Duration: 4 years

Salary (approx. before taxes):

• 1st year: ~€19,479

• 2nd–4th years: ~€24,348/year

Additional Benefits:

• Teaching opportunities with additional remuneration

• €7,000 for research stays abroad

Contact: eva.miranda@upc.edu, josep.alvarez@upc.edu 

Application THROUGH the website of the university open 14/10/2024 a 09:00 until a 27/10/2024 a 14:00 (Europe/Madrid / UTC200)

Interested individuals must complete the form available in the corresponding procedure on the UPC electronic headquarters: Call for applications for predoctoral contracts for the training of doctors, and attach the required documentation as well as confirm the submission of the form.

Documentation: (point 8 of the call) see the Application Submission section.

• A copy of a valid DNI, NIE, or passport. A copy of the passport is required only for foreign nationals not residing in Spanish territory, as residents must submit a copy of their NIE.

• Curriculum vitae in Catalan, Spanish, or English (use the document template provided on this webpage).

• Academic certificate of the qualifications obtained at the time of submission, indicating the completion date of the studies, the grades obtained, and the dates they were awarded, corresponding to the subjects that make up the full program of the stated degrees.

• For certificates issued by foreign institutions, the maximum and minimum grades within the respective grading system, as well as the minimum passing grade, must also be included. If the academic certificate is issued in a language other than Spanish or English, an official translation into one of these two languages must be provided.

• In the case of studies completed abroad: declaration of equivalence of the average grade of undergraduate and master's studies, using the form provided by the Ministry of Universities.

• Document accrediting a disability degree of 33% or higher, in the case of applicants applying under the disability category.

In order to apply you need to follow the link: https://eadministracio.gdc.upc.edu/formulariTramitGeneric/CONV_AJUTS_CONTRACTES_PREDOC_FORMACIO_DOCTORS_UPC_2CONV?lang=en (If you are from the EU)

Otherwise follow the link: https://eadministracio.gdc.upc.edu/formulariTramitGeneric/noaut/CONV_AJUTS_CONTRACTES_PREDOC_FORMACIO_DOCTORS_UPC_2CONV

More information on application:

https://rdi.upc.edu/ca/financament/carrera-investigadora/r1/ajuts-formacio-de-doctors-2024/ajuts-formacio-de-doctors-2024

If you have doubts or concerns about the application contact: eva.miranda@upc.edu, josep.alvarez@upc.edu 

Application open 14/10/2024 a 09:00 until a 27/10/2024 a 14:00 (Europe/Madrid / UTC200)

We are an internationally recognized research group at the forefront of geometry and algebra, with a strong tradition of exploring their interactions. Our work spans the cutting edges of Poisson and Symplectic Geometry and the intersection of Commutative Algebra and Algebraic Geometry. Beyond pure mathematics, we tackle interdisciplinary challenges in Biology, Robotics, Astrodynamics, Computer Science, Fluid Dynamics, and Physics. Led by Eva Miranda and Josep Álvarez, our group includes renowned researchers like Maria Alberich, Jaume Amorós, Miguel Ángel Barja, Guillem Blanco, Marta Casanellas, Jesús Fernández, Marco Gualtieri, Marta Mazzocco, and Francesc Planas. Visit our website  for more details.

Our research is organized into two main blocks: Geometry and Applications (led by Eva Miranda) and Algebra and Applications (led by Josep Álvarez). These blocks interact dynamically, sharing ideas across themes like singularity theory, cohomology, Floer homology and computational methods, with the goal of advancing both theoretical and applied aspects of Mathematics and Physics.

1.Singular Symplectic Geometry, its Mirrors, and Applications
This line explores the impact of singularities on geometrical structures, with applications ranging from celestial mechanics to fluid dynamics. Building on Miranda’s pioneering theory of b-symplectic structures, we address long-standing open problems like the Weinstein and Arnold conjectures and develop key tools in Floer homology.  We also plan to consider classification problems concerning group actions and integrable systems, using cutting-edge geometrical and topological techniques in contact and symplectic geometry.  We plan to use geometrical and topological techniques in contact and symplectic geometry to tackle open challenges in the Euler and Navier-Stokes equations, which are foundational to understanding the complexity of fluid motion.
Concrete Goals:

1. • GEO1: Generalized singular Weinstein conjecture

   • GEO2: Floer homology and Arnold conjecture

   • GEO3: Poisson manifolds as limits of E-symplectic manifolds

   • GEO4: Group actions, quantization, and the [Q,R]=0 conjecture

   • GEO5: Singular Mirrors and Fluid Dynamics

   • GEO6: Applications to the complexity of Fluid Dynamics

   • GEO7: Applications to Physics, including General Relativity, galaxy morphology, and astrodynamics

2. GEOBOT: Applications of Differential Geometry to Computer Science and Robotics
This innovative line leverages advances in geometry and algebra to drive progress in robotics and computer science. A key focus is the development of a fluid computer that mimics computational processes via fluid dynamics, opening exciting possibilities for creating hybrid computers that combine fluid mechanics with quantum field theory, potentially outperforming current quantum computing models. We also apply geometric techniques to simulate realistic cloth behavior for robotic manipulation, driving advancements in neural networks and robot control.
Concrete Goals:

1. • GEOBOT1: The hybrid computer

   • GEOBOT2: Mechanical Modelling of Cloth and Planning for Robotic Manipulation of Cloth

1.Algebraic and Geometric Aspects of Singularities
This line investigates singularities from an algebraic perspective, focusing on key structures like Bernstein-Sato polynomials, Hodge spectral numbers, and multiplier ideals. We aim to solve deep problems in stratification of singularities, a central topic in algebraic geometry with far-reaching implications for deformation theory. Additionally, we study the geography of fibred varieties, focusing on the role of slope inequalities in understanding the geometry of singular varieties, an important question in both mathematics and theoretical physics.
Concrete Goals:

1. • ALG1: Stratification by roots of Bernstein-Sato polynomials

   • ALG2: Limit distribution of Hodge spectral numbers

   • ALG3: D-modules over singular varieties

   • ALG4: Geography of fibred varieties

   • ALG5: Prime ideals in three-dimensional regular local rings

2.BIOALG: Applications to Phylogenetics
This line uses algebraic geometry and statistics to solve problems in phylogenetics, the study of evolutionary relationships among species. By employing algebraic methods, we go beyond traditional parameter estimation, tackling complex evolutionary networks with models tailored for amino acid substitutions and phylogenetic reconstruction. Our work has applications in evolutionary biology and artificial intelligence, addressing challenges such as model selection and identifiability in complex data sets.
Concrete Goals:

1. • BIOALG1: Algebraic substitution models

   • BIOALG2: Identifiability and phylogenetic reconstruction