Research
Two overarching questions in my research are:
For more detail, please see my Research Statement. |
Publications
A Fractal Dimension for Measures via Persistent Homology
with Henry Adams, Manuchehr Aminian, Elin Farnell, Michael Kirby, Joshua Mirth, Chris Peterson, Clayton Shonkwiler
(Submitted 2018)
{arXiv preprint: 1808.01079, pdf}
with Henry Adams, Manuchehr Aminian, Elin Farnell, Michael Kirby, Joshua Mirth, Chris Peterson, Clayton Shonkwiler
(Submitted 2018)
{arXiv preprint: 1808.01079, pdf}
Measures of Order for Nearly Hexagonal Lattices
with Mark Bradley, Francis Motta, Daniel Pearson, and Patrick Shipman
Physica D: Nonlinear Phenomena, Vol 380-381. (2018)
{Publisher's Link, pdf}
with Mark Bradley, Francis Motta, Daniel Pearson, and Patrick Shipman
Physica D: Nonlinear Phenomena, Vol 380-381. (2018)
{Publisher's Link, pdf}
Pseudo-multidimensional persistence and its applications
with Catalina Betancourt, Mathieu Chalifour, Matthew Pietrosanu, Mimi Tsuruga, Isabel Darcy, Giseon Heo
AWM-IMA Springer Series: Research in Computational Topology (2018). As a part of the Women in Computational Topology Workshop {Publisher's Link, pdf}
with Catalina Betancourt, Mathieu Chalifour, Matthew Pietrosanu, Mimi Tsuruga, Isabel Darcy, Giseon Heo
AWM-IMA Springer Series: Research in Computational Topology (2018). As a part of the Women in Computational Topology Workshop {Publisher's Link, pdf}
Persistence images: A stable vector representation of persistent homology.
with Henry Adams, Sofya Chepushtanova, Tegan Emerson, Eric Hanson, Michael Kirby, Francis Motta, Chris Peterson, Patrick Shipman, and Lori Ziegelmeier.
Journal of Machine Learning Research 18 (2017), Number 8, 1-35.
{Publisher's Link} {Software on GitHub, python version included in scikit-tda}
with Henry Adams, Sofya Chepushtanova, Tegan Emerson, Eric Hanson, Michael Kirby, Francis Motta, Chris Peterson, Patrick Shipman, and Lori Ziegelmeier.
Journal of Machine Learning Research 18 (2017), Number 8, 1-35.
{Publisher's Link} {Software on GitHub, python version included in scikit-tda}
Applied Mathematics for Chemistry Majors
with Amber Krummel, Nancy Levinger, and Patrick Shipman
Invited Paper for ACS CHED CCCE Online ConfChem conference, Fall 2017
{CCCE Conf Chem Paper}
Communication: Journal of Chemistry Education (2018)
{Publisher's Link, pdf}
with Amber Krummel, Nancy Levinger, and Patrick Shipman
Invited Paper for ACS CHED CCCE Online ConfChem conference, Fall 2017
{CCCE Conf Chem Paper}
Communication: Journal of Chemistry Education (2018)
{Publisher's Link, pdf}
N-gram Modeling for Document Retrieval.
Internal Paper, Enterprise Operations Research, Modeling Simulation; Department of Defense (2015)
Internal Paper, Enterprise Operations Research, Modeling Simulation; Department of Defense (2015)
Talks
Upcoming
Invited
Contrubuted
Greenslopes Graduate Seminar: Colorado State University
- SIAM Sectional Meeting (Louisiana-Texas) November 2019
- Applied Algebraic Topology Research Network (Virtual Seminar) November 2019
- Joint Mathematics Meeting, January 2020
- SIAM Conference on the Mathematics of Data Science, May 2020
Invited
- AWM WinComTop Special Session on Computational Topology, Joint Math Meeting. Baltimore, MD, January 2019
- AWM Research Symposium. Houston, TX, April 2019
- SIAM Applications of Dynamical Systems. Snowbird, UT, May 2019
- Texas A & M Industrial and Applied Math Seminar, April 2019
- Equadiff, Leiden, the Netherlands, July 2019
- Topological Methods on Ion Bombardment Patterns. SIAM Central Section Meeting. Fort Collins, CO (September 2017)
- Classification of Pattern Forming Systems Using Persistence. SIAM Conference on Applications of Dynamical Systems. Snowbird, UT (May 2017)
- Topological Measure of Order on Lattice Patterns. SIAM Central Section Meeting. Little Rock, AK (September 2016)
- Patterns in Networks of Discrete Ecological Dynamical Systems Revealed Through Persistent Homology. SIAM Conference on Applications of Dynamical Systems. Snowbird, UT (May 2015)
Contrubuted
- Topological Techniques for Characterization of Nanodot Patterns. University of Arizona ADA Seminar (September 2017)
- Topological Measure of Order on Lattice Patterns. SIAM Annual Meeting (July 2017)
- Topological Measure of Order on Lattice Patterns. Joint Math Meetings. Atlanta, GA (January 2017)
- Persistent Images: A Stable Vector Representation of Persistent Homology( poster) Topological and Geometric Data Analysis. Columbus, OH (May 2016)
- Persistent Homology of Dynamical Systems on Networks. Joint Mathematics Meetings. Seattle, WA (January 2016)
- N-gram Modeling. Briefing to Technical Senior Executives; Department of Defense. Fort Meade, MD (July 2015)
- Patterns in Persistence: Persistent Homology of Chaotic Dynamical Systems. Joint Mathematics Meetings. San Antonio, TX (January 2015)
- Persistence Images: A Look at Persistent Homology. Front Range Applied Mathematics Student Conference. Denver, CO (February 2015)
- A Pattern in Chaos: Persistent Homology of the Logistic Map. Front Range Applied Mathematics Student Conference. Denver, CO (March 2014)
Greenslopes Graduate Seminar: Colorado State University
- The Parable of the Polygons - Mathematical Modeling of Segregation (January 2017)
- N-gram Modeling and Interning at the DoD (September 2015)
- Persistent Homology and Dynamics (March 2015)
- Persistence Images (February 2015)
- The Math Behind Snowflakes (December 2014)
- Persistent Homology of Dynamical Systems speed talk (March 2014)
- Persistent Homology (October 2013)