2023 - International Women in Math Day

Schedule of Events:

9:50 - 10:00: Morning snacks and beverages

10:00 - 10:40: Plenary 1: Holly Swisher

10:45 - 11:15: Short talks: Leah Sturman and Addie DeChenne

11:20 - 12:00: Plenary 2: Mary Beisiegel

12:00 - 12:10: Afternoon snacks and beverages

12:10 - 12:40: Short talks: Jo O'Harrow, Madison Phelps

12:45 - 1:25: Plenary 3: Swati Patel

1:25 - 1:45: AWM presents Highlights of Women in Mathematics

1:45 - 2:00: Trivia! Bring your phone or a mobile device :D

2:00 Thanks and closing remarks

List of Talks:

Holly Swisher

Title:  Generalized Ramanujan-Sato series arising from modular forms

Abstract:  In 1914, Ramanujan gave several fascinating infinite series representations of 1/π.  In the 1980's it was determined that these series provide efficient means for approximating π. Since then discovering and proving series of this type have been of interest. Motivated by work of Chan, Chan, and Liu, we obtain a new general theorem yielding corollaries that produce generalized Ramanujan-Sato series for 1/π. We use these corollaries to construct explicit examples arising from modular forms on arithmetic triangle groups.  This work is joint with Angelica Babei, Lea Beneish, Manami Roy, Bella Tobin, and Fang-Ting Tu. It was initiated as part of the Women in Numbers 5 workshop.

Mary Beisiegel

Swati Patel

Title: The mathematics of species coexistence

Abstract: A fundamental problem in ecology is to understand the mechanisms within and between species that enable them to coexist with one another.  This is important for conservation (in which case we may want to promote the persistence of a particular species) and public health against infectious diseases (in which case we may want to drive a species to extinction).  In mathematical ecology, we address this problem systematically by modeling ecological systems (for example, by differential equations) and building analytical theory to study these kinds of models. In this talk, I will present one general form of model equations and some precise mathematical results of this coexistence problem.  Finally, I will discuss an application of these results to studying a particular infectious disease, which is of public health importance.

Leah Sturman

Title: Partition Inequalities

Abstract: Partitions are a combinatorial object which relate to many other mathematical fields. We will give a quick introduction into the history of Alder’s Conjecture in partition theory including the work of Andrews, Yee, and Alfes Jameson and Lemke Oliver whose combined efforts proved Alder’s Conjecture using combinatorial methods and analytic methods. If time permits, we’ll talk about some recent generalizations of Alder’s Conjecture.

Addie DeChenne

Title: Problems with Counting Problems

Abstract: Counting problems in combinatorics are simultaneously described as approachable and difficult. This contradiction stems from observing that counting problems task us with counting objects that can be described easily (approachable), and yet appropriate counting strategies can be challenging to construct (difficult). I focus on one solution strategy, where counting is mediated through auxiliary representations: the primary objects being counted are encoded into secondary representations, and the counter solves the problem by counting the secondary representation rather than the primary. This strategy motivates the following questions: what features of the primary objects are encoded? Does the choice of secondary representation affect the solution? How might students choose secondary representations?

Jo O'Harrow

Madison Phelps

Title: Modeling Traffic with "Traffic Awareness" of Multiple Species in an Urban Environment

Abstract: We consider traffic flow of multiple species in an urban environment such as mixed-use campus network. The species are humans and robots, and humans on bicycles, and some species move only on paved paths, while some are allowed to move off the paths to avoid (possible) congestion. The model is a coupled system of hyperbolic PDE conservation laws, and the couplings are in the flux functions and in the trajectories for the species for which we solve a flow model. Behavior of species is incorporated in the flux functions and flow models: in particular, we fully explore "traffic awareness" and "traffic un-awareness" for which we assume the species to not "care" about their respective positions and those of other species. Our "traffic awareness" model is inspired by the well known LWR traffic flow for density of cars which was later interpreted by [Rossa, D'Angelo, Quarteroni et al, 2010] as a continuous limit of a stochastic network model, where the mean values and standard deviations of transitional probabilities at each time step are linked to the preferred direction of movement and speed of each species. However, this model does not allow for coupled interactions between multiple species. Other extended models that allow interactions between multiple species are individual based models, but come with a high computational cost on complex networks. We build our computational model with CCFD and Godunov scheme, discuss convergence, and show examples in 1d and 2d.