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mSPACE COST Action
About mSPACE
mSPACE (multiscale Stochastics, Patterns, and Analysis of Combinatorial Environments) is a COST Action dedicated to developing a unified mathematical framework for multiscale systems. Such systems arise when interactions across different spatial, temporal, and stochastic scales jointly determine the behavior of natural and engineered phenomena.
Multiscale systems are ubiquitous: from porous materials and battery electrodes, to complex networks in biology, ecology, and social systems, and to hybrid discrete-continuous structures encountered in data science and physics. mSPACE brings together researchers in analysis, geometry, probability, and combinatorics to address the theoretical challenges posed by these systems and to translate mathematical insights into real-world applications.
mSPACE poses a strong emphasis on bridging discrete and continuous models, combining spectral theory, gradient flows, stochastic geometry, and optimal transport. The Action fosters interdisciplinary collaboration, knowledge transfer, and capacity building across Europe, with a strong commitment to inclusiveness, gender balance, and the involvement of early-career researchers.
Aims, Objectives, and Background
Background
Traditional mathematical models often focus on a single scale or on either discrete or continuous structures. However, modern scientific and technological challenges––such as materials design for the green transition, network resilience, and data-driven modeling of complex systems––require tools capable of handling multiple interacting scales, non-smooth geometries, and randomness.
Recent advances in areas such as spectral geometry, optimal transport, stochastic processes, and non-smooth analysis provide powerful but often disconnected tools. mSPACE responds to this fragmentation by creating a coherent and flexible framework that integrates these approaches.
Main Aim
The overarching aim of mSPACE is to construct a unified mathematical framework to study multiscale geometrically structured spaces using analytic, combinatorial, and stochastic methods, and to tailor this framework to a broad range of applications, particularly in materials science and complex systems.
Specific Objectives
Research Coordination Objectives
- Leverage research collaborations across mathematical subfields and geographic areas.
- Delve into transferable models from applied sciences; translate them into the frameworks of spectral geometry or gradient flows.
- Utilize discrete analysis models as insightful, computationally efficient test cases.
- Bridge the divide between applied research focused on discrete and continuous metric spaces by employing the unifying power of gradient flows and spectral geometry.
- Harness the synergy between established spectral theory and optimal transport with the cutting-edge tools of random geometry.
- Achieve advances in materials science, complex systems analysis, and beyond.
Capacity-Building Objectives
- Establish a sustainable and inclusive network of European researchers across genders, studying discrete and continuous spatial models using analytic and statistical methods.
- Bridge separate mathematical areas (from optimal transport to graph theory and spectral theory) to unlock breakthroughs in the analysis of complex systems.
- Promote collaboration between researchers from Inclusiveness Target Countries (ITC) and those from non-ITC, with a particular focus on empowering Young Researchers (YRs).