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Geometry and topology of varieties, algebra and applications

Total activity: 31
Type of activity
Competitive project
Funding entity
MIN DE ECONOMIA Y COMPETITIVIDAD
Acronym
GAP
Funding entity code
MTM2015-69135-P
Amount
182.226,00 €
Start date
2016-01-01
End date
2019-12-31
Keywords
cohomología de haces, cosmology, cosmología, fibraciones, fibrations, filogenética, phylogenetics, sheaf cohomology, singularidades, singularities, symplectic and Poisson manifolds, variedades simplécticas y de Poisson
Abstract
This project focuses on various aspects of the areas of algebraic geometry, symplectic geometry, commutative algebra, algebraic topology
and their interactions, and their applications to biology, physics and robotics. We propose to approach the problems considered both from
the traditional view of research in mathematics and from a multidisciplinary perspective on the part of applications.
This project is the continuation of MTM2012-38122-C03-01, which has been very successful and has had a major impact both within the
mathematical community and other disciplines and even outside the scientific community (to name a few indicators, we have 160
publications since 2005, the group's work has received more than 700 citations according to Scopus and there are members of the group
with h-index between 6 and 8). The current group has 23 researchers; 15 of them doctors (of which 11 are senior and 4 are postdoc) and 8
tPhD students.
In the last decades, algebraic geometry has experimented a spectacular development in interaction with affine
areas of research. For instance, some ideas of algebraic geometry find its generalization in symplectic geometry; in Poisson Geometry, the algebraic techniques are omnipresent in the study of generalized complex geometry also the algebraic topology techniques
are present in the modern homotopy theory of schemes. Other examples of interaction of disciplines is observed in the recent applications
of geometric analysis techniques to the realm of Poisson Geometry and Complex geometry.
In this project we will keep on exploring the connection among these areas and we will endeavour to solve important problems relative to
known conjectures such as Xiaos conjectures for irregular varieties in Algebraic Geometry, Voevodskys nilpotence conjecture in K-theory
or the conjecture of Guillemin-Sternberg concerning quantization and reduction for symplectic manifolds and their generalizations, or the
Sturmfels-Sullivant conjecture on phylogenetic varieties.
Given the success of the results obtained in the preceding project, in this project we plan to consolidate the interdisciplinary aspects of the
project. A strong mathematical component is observed in the publications of the group in the areas of biomathematics, robotics and
physics. Notwithstanding, those results can really be applied to those disciplines as observed in the list of high-impact journals where
these results are published (Nature Methods, Systematic Biology, Molecular Biology and Evolution, BMC Evolutionary Biology,
International Journal of Computer vision, Physical Review Letters, Journal of Cosmology and Astroparticle Physics, Physical Review D,
Physical Reviews E).
Our team collaborates with various national and international groups. We enclose details of the collaborators in the scientific proposal and
highlighting now the following national collaborative centers: ICMAT, IRI, Centre for Genomic Regulation, UAB and UB and international:
MIT-Northeastern, U. Pavia, U. Bayreuth, U.Kansas, U .Leicester, KU Leuven, UC Berkeley, Mathematical Institute of the Polish Academy
of Sciences, U. Tasmania, New Zealand Biomathematics Research Centre.
Scope
Adm. Estat
Plan
Plan Estatal de Investigación Científica y Técnica y de Innovación 2013-2016
Call year
2016
Funcding program
Programa Estatal de Fomento de la Investigación Científica y Técnica de Excelencia
Funding subprogram
Subprograma Estatal de Generación de Conocimiento
Funding call
Excelencia: Proyectos I+D
Grant institution
Gobierno De España. Ministerio De Economía Y Competitividad, Mineco

Participants

Scientific and technological production

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