Topology, Geometry & Data Seminar - Benjamin Schweinhart

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Benajmain Schweinhart
April 3, 2018
4:10PM - 5:10PM
Location
Cockins Hall 240

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Add to Calendar 2018-04-03 16:10:00 2018-04-03 17:10:00 Topology, Geometry & Data Seminar - Benjamin Schweinhart Title: Persistent Homology and the Upper Box Dimension Speaker: Benjamin Schweinhart (Ohio State University) Abstract: We prove the first results relating persistent homology to a classically defined fractal dimension. Several previous studies have demonstrated an empirical relationship between persistent homology and fractal dimension; our results are the first rigorous analogue of those comparisons. Specifically, we define a family persistent homology dimensions for a metric space, and exhibit hypotheses under which they are comparable to the upper box dimension. In particular, the dimensions coincide for subsets of R^2 whose upper box dimension exceeds 1.5. This work also raises interesting questions in extremal combinatorics and geometry. Seminar URL: https://research.math.osu.edu/tgda/tgda-seminar.html Cockins Hall 240 Department of Mathematics math@osu.edu America/New_York public
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Title: Persistent Homology and the Upper Box Dimension

Speaker: Benjamin Schweinhart (Ohio State University)

Abstract: We prove the first results relating persistent homology to a classically defined fractal dimension. Several previous studies have demonstrated an empirical relationship between persistent homology and fractal dimension; our results are the first rigorous analogue of those comparisons. Specifically, we define a family persistent homology dimensions for a metric space, and exhibit hypotheses under which they are comparable to the upper box dimension. In particular, the dimensions coincide for subsets of R^2 whose upper box dimension exceeds 1.5. This work also raises interesting questions in extremal combinatorics and geometry.

Seminar URLhttps://research.math.osu.edu/tgda/tgda-seminar.html

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