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Main Objectives
The primary objectives of the TAG are:
• To promote and consolidate international collaboration within the ANPDE community, which connects numerous research groups from institutions spread across Europe and beyond. The network gathers experts in nonlinear analysis, partial differential equations (PDEs), and topological and variational methods, providing a fertile environment for interdisciplinary interactions.
• To enhance the engagement and research skills of PhD students and postdoctoral fellows, within established ANPDE groups. Special attention will be given to gender balance, diversity, and the inclusion of researchers from developing or less research-intensive regions.
• To initiate and coordinate cross-institutional research initiatives addressing contemporary challenges in topological and nonlinear analysis, while establishing a solid foundation for future European project proposals.
Scientific Themes
The strategic focus will center on the application of topological, variational, and analytical methods to the study of nonlinear partial differential equations (PDEs) arising in physics, geometry, and biology. The proposed research themes include, but are not limited to
• Dispersive PDEs and Fluid Mechanics. Analytical study of nonlinear dispersive equations and fluid dynamics, including wave propagation, nonlinear Schrödinger and wave equations, Euler and Navier–Stokes systems. Topics include well-posedness, long-time behavior, stability, singularity formation, turbulence, and the interplay between dispersive effects and nonlinear dynamics.
• Geometric and Conformal PDEs. Investigation of existence, multiplicity, and qualitative properties of solutions to elliptic and parabolic equations with geometric significance—such as Yamabe-type problems, Liouville equations, and curvature prescription problems—arising in conformal geometry.
• Interfaces Between Nonlinear Analysis and Mathematical Physics. Exploration of PDE models bridging nonlinear analysis, geometry, and quantum mechanics, including semiclassical limits, multi-scale phenomena, and nonlocal or fractional operators.
• Nonlinear Schrödinger and Coupled Systems. Analytical and variational study of Schrödinger-type systems modeling Bose–Einstein condensates, optical solitons and dynamic of populations with Lotka–Volterra interactions . Topics include standing wave solutions, symmetry breaking, concentration phenomena, and stability analysis.
• Topological Methods in Nonlinear Analysis. Development and refinement of degree theories, critical point theorems, bifurcation and continuation principles, for nonlinear operators in infinite dimensional settings.
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