Our research
The applied topology group at Oregon State University employs topology to investigate a variety of complex systems. Primarily, we focus on the following three areas of research:
Develop applied topologyThe connection between topology and data is not yet solved. We continue to uncover and share methods for using topology in data analysis. Read more
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Investigate neural systemsTopology and neuroscience is important. We also do this. Read more.
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Expand to other systemsMany processes have topological tendencies. We find topology in cellular systems, geography, and a third thing.
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Advances in applied topology
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Paper 1It was really good. Please send svgs of any of the images we'll put in these sections. We can add as many papers/topics in this section as you'd like.
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Topology in neural systems
Paper 1 It was really good. Please send svgs of any of the images we'll put in these sections. We can add as many papers/topics in this section as you'd like.
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Topology in other systems
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Paper 1It was really good. Please send svgs of any of the images we'll put in these sections. We can add as many papers/topics in this section as you'd like.
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Network science has proven itself an invaluable tool in modern neuroscience. However, network models intrinsically assume that their objects of study are dyadic, i.e., that all pertinent information can be recorded in pairwise relations. This assumption is suspect in many complex systems, even those whose underlying structure is clearly a network. Methods from algebraic topology allow us to move beyond this limitation, providing a powerful mathematical tool set for understanding the mesoscale structure and dynamic properties of systems built on non-linear, higher-order interactions., as well as sophisticated but unexplored techniques for the study of networks. On the other hand, problems from neuroscience provide a steady stream of new questions that lie just beyond the frontiers of current methods in applied topology, practically begging for new collaborative efforts.
- Chad Giusti, Robert Ghrist and Danielle S Bassett, "Two's company, three (or more) is a simplex" in Journal of Computational Neuroscience, 2016
