Thematic Research Programme

The goal of the programme is to discuss recent development in calculus of variations, including variational and geometrical methods in nonlinear differential equations arising from models in physics, including (but not limited to) nonlinear optics, quantum mechanics, liquid crystals and astrophysics. Such problems can often be given a variational formulation, or more precisely, can be formulated in terms of differential equations whose solutions are critical points of a suitable Euler-Lagrange functional. Topics which we would like to particularly emphasize are: segregation, interaction of species and related free boundary problems, semilinear Schrödinger-type equations, curl-curl equations, and nonlocal interaction functionals, but the goal is not limited to them.

Organizing Committee:

• Bartosz Bieganowski, Faculty of Mathematics, Informatics and Mechanics, University of Warsaw, Poland
• Silvia Cingolani, Dipartimento di Matematica, Università degli Studi di Bari Aldo Moro, Italy
• Jarosław Mederski, Institute of Mathematics, Polish Academy of Sciences, Warsaw, Poland
• Jacopo Schino, Faculty of Mathematics, Informatics and Mechanics, University of Warsaw, Poland

Objectives

Our main objectives are to inspire and train young researchers in the area of calculus of variations, faciliate research groups in order to share recent developments in the field, and to enhance collaboration by providing comfortable environment to exchange ideas and projects.

Events

The interest on the field has intensified considerably in the last years. It engages a large community of excellent researchers, many of whom will be involved in this research programme. The problems we consider, including nonlocal equations, strongly indefinite problems and solutions with mass constraints, often require spohisticated and modern tools to build an appropriate framework. For this reason, frequent discussions and brainstorming are very important, therefore we plan to organize several events that serve this purpose.

With the aim of educating students and early-stage researchers, we invite lecturers, recognized experts in the field of calculus of variations, to lead the summer school.

Concerning the conference, being a platform for international collaboration, we invite renowned experts as well as outstanding early-stage researchers from various research institutions and with diverse backgrounds. We also encourage young attendees to participate with contributed talks, so that they can consult senior researchers about their research and ideas.

Additionally, we plan several visits of potential collaborators to consolidate cooperations born during the aforementioned events.

Related events

• Symposium on Nonlinear Analysis in Toruń (with a connected thematic session Variational methods and critical points)
• Session Variational and topological methods in PDEs during the 9th European Congress of Mathematics (9ECM 2024)
• The Sonata grant (funded by National Science Centre, Poland) Variational Problems with Singularities Arising from Mathematical Physics; Principal Investigator: Bartosz Bieganowski

Research Programme Schedule (main and related events)

• 10-14 June 2024: Summer School on Calculus of Variations: variational and geometrical methods
• 17-21 June 2024: Symposium on Nonlinear Analysis in Toruń (a connected thematic session)
• 15-19 July 2024: Session Variational and topological methods in PDEs during 9ECM
• 26-30 August 2024: Conference Variational methods in applications to PDEs