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Invited Paper Session Abstracts - Women in Math: Math In Action

Please note: all sessions are listed in Mountain Daylight Time (MDT = UTC-6:00)

Saturday, August 7, 1:00 p.m. - 4:00 p.m.

Mathematics is in action within so many exciting non-mathematical settings, spanning from classical historical and cutting edge interplays between mathematics and physics, biology, and other sciences, to beautiful applications of mathematics to games, art, social justice, economics, and climate change, to name a few. Topics with possibly unexpected applications outside of mathematics include complexity classes, Ramsey colorings, tropical numbers, topology, hyperbolic surfaces, geodesics, and more.

In this session, we showcase current research done by women (and their students) of mathematics and statistics applied to a variety of non-mathematical settings.

Math, Medicine and Mysteries

1:00 p.m. - 1:20 p.m.
Ami Radunskaya, Pomona College


The title is meant to suggest that mathematics can be used to understand mysteries and answer questions about our health and well-being. I will tell you about some collaborations between mathematicians and scientists in which I have taken part where the goal was to answer questions like: How can we design cancer vaccines? How much blood-thinner should we prescribe? What are the best shoes to wear to improve your balance? How can we address the current opioid epidemic? These problems illustrate different types of mathematical models, and different mathematical techniques used to reach different goals. But the focus is the same: to understand the mysteries of diseases and their treatments.

Finding Atmospheric Features via Topological Data Analysis

1:30 p.m. - 1:50 p.m.
Lynne Seymour, University of Georgia


Topological Data Analysis (TDA) is a recently-developed (within the last 10-15 years) mathematical tool for understanding shape based on a sample of points on that shape. We briefly explain the basics of TDA and then present TDA-based tools we have developed specifically for understanding wave features in the atmosphere, as one might see in the geopotential height record.

Analyzing Collective Motion with Machine Learning and Topology

2:00 p.m. - 2:20 p.m.
Lori Ziegelmeier, Macalaster College


From nanoparticle assembly to synchronized neurons to a flock of birds, collective behaviors abound anywhere in nature that objects or agents interact. The study of collective behavior typically involves large data sets generated by experiment and/or simulation, and there is sometimes a need to simplify or summarize this dynamic behavior. This talk presents topological data analysis (TDA) as an approach for carrying out data science tasks in the context of collective behavior. The key approach is to characterize a system’s dynamics via the time-evolution of topological invariants called Betti numbers, accounting for topological features across multiple scales. We show that this approach can be combined with machine learning to classify various collective behaviors.

Identifying Geohazards with Mathematics and Statistics

2:30 p.m. - 2:50 p.m.
Celes Woodruff, James Madison University


Geohazards such as sinkholes and landslides can be dangerous for people, property, and infrastructure. Mapping these features is important for studying their development as well as for creating hazard maps. High resolution digital elevation models (DEMs) can be used to show a topographic layout of the land and geologists can use them to visually identify these geohazards. However, the large number of regions that look like they could be sinkholes or landslide sites makes this a painstaking task. In our work we used a combination of mathematical and statistical techniques to describe the characteristics of known regions and determine which characteristics were significant. We then used these characteristics to automatically identify other such regions.

The Role of RdCVFL in a Mathematical Model of Photoreceptor Interactions

3:00 p.m. - 3:20 p.m.
Erika Tatiana Camacho, University of Arizona / National Science Foundation


Recent experimental and mathematical work has shown the interdependence of the rod and cone photoreceptors with the retinal pigment epithelium in maintaining sight. Accelerated intake of glucose into the cones via the theoredoxin-like rod-derived cone viability factor (RdCVF) is needed as aerobic glycolysis is the primary source of energy production. Reactive oxidative species (ROS) result from the rod and cone metabolism and recent experimental work has shown that the long form of RdCVF (RdCVFL) helps mitigate the negative effects of ROS. In this work we investigate the role of RdCVFL in maintaining the health of the photoreceptors. The results of our mathematical model show the necessity of RdCVFL and also demonstrate additional stable modes that are present in this system. The sensitivity analysis shows the importance of glucose uptake, nutrient levels, and ROS mitigation in maintaining rod and cone health in light-damaged mouse models. Together, these suggests areas on which to focus treatment in order to prolong the photoreceptors, especially in situations where ROS is a contributing factor to their death such as retinitis pigmentosa.

Crochet Topology

3:30 p.m. - 3:50 p.m.
Moira Chas, Stony Brook University


An interesting question surfaced (pun intended) in the 1800's: What is the largest number of regions into which one can divide a given surface so that every two regions share a segment of boundary? (This question is related to, but not the same as the generalization of the four color theorem to all surfaces) The answer was found in 1968 after a long and winding math road.

This talk will consist of a discussion of some stretches of this fascinating road, profusely illustrated by surfaces crocheted by the speaker with maps of maximal number of regions (with each pair of regions sharing a segment of boundary). Some of these maps were recently discovered by undergraduate students Yanbing Gu, Connor Steward and Ajmain Yamin.

(Note for the uninitiated: crochet is a fiber craft similar to knitting)