Interactions of Geometry with Algebra and Applications (INTERGAP)
Interactions of Geometry with Algebra and Applications (INTERGAP)
FPI predoctoral Research Position: PID2023-146936NB-I00 - Interactions of Geometry with Algebra and Applications (INTERGAP)
Information
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)
To apply
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:
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)
Our Group
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.
Principal Investigators
Researchers
Research Lines
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.
Geometry and Applications Block
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:
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:
GEOBOT1: The hybrid computer
GEOBOT2: Mechanical Modelling of Cloth and Planning for Robotic Manipulation of Cloth
Algebra and Applications Block
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:
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:
BIOALG1: Algebraic substitution models
BIOALG2: Identifiability and phylogenetic reconstruction
We welcome applications from motivated candidates eager to contribute to cutting-edge research in geometry, algebra, and their broad applications.