The study of regular and coherent spatio-temporal structures in nature has fascinated scientists for centuries, ranging from the formation of the regular chemical precipitates, to solitary waves, or to the studies in biological form and structure. Arising out of these various disciplines, the mathematical study of patterns has blossomed over the past 70 years, with patterns being observed and studied in nearly every area of science, from fluids, chemistry, material science, ecology, and numerous areas of biology. Correspondingly, a mathematical theory of patterns has grown alongside these developments, drawing from, and helping advance, multiple areas of mathematics, including dynamical systems, partial differen- tial equations, and numerical computing. It has has played a prominent role in several SIAM activity groups and their bi-annual conferences, including Dynamical Systems, Nonlinear Waves and Coherent Structures, Material Science, and Analysis of PDE, through various plenary talks and minisymposia. Indeed, pattern formation was one of two minitutorials at the recent SIAM DS 23 meeting.

This summer school will study the current frontiers of research in the mathematical study of patterns, with a particular emphasis on the study of patterns in multiple space dimensions. Planned courses will highlight the important aspects of the known theory (mainly focusing on developments in the past 20 years), while providing a spring board for students to begin work in the frontiers of the field. The topics and methods proposed for this summer school are regularly used in research, but span several different areas of mathematics and are generally not taught in a unified manner in the standard graduate curriculum. Courses and tutorials will be give on the following topics:

•  existence theory of patterns

•  stability theory of patterns,

•  numerical continuation of patterns, 

•  use of computational algebraic geometry to study patterns

•  computer assisted proofs.

The summer school will be held at Concordia University, Montreal, Quebec, CA. In person attendance is required. Graduate and advanced undergraduate students highly motivated to learn about mathematical pattern formation are encouraged to apply. The summer school plans to provide travel and local expense support for all attendees. Experience in the above areas is not required.  

 Organizers

• Jason Bramburger, Assistant Professor, Concordia University; website

• Ryan Goh, Assistant Professor, Boston University; website

• Priya Subramanian, Senior Lecturer, University of Auckland; website