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Geometry, Algebra, Topology, and multidisciplinary Applications

Total activity: 4
Type of activity
Competitive project
Acronym
GATA-TECH
Funding entity
AGENCIA ESTATAL DE INVESTIGACION
Funding entity code
PID2019-103849GB-I00
Amount
160.809,00 €
Start date
2020-06-01
End date
2024-05-31
Keywords
D-modules, D-módulos, b-simpléctico, b-symplectic, cohomology, cohomología, cosmology, cosmología, cuantización, filogenética, periodic orbits, phylogenetics, quantization, robotics, robótica, singularidades, singularities, variedades, varieties, órbitas periódicas
Abstract
The present project is the sequel of MTM2015-69135-P which has had a great impact inside and outside the mathematical community.
Just to mention some indicators: In the last 10 years our research team of 12 permanent members at UPC has a total of 192 publications
and 1438 citations according to Scopus and several members have h-index between 9 and 12. We now present an extended group with 8
Phd students, 5 postdocs and 5 senior researchers abroad in the working group, so a total of 30 members.
Our research is addressing fundamental questions in several areas of Mathematics focusing on Geometry, Algebra, Topology and it is
multifaceted with a view towards interactions among different research branches and applications to Biology, Celestial mechanics,
Robotics and Physics. Our publications in these areas have a strong mathematical component and the impact of the applications to those
disciplines is reflected by the high-impact journals where these results are published like Systematic Biology or Physical Review Letters.
In the last decade we have become active contributors in interdisciplinary science and we are now focused on both a theoretical point of view and the transversal applications: Yanos conjecture, Shimodas conjecture, singular Weinstein conjecture, the
Riemann-Hilbert correspondence for D-modules over singular varieties, Baez conjecture, minimal models and formality of operads,
phylogenetic reconstruction and machine learning, reconstruction in robotics, quantization and rigidity and flexibility for singular objects are
just some of the challenging goals on our to-do-list for the next 4 years.
One of the strengths of our group is the interaction among different lines either in the theoretical or the multidisciplinary sides. This
interaction is bidirectional. More theoretical mathematics are applied to multidisciplinary sciences for instance algebraic statistics is an
interdisciplinary field that uses tools from algebraic geometry, commutative algebra, combinatorics, and their computational sides to
address problems in statistics and its applications. Sometimes multidisciplinary sciences serve as an inspirational white canvas where
formulas are written in pure maths enhancing theoretical advances. This is the case of the Weinstein conjecture on the existence of
periodic orbits considered in this project where inspiration comes from the restricted 3-body problem in Celestial Mechanics where periodic
orbits accumulate close to the line at infinity (observed by Poincaré) giving rise to singularities which play a central role in the project.
In this project this multidisciplinary to theoretical inspirational trend appears in the following binomials: Robotics/persistent homology,
Phylogenetics/embedding of Markov matrices and quantum states/geometric quantization. Interplay among other lines as Algebraic
Geometry and Commutative algebra and also Geometry and Dynamical Systems will also be exploited: Algebraic geometry and
commutative algebra have always been closely intertwined but recently there has been a big interest from the birational geometry
community in the use of algebraic positive characteristic methods as a complementary of resolution of singularities. Geometry, Topology
and Dynamics will interplay at different levels including applications of the h-principle to Fluid Dynamics, Floer homology to periodic orbits,
group actions to perturbation and KAM theory and to planar polynomial vector fields.
Scope
Adm. Estat
Plan
PLAN ESTATAL DE INVESTIGACIÓN CIENTÍFICA Y TÉCNICA Y DE INNOVACIÓN 2017-2020
Resoluton year
2020
Funcding program
PROGRAMA ESTATAL DE GENERACIÓN DE CONOCIMIENTO Y FORTALECIMIENTO CIENTÍFICO Y TECNOLÓGICO DEL SISTEMA DE I+D+I
Funding subprogram
SUBPROGRAMA ESTATAL DE GENERACIÓN DE CONOCIMIENTO
Funding call
PROYECTOS DE I+D DE GENERACIÓN DE CONOCIMIENTO (ANTIGUES EXC)
Grant institution
Agencia Estatal De Investigacion

Participants

Scientific and technological production

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