Akademik Veri Yönetim Sistemi
TÜBİTAK - AB COST Projesi , 2025 - 2029
The mathematical concept of "space" provides a foundational framework for modeling a vast array of physical and synthetic systems, from curved spacetimes in general relativity to vector representations of words in natural language processing [M+13]. These mathematical models rely upon choosing suitable spatial and/or temporal setups, and call for an appropriate version of the Laplacian to describe fundamental properties like evolution dynamics, conservation laws, or quantum phenomena. Pinning down an appropriate spatio-temporal setup may be delicate when multiscale phenomena occur, that is, when important features of a system appear at different space/time/randomness scales. mSPACE will be committed to advancing the mathematical foundations of battery technology, which embody the challenges of multiscale issues well. In electrode materials, the highly heterogeneous morphology on the nanoscale and microscale strongly influences deterministic and dynamic transport phenomena on the macroscale: these, in turn, are crucial for the performance of the battery. While continuous spatial geometries are still canonical in many fields, graphs and other branched models displaying a coarser nature offer a valuable complementary perspective for describing interconnected systems. The interplay between discrete and continuous frames has been a fundamental change of paradigm [Gow00, Lov10] which is, in many regards, still resonating. For instance, the mathematical foundations of topological data analysis [CM21] and image processing [BB22] are prominent combinations of toolboxes borrowed from discrete and continuous mathematics, while discrete-to-continuous spectral convergence is key for the mathematical justification of manifold learning [MZ24]. The implication of these fields in critical technology areas like artificial intelligence and digital health are, thus, long-term applications of new mathematical ideas. In fact, the interacting agents of a system are often subsystems themselves, with their own internal dynamics causing evolving interconnections which have to be recognized and modeled too. For example, global climate change compels us to better understand how the Earth's complex, interconnected network of living and non-living processes, operating and interacting across very different length and time scales, shapes our planet's habitability [R+19]. Brain networks provide a further example which is based both on predefined spatial structure, as well as on correlations between different parts of the brain [Spo11], and on motifs for hormonal systems [NT08]. These and further systems’ resilience, efficiency, or adaptability can be evaluated by mathematical measures. Introducing centrality measures that accurately capture subtler features is a key challenge in the theory of complex systems: so far, this task has been pursued to a large extent by applying Laplacian-based methods of discrete mathematics [CL06, BV14, DSP18]. Generalizing these toolboxes to structures with richer topology, like hypergraphs or multilayer networks, and studying their behavior for systems of increasing size is a goal that mSPACE aims to achieve by bringing together experts in pure mathematics, modeling and applications. To provide a unified mathematical set-up for differently grained spatial structures, cutting-edge techniques in the area of non-smooth analysis have been developed through the extension of Laplacian-based notions such as spectrum, diffusive processes or functional inequalities, to environments without a canonical spatial structure [Stu06, Oll09, Gig15, CM17]. Many time-dependent physical systems are dynamically driven by energy minimization principles, corresponding to gradient flow structures [AGS08]. The theory of optimal transport has benefited from recent advances in numerical methods to become increasingly influential throughout mathematics, computer science and beyond [Vil10, PC19, BD23]. The interplay of gradient flows with the theory of optimal transport has proven highly influential (Villani’s and Figalli’s Fields medals in 2010 and 2018, respectively) and furnished fruitful applications in spectral comparison of geometric structures (notably including manifolds and networks), sampling for inference in Bayesian statistics, or training of neural networks via stochastic gradient descent [DHS11, KB15, Fig17]. Indeed, a deterministic approach is not enough to model the evolution of a system which may follow unpredictable rules, or whose geometry may be so poorly understood as to be aleatory for all purposes. It is, thus, natural to let randomness enter the picture. In this regard, stochastic methods have been a crucial driving force in the mathematical analysis of physical systems, as exemplified by the achievements of Parisi (Nobel Prize 2021) and Talagrand (Abel Prize 2024) in explaining the behavior of spin glasses. Percolation theory is another relevant example of the interplay between stochastics, statistics, and physics [HS21], which lies at the core of many modern developments in natural sciences. Among them, let us emphasize the recent breakthroughs in materials science [Mit21, Sah23] which notably aim at enhancing photovoltaic materials, developing better insulating materials, or boosting the efficiency of batteries — a cornerstone of the EU’s Industrial Strategy and the Green Deal Industrial Plan. mSPACE will endeavor to match newly introduced mathematical notions with the concrete demands of materials science and actively explore other potential fields of application, like network design optimization. To this end, the Action will bring together stakeholders with different scientific backgrounds to advance fundamental research, to facilitate knowledge transfer, and to make long-term breakthroughs possible. Through networking and dissemination, this collaboration bears great promise of advances for the European research landscape, and in fact for the whole European society. Historically, research and technology transfer in these fields has been unevenly distributed among COST countries. To address this imbalance, the Action will prioritize increased engagement with stakeholders from regions with lower research output. By leveraging COST's educational and networking programs, such as Training Schools and Short-Term Scientific Missions, mSPACE will actively seek to include these stakeholders in the network. This will foster stronger connections with non-academic entities and catalyze collaborations between European laboratories and startups focused on the green transition.