The workshop, Mathematics of the Origin of Life and Self-Organized Complexity, will bring together theorists and experimentalists interested in emergent complexity, specifically in the contexts of the origin of life, self-organization, and self- assembly. The program will center on the following themes:

 

• Mathematics of the Origin of Life: The origin of life, understood as the self-organization of complex matter, remains a profound mystery. Inspired by Erwin Schrödinger’s idea of life as low-entropy systems that extract order from the environment, recent models propose systems capable of similar self-organization. The RNA world hypothesis, which suggests that RNA molecules played a central role in life’s beginnings, has been extended to include other information-bearing polymers capable of Darwinian evolution. Researchers in soft condensed matter investigate self-replicating systems using colloids and DNA origami, while biophysics advances focus on engineering synthetic cells and life forms.

• Frontiers in Self-Assembly: Self-assembly has progressed from theory to practical applications, showing how particle shapes, entropy, and molecular interactions can create complex organizations in soft matter. There is a growing need for inverse design principles to create systems with specific complex
  organizations and functions.

• Mathematical Descriptions of Emergent Complexity: Rigorous complexity measures are essential for advancing self-assembly and functional systems, yet they remain underdeveloped in many areas. While information theory offers some metrics, it falls short for dynamic, history-dependent self-assembled
  structures. Developing a framework that addresses challenges like sustained Darwinian evolution, learning, or self-healing would enable design strategies and comparative analysis. Advances in programmable self-assembly, particularly with DNA, offer new pathways for defining complexity and applying mathematical and physical tools to these challenges.

 

This workshop is unique in bringing together experts from traditionally separate fields that share common themes. While the origin of life has often been explored through prebiotic chemistry, this workshop will adopt a mathematical perspective, viewing life as a generic emergent phenomenon. This approach aligns it with studies of self-organization in materials and other complex systems, where defining and characterizing complexity is a unifying theme. We anticipate that this focus will attract mathematicians and computer scientists working on dynamical systems, graph theory, information processing, and mathematical measures of complexity.