# Open call for PhD positions (Ministry of Science) 2018

# Open call for PhD positions (Ministry of Science) 2018

**Application deadline**

**29 October 2018, 15.00 (CET)**

Applications must be done through the **Ministry web page **(in Spanish).

The call opened on 9 Oct 2018.

The **Spanish Ministry of Science, Innovation and Universities **has opened the PhD positions listed below.

Interested candidates should contact the corresponding PIs.

The call will NOT be handled by BGSMath.

Application deadline

**29 October 2018, 15.00 (CET)**

Applications must be done through the **Ministry web page **(in Spanish).

The call opened on 9 Oct 2018.

The **Spanish Ministry of Science, Innovation and Universities **has opened the PhD positions listed below.

Interested candidates should contact the corresponding PIs.

The call will NOT be handled by BGSMath.

#### Additional information

##### 2 PhD positions in BGSMath are opened in the following areas associated to the "María de Maeztu Unit of Excellence" (MDM-2014-0445):

- Analysis & PDEs. PI: Xavier Cabré (xavier.cabre@upc.edu)

- Algebra, geometry, topology. PI: Rosa María Miró-Roig (miro@ub.edu)

##### 8 additional positions associated to the following research projects:

**MTM2017-82166-P**: Geometric, algebraic and probabilistic combinatorics.

PI: Oriol Serra, Juanjo Rué

*Abstract*

*A potential candidate must have a strong background in combinatorics, graph theory and related topics in computer science. She/he will work in the context of our research group GAPCOMB in one of the following areas: finite geometries, additive combinatorics and combinatorial number theory, random graphs, analytic combinatorics and matroids.*

——————————-**MTM2017-84214-C2-1-P**: Ecuaciones en derivadas parciales: problemas de reacción-difusión, integro-diferenciales y geométricos

PI: Xavier Cabré

Abstract

*This project concerns the analysis of Partial Differential Equations and their applications. Our main topics of interest are: regularity theory for nonlinear elliptic and parabolic integro-differential equations; the study of nonlocal minimal surfaces; stable solutions to local and nonlocal reaction-diffusion elliptic equations; Sobolev and isoperimetric inequalities for classical or fractional perimeters.*

——————————-**MTM2017-86795-C3-3-P**: Holomorphic dynamics

PI: Núria Fagella

*Abstract*

*Dynamical systems coming from the iteration of complex analytic functions form a very special class of systems, which exhibit interesting fractal invariant sets in their phase spaces. In this project, we concentrate on the global dynamics of meromorphic maps with an essential singularity at infinity. These may include systems coming from numerical methods, like Newton’s method of entire maps, studied on the whole complex plane.*

——————————-**MTM2017-86795-C3-1-P**: Sistemas dinámicos en baja dimensión y aplicaciones

PI: Lluís Alsedà

*Abstract*

*This project focuses on the study of combinatorial dynamics and combinatorial objects: permutations, graphs, etc. Also it considers the most complicated case of combinatorial dynamics and entropy in quasiperiodically forced systems.*

*The project is structured along the following lines and goals:**Line 1. Low-dimensional topological and combinatorial dynamics*

*Goal 1.1. Cycles and entropy in discrete dynamical systems*

*Goal 1.2. Rotation theory and periods of graph maps*

*Line 2. Applications to astrodynamics and complex multilayer networks*

*Goal 2.1. Multilayer network overlap and epidemic containment strategies*

*Goal 2.2. Globalization of dynamics around collinear hover points.*

*Goal 2.3. Applications of the parametrization method to astrodynamical models.*

*Line 3. Qualitative theory of differential equations*

*Goal 3.1. Monotonicity in generalized Lotka-Volterra quadratic centres*

*Goal 3.2. Centre Mechanisms in Generalized Abel Equations*

*Line 4. Quasi-periodically forced systems*

*Goal 4.1. Numerical and analytical studies on SNA*

*Goal 4.2. Numerical and semi-analitic computation of invariant objects using wavelet bases*

*Goal 4.3. Quasi-periodically forced complex systems.*

——————————-**MTM2017-83487-P**: Structure and classification of rings, modules and C*-algebras: interactions with dynamics, combinatorics and topology

PI: Pere Ara

*Abstract*

*We will study several questions and problems concerning the structure and the classification of rings and algebras, through the use of suitable invariants associated with these objects and their module categories. We will initiate a study of Homological Algebra for the category Cu of Cuntz semigroups, studying the structure of the injective objects, and duality theory with respect to them. We will analyse the type semigroup of dynamical systems on the Cantor set, and the relationships with the non-stable K-theory of the crossed product algebras. We will study the structure group of a finite multipermutation solution of the Yang-Baxter equation, and advance in the problem of classifying the finite simple left braces. We will explore the structure of the pure projective modules over commutative Noetherian rings, with special emphasis in the class of direct sums of Maximal Cohen-Macaulay modules.*

——————————-**MTM2017-85666-P**: Probabilistic and geometrical aspects of function theory

PI: Artur Nicolau

Abstract

*We present a research project in an area where Classical Analysis interacts with Stochastic Processes and Partial Differential Equations, organized in three sections.*__Dyadic martingales and the Zygmund Class__. We plan to describe the closure of the space of Lipschitz functions in the Zygmund class and its discrete analogue, which concerns the closure of bounded dyadic martingales in the space of dyadic martingales with bounded jumps. A version of Kolmorogorov’s Law of the Iterated Logarithm for the oscillation of functions in the Besov space will also be considered.__The p-Laplace Equation__. We propose several open problems related to p-harmonic functions and its associated mean value property, such as the unique continuation problem, the optimal regularity for p-harmonic and infinity-harmonic functions, the asymptotic mean value property for the p-Laplacian and the existence of functions satisfying certain nonlinear mean value properties in the Euclidean space or in the more general setting of measure metric spaces.__The Nevanlinna Class__. Several spectral problems, such as the description of the Hidden Spectrum and the Weak Embedding Property introduced by N. Nikoslki, will be considered in the context of the Nevanlinna class. We will also consider problems in the context of the Nevanlinna classweighted approximation in the Nevanlinna class, which can be understood as natural analogues of the Garnett-Jones problem, one of the main open problems in the area. Finally, we will study geometric properties of the critical points of inner functions in Hardy-Sobolev spaces, and their relation to dynamical properties of the mapping from the unit circle into itself given by the inner function.

*——————————-*

**MTM2017-83499-P**: Holomorphic function spaces and point processes

PI: Carme Cascante, Joaquim Ortega-Cerdà

Abstract

*The project has two main lines of research: one is centred in classical function theory problems and operator theory, mostly in functions of several complex variables. The other is a relatively new line. We use techniques of complex analysis, mainly exploiting the structure of reproducing kernel Hilbert spaces of some function spaces defined on manifolds, to define processes of points with good statistical properties. We plan to**pursue both research lines and explore their potential interactions.*

*——————————-***BFU2017-86026-R**: Dinámica de los circuitos neuronales distribuidos en la toma de decisiones.

PI: Klaus Wimmer

*Abstract*

*This is an interdisciplinary project in the research area of “computational neuroscience”. The neural basis of decision making and working memory has been studied extensively, yet our understanding of how distributed circuits in the brain perform these cognitive functions is only at the beginning. Mathematical models of cortical circuits can shed light on the underlying neural network dynamics. The PhD project combines the development and analysis of such models with cutting-edge analysis of large-scale neural activity recordings (neuronal population recordings, fMRI, EEG).*