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Natural systems often sustain its functions through the interaction between numerous components, who are themselves systems with many interacting components — think about a biological organism that is made of many cells constantly signaling each other, while within those cells, diverse molecules are busy coordinating with one another. If the components stop interacting in the right way, the system will start to malfunction or even collapse. That is, the systems as a whole is more than the sum of its parts — the invisible web of dynamic interactions across nested scales is defining. Think about what the brain or a social organization could possibly do if neurons or people stop talking to each other.

Complex systems science is the transdisciplinary study of the common organizing principles of this type of systems and to leverage those principles to classify, predict, and control their behavior. Dynamical systems theory provide the common mathematical language and basic machineries to connect the component level interactions to system level behavior regardless of the specific physical instantiation of the system — a natural backbone for the study of complex systems. However, high-dimensional dynamical systems such as those modeling the brain and social systems are themselves non-trivial to understand mathematically. New computational tools are necessary to characterize what they do. Recent advances in computational topology and geometry provide promising new approaches.

Our vision is to unify topology and dynamics to create new computational and mathematical frameworks for studying complex systems. It is imperative that the frameworks are tailored to the reality of relevant disciplinary sciences and clinical applications. In particular, our tools are designed to handle complex datasets of multimodal recordings of human and animal brain activities and behavior in experimental and clinical settings. This enables us to better translate the computation back to empirical predictions to inform the design of new experiments and clinical treatments of neuropsychiatric disorders.

This scientific vision is inseparable from a broader vision of providing a collaborative, supportive, and respectful lab environment where people with different backgrounds, experience, and identities can find intellectual and personally growth and fulfilment by learning from each other.