Anna Schenfisch (Montana State University) "Posets of Topological Descriptors"
- Monday, April 12, 2021 from 4:10pm to 5:15pm
- Zoom meeting: 989 6034 6659 Password: math
Virtual Math Seminar.
Monday, April 12, 4:10-5:15pm MT
Zoom link, meeting, and password:
- 989 6034 6659
Anna Schenfisch (Montana State University)
Posets of Topological Descriptors
Given a general simplicial complex embedded in R^d, there exist finite sets of topological descriptors (persistence diagrams, etc.) that fully represent the complex. These sets have an interesting connection to a particular stratification of the sphere. By comparing the cardinalities of such sets for different topological descriptor types, we build a framework through which descriptor types can be ordered. We then partially order six common descriptor types as a case study, as well as describe a construction of a simplicial complex that requires surprisingly many augmented descriptors to form a representation. Throughout, we will pause to note research highlights as well as proposed work and conjectures.
- Department of Mathematical Sciences