, measuring and modelling intangibles or social behavior using, for example, decision algorithms such as the Analytic Hierarchic Process or employing multilevel equations (or structural equations).

Thus, it becomes clear that economic science cannot be assigned to a specific area of knowledge, and therefore, mathematical applications require the use, usually together, of different models and techniques.

The aim of this session is to provide a framework for the presentation of research papers related to the broad field of the mathematics and statistics applications in economics and social sciences. The focus of the research that can fit in this session is large and open and not limited neither by any particular methodological approach nor the sources of information used.

Solving nonlinear equations is one of the problems that appears more frequently in different scientific disciplines. It is well known that the solutions of different kind of problems can be modeled by means of nonlinear equation, and iterative processes play a key role for approximating the solutions of such equations. So, the problem of solving nonlinear equations by using iterative methods is a research topic with interest from the point of view of pure and applied mathematics.

The target of this session is to show some research lines developed on this discipline, such as the study of the convergence of the considered iterative process, the analysis of their dynamical behavior or the numerical treatment of some particular problems, such as systems of nonlinear equations, optimization problems, matrix equations, differential or integral equations, etc.

**SS 18.**

With Celestial Mechanics begin differential equations, when Newton formulate the gravitational laws as the explanation of the motion of celestial bodies. Both the n-body problem with its simplifications, the restricted problems, and the ones defined by the rotational dynamics, have posed ongoing challenges to successive generations of astronomers, physicists, and mathematicians from Euler to Arnold through Hamilton and Poincaré, to mention some of them. The non-integrability of such systems leads soon to the proposal of approximate quantitative and qualitative methods, theory of stability, integrability criteria, etc., which have helped to develop both the well known methods for the search of periodic and quasi-periodic solutions and new techniques based on invariant manifolds.

Another chapter, already classic, is the introduction of geometric methods for reducing many systems is great interest, thereby finding relative equilibria relevant in the classification of the various families of solutions. Such methods, today framed within

dynamical systems theory, are now used in other branches of science like biology and economy.

With the irruption of Space Age more than 60 years ago Astrodynamics is born, in which aerospace engineers deal with the new challenges where maneuvers are designed, either through instantaneous impulses or low-thrust propulsion, which allows to modify the natural dynamics. It follows that both orbital and rotational dynamics are treated as problems of control, and optimization techniques acquire a relevant role.

The main objective of this session is to display the state of the art of different problems investigated, as well as the tools which have been developed by the different Spanish research groups. In particular, is it encouraged the presentation of results in the fields of integrability, three and n-bodies solutions, interplanetary motion and propagation of invariant manifolds, KAM theory and reduction, general and special perturbations, relative motion, rotation theory, problems of variable mass, low-thrust propulsion and uncertainty propagation, among others.

**SS 22.**

The observed Earth’s rotation is close to the simple steady rotation of a rigid body around its axis of major inertia. However, the actual Earth is subject to various perturbations that produce deviations from such ideal equilibrium solution and give rise to the precession, nutation and other irregular variations of the motion of the Earth’s figure and rotation axes. These variations are caused by processes acting external to the Earth such as the gravitational attraction of the Sun, Moon, and planets, by processes acting at the Earth’s surface such as fluctuations in the mass transport within the atmosphere and oceans, and by processes acting within the Earth such as core-mantle dissipative torques. Studying the Earth's time varying rotation can therefore be used to gain greater understanding of these and other global-scale processes of the Earth, e.g. the sea level variations.

Knowledge of the Earth's time varying rotation is primarily needed to connect the terrestrial reference frame attached to the solid Earth and celestial reference frame to each other. Knowing the relative orientation of the terrestrial and celestial reference frames and how it varies in time allows the positions of objects such as interplanetary spacecraft tracking stations to be known in both frames and is essential either to observe astronomical bodies from the Earth, or to navigate satellites, pinpointing objects at the Earth’s neighbourhood and observing the Earth system from the space. Those applications impose stringent accuracy requirements on the solutions to the Earth’s rotation and the need of predicting it. In spite of the remarkable advances got in the past decades, our capability to model the Earth’s rotation solution is still insufficient. Accurate prediction entails serious problems of accuracy degradation, either when using stochastic methods, integration of deterministic equations or combined approaches.

The session is conceived to accommodate a variety of mathematical methods with actual or potential capability to contribute to the investigation of the Earth rotation problem and its solution. Fundamentals of methods and specific applications to the actual problem are both welcome. Examples are:

Asymptotic analytical solutions typical of Celestial Mechanics approaches; the scope is not limited to the Earth and can gather other bodies like the Moon or Mercury in spin-orbit resonance states.

Numerical solutions by general-purpose methods of after transformation of the equations of motion into forms allowing the application of special-purpose integrators.

Qualitative study of the Earth’s rotational dynamics; in this field the degree of agreement among observed behaviour and postulated models is still clearly insufficient.

Tools for the analysis of empirical time series of parameters, determined from observations, especially those assumed to have high stochastic excitation like polar motion of length of day and their application; Fourier analysis, filtering, wavelets, statistical techniques, etc.

Empirical modelling of signals and prediction. Basic problems of interest for non-rigid body motion: spin-orbit coupling, anelastic yielding, motion of fluids in cavities, proper frequencies of multi-layered bodies, redundant variables, multiple time scales, symbolic processing, etc.

This session is devoted to advances in pure and applied approximation theory and related areas in their broadest sense: function theory, functional analysis, interpolation spaces and interpolation of operators, numerical analysis, space of functions, special functions, and applications.The goal is to provide a useful and nice forum for researchers in the subjects to meet and discuss.

In last years, the use of new technologies has revolutionized the Education. The use of mathematical software, educational videos and their evolution Courses Massive Open online, are a clear evidence that everything is changing. Any student can learn from a teacher located very far away and solving his/her questions.

So, this session is planned with the objective of exchange experiences in these areas. In addition, we will discuss on new trends and tendencies in the teaching and learing of Applied Mathematics as project-based learning (PBL or PBL), where the development of the subject has the aim of the solution of a real Project, the use of teaching educational platforms or social nets to support the teaching job, and we do not forget to discuss on traditional issues, like what should the approach that we should give to our subjects depending on the degree where are located.

The development of mathematical methods for science attains a special synergy in the case of physical sciences, where traditionally existed a mutual benefit between both disciplines and where many important branches of analysis, algebra and geometry have flourished.

Special attention must be paid to progress in the study of differential equations that arise when modeling physical problems. Mainly the nonlinear case, where we find important

mathematical challenges and advances as much physical interpretation.

The purpose of the Mathematical Physics session of CEDYA + CMA 2017 is to attract researchers in this area and to serve as a forum of discussion and mutual enrichment.

Environmental phenomena have a great social and economic impact. This makes necessary to provide advances in the tools that contribute to improve their planning and management.

In this session, we intend to group presentations on environmental models and its numerical treatment. Especially, we consider the numerical simulation of wind fields, solar radiation, dispersion of pollutants into the atmosphere and the sea, forest fires, as well as the analysis of flows in the subsoil, by using finite elements, finite volumes, or finite differences.

The combination of numerical applications with meteorological predictive models will also be very interesting.

The application of the models in real cases, as well as the adequacy of the tools for practical use in the industry, is one of the objectives of the session.

Discrete Mathematics is a branch of the mathematical sciences which poses a wide range of challenging problems with important applications in all the mathematical fields (Álgebra, Geometry, Topology, Statistics, Graph Theory, Algorithms, Operation Research,..) as well as in many other disciplines as Computer Science, Engineering, Industry, Physics, Biology and others.

This session seeks to bring together participants from the many different environments where discrete mathematics is developed and applied, among them (but not exclusively):

- Algorithms and Data Estructures
- Graph Theory. Complex Networks
- Cryptography
- Complexity Theory
- Combinatorics. Rankings
- Game Theory
- Discrete and Computational Geometry.
- Data Mining
- Probabilistic Graphical Models
- Decision Analysis

All real-life processes are related to forms of uncertainty and imprecision. These two aspects are challenging in both theoretical and computational regards. The main goal of this minisymposium is to present analytical and numerical approaches as well as their applications to real problems.

A large class of applications like collision avoidance cidubannot tolerate that events are neglected just because a stochastic model predicts a relatively small probability. This arouses our interest in an alternative approach to uncertainty which is of more deterministic character.

Sets and multivalued maps lay the foundations for an interesting alternative. Indeed, a set-valued formulation can incorporate “imprecise” modifications of the right-hand side of the modelling differential equations leading to differential inclusions. This set-based notion is completely deterministic and considers all attainable states simultaneously, i.e., in particular, no “rare” events are neglected. Hence, it provides an analytical framework for robustness. Finally nonsmooth state constraints and obstacles can be formulated in terms of sets and handled in terms of level sets.

The notion of vector-valued states evolving along control equations or (more generally) differential inclusions and satisfying state constraints is the starting point of the well-established viability theory. It has already provided useful conclusions about technical and financial applications and so, it represents the first focus of this minisymposium.

Secondly, the talks will concern new results about the dynamics of *set*-valued states. Motivated by deterministic approaches to robust control problems and uncertainty, the analytical challenge is due to simple observation that the underlying basic set for states is just metric, but nonlinear.

A considerable amount of real systems exhibit variables evolving with very different speed. From a mathematical point of view, these systems can be modeled by the so called slow fast systems or singularly perturbed systems. The dynamical behaviour of the singularly perturbed differential systems is specially complex, see for instance the canard phenomenon. The analysis of these systems is carried out in the context of the Geometric Singular Perturbation Theory, and traditionally this theory only applies when the vector field is smooth enough. The extension of the theory to non-smooth vector fields allows revisiting the theory, and their applications, in an easier way both for the definition of the main dynamical objects and for their analytical computations.

The main object of this session is to collect the works on singularly perturbed dynamical systems, slow-fast dynamics, and their applications. In particular, we will focus in neuroscience.

Fluid Mechanics is present in an important number of interesting research fields. Among its diverse applications we mention here the study of blood flow in the presence of clots or the design of nuclear fusion reactors. We also recall those classical problems in the field that have been and continue to be a source of research topics in several areas of Mathematics. This in turn relates to important problems in the fields of mathematical modeling, mathematical analysis and numerical simulation.

From a historical perspective, both posing and solving research problems in Fluid Mechanics has boosted a number of important advancements in Mathematics and has contributed to open new research fields.

Among those mathematical problems considered to be of paramount interest nowadays we find that some of them bear an important relation with Fluid Mechanics and have been the subject of an intense research activity during the recent years. We are currently experiencing a renewed interest in classical problems in the field, e.g. studying multiphase fluids, retrieving non-Newtonian interaction phenomena from first principles or studying viscoplastic and polymeric fluids. These problems, while being motivated by mathematical considerations, have a wide range of applications.

Fluid Mechanics is a well-established research area in España. There are several teams whose research topics cover the various aspects mentioned above, being international reference teams in their respective research areas. Our aim is to gather in this session a representative sample of researchers from the aforementioned teams, with the purpose of presenting the main recent developments and discussing open problems of current interest.

In the last years there have been an increasing scientific and social interest in the simulation of the behaviour of living systems, for example in processes related to the development of human diseases. To this aim, the use of PDEs for the modelling of these phenomena has been increasing, both from a theoretical point of view and numerical analysis and simulation.

The purpose of this session is to show results on EDPs that model the spatial distribution of living organisms interacting with each other or with chemical and / or physical factors in the environment where they live, appearing phenomena that include, among others, self-diffusion, Chemotaxis, haptotaxis, etc.), convection and reaction. Both theoretical and numerical analysis and simulation results would be very interesting for this session.