Abstract 

This symposium, organized by Tsinghua University and the Beijing Institute of Mathematical Sciences and Applications (BIMSA), and co-organized by the Institute of Mathematics for Industry (IMI), Kyushu University, and the Faculty of Mathematics and Information Sciences, Warsaw University of Technology, aims to bring together experts from various domains of singularity theory, its applications, and computational intelligence to discuss cutting-edge research developments. The conference will focus on algebraic and geometric approaches to singularity theory, including but not limited to singularities of smooth maps and differential forms, Lipschitz stratifications, symplectic singularities, local invariants, topology of singularities, Hamiltonian systems and their generalizations, and singularities in algebraic geometry. Additionally, the symposium will highlight the crucial role of mathematics in industry, computational intelligence, and nanoscale sciences, particularly nanomedicine, emphasizing mathematical modeling, simulation, and data analysis in interdisciplinary research. Featuring keynote speeches and thematic sessions, the event establishes a cross-disciplinary exchange platform to foster deeper integration between mathematical theories and computational sciences.  

Description of the aim 

The aim of the symposium is to bring together specialists of various domains of singularity theory its applications and computational intelligence. The field of computational intelligence is breaking records in popularity. We are seeing its progress in both new fields of application and ever-improving algorithms. At the intersection of mathematics and computer science, an area of knowledge has emerged that can be said to affect (almost) everyone and is difficult to pass by indifferently. At the meetings of the Symposium, we expect, in this direction, to address issues such as data representation,new methods of computational complexity and many others. We expect invited talks represent various approaches, algebraic and analytic to singularity theory problems based mainly on geometry. The topics are related to algebraic and geometric aspects of singularity theory and its related areas such as Singularities of smooth maps and differential forms, Subanalytic and semialgebraic sets, Lipschitz stratifications, Real algebraic aspects of singularities, Lagrangian and Legendrian singularities, Asymptotic behaviour around caustics and wavefronts, symplectic singularities, local invariants, Singular symplectic, contact and Poisson spaces, Local Algebras of singularities, resolution algebras, Hamiltonian systems and their generalizations, Differential geometry of singularities, Affine invariants of curves and surfaces. Free divisors, Torus actions, Topology of singularities, Singularities in positive characteristics and  singularities in algebraic geometry.  

The proposed Initiative aims also to highlight the importance of mathematics in industry, computational intelligence and nanoscale science, especially nanomedicine. The major role in the theoretical understanding of nanosized materials  is played by mathematics and computational methods. Both methods can provide effective theory and simulations for analysis and interpretation of experimental results, model-based prediction of quantitative and qualitative behaviour, and control of nanoscale systems. Mathematics also plays a vital role in the interaction of these different disciplines, since they all use data, simulation and visualization.  

We plan to use the conference to provide a good exchange platform on exciting new results on singularities and their applications and promote further the development of interactions of mathematical ideas and new branches of practical computational sciences. It is organized  with the special collaboration with IMI – Institute of  Mathematics for Industry, Kyushu University and Faculty of Mathematics and Information Sciences of Warsaw University of Technology.