PI1: Antonio ViruelPI2: Aniceto Murillo Abstract: The aim of this project is to study higher structures in both Differential Geometry and Homotopy Theory. So we plan to attain the following goals: (O1): On L-infinite algebras: We give a completely new approach to rational homotopy theory from the Quillen framework which extends his theory and will …
Higher structures in Differential Geometry and Homotopy Theory Leer más »
PI1: Antonio Rojas León PI2: Luis Narváez Macarro Abstract: In this project our goal is to study different problems related to Algebraic Geometry and Number Theory. Specifically, we have divided the work plan in 5 reseach lines: (A) Differential structures and cohomological methods in Algebraic Geometry and Singularities. It is divided in two sub-lines, corresponding …
PI1: Fernando Muro PI2: Juan González-Meneses Abstract: Problems in low-dimensional topology, traditionally linked to group theory, are being currently treated by means of homological methods. In upper dimensions the use of higher categories has led to solutions of long-standing open problems. Higher homotopical structures are being used in such diverse topics as quantum field …
Cross-cutting challenges in homotopy theory, knots, and groups Leer más »
PI1: Fernando Muro PI2: Ramón J. Flores Abstract: Since their inception as fields of science at the beginning of the XX century, topology and group theory have followed parallel path more often than not. Interaction between them are prevasive. For instance, unstable homotopy theory grew interwoven with finite and compact Lie group theory. The modern …
PI: Fernando Muro Abstract: Triangulatec categories play a central role in several areas of mathematics and theoretical physics. However, this algebraic structure is not yet known well enough. There are upsetting results related to invariants such as K-theory: we know there cannot be any reasonable K-theory for triangulated categories, yet we can recover the …
Triangulated structures in algebra, geometry, and topology Leer más »
PI1: Sara Arias de ReynaPI2: Francisco J. Castro Jiménez Abstract: Our project comprises different areas of mathematics, namely D-module theory, singularities, representation theory and number theory. We propose a series of open problems at the frontier of mathematical knowledge, including questions of a theoretical as well as computational nature. These problems concern cohomology, quasi-free divisors …
Algebra, singularities, number theory and applications Leer más »
PI1: Francisco J. Castro JiménezPI2: Mercedes Rosas Celis Abstract: The project deals with applications of Computer Algebra Methods to D-module theory and singularities, Representation and invariant theory, algebraic combinatoric, Lie, Leibniz and Malcev algebras and integer programming. Partners: Centro Informático Científico de Andalucía (CICA), The Singular Group (TUK Kaiserslautern), Addlink Software Científico SL. Implied …
Computational Methods in Algebra, D-modules, Representation Theory and Optimization Leer más »
PI1: Fernando Muro PI2: Juan González-Meneses Abstract: Problems in low-dimensional topology, traditionally linked to group theory, are being currently treated by means of homological methods. In upper dimensions the use of higher categories has led to solutions of long-standing open problems. Higher homotopical structures are being used in such diverse topics as quantum field theories …
Cross-cutting challenges in homotopy theory, knots, and groups Leer más »
PI: Juan González-Meneses Abstract: Braids groups are mathematical objects of particular relevance, as they appear as an important component in several fields of Mathematics, not only in Group theory but also in Knot Theory, Geometric Theory of surface automorphisms, Algebraic Geometry or even Cryptography. This project brings together a team of first level specialists in …
Braids: Knots, Garside Groups and Mapping Class Groups Leer más »
PI: Juan González-Meneses (coordinator) Abstract: The Spanish Topology Network is a 25-years old organization of topologist in Spain, with 10 nodes all around Spain and researchers from around 30 research projects in Topology. It organizes annually the Spanish Topology Meeting, and the Spanish Meeting of Young Topologists. Source of Funding: Excellence R+D networks / …
