ALI ARAB:  'Data and Data Science for All: Striving for Human Rights, Equity and Justice'

In the era of digital transformation, all aspects of our lives are impacted by data and what we infer from them. Critically, the transformative role of data and analytics has enabled us to consider deeper analytical approaches to study complex social phenomena. This is especially important for studying systems at the intersection of multiple disciplines such as social, environmental, and heath issues. In this talk, I will highlight examples from past and ongoing research projects on applying mathematical, statistical, and computational tools to better understand, and raise awareness on, environmental, health, and social justice issues with the ultimate goal of making an impact on policy and achieving social change. In particular, I will discuss the added-value of organic data in this process including data generated through social media as well as citizen science projects.

REBECCA GARCIA: 'Building Your Own Research Community'

As a doctoral student in mathematics, our final years are spent working essentially alone on our dissertation. This tends to lead most of us toward working alone on mathematical research at the start of our profession, which defies a core human element: we are social creatures. In this talk, I will share my research experiences that have helped me make it through the academic pipeline. We will also take a look at other ways to create fruitful and healthy collaborations that will empower you to do the same.

ALICIA PRIETO LANGARICA: 'Mathematics: and exact and perfect science' 

Many times, when talking about our journey, we talk about our success and how we overcame struggles. This is a different talk. This is a talk about my own personal failures. Some that I learn from, some that are simply part of my journey. I hope that after this talk, we all become more comfortable making mistakes, failing at things, and that we start seeing failures like successes, simply a part of life. There will be pictures, there will be anecdotes, there will be stories and there will be math. 

TARAK SHAH: 'Why we need math in the fight to defend human rights'

For over 30 years, the Human Rights Data Analysis Group (HRDAG) has worked with truth commissions, UN missions, and local activists, to apply data analysis to the investigation of human rights violations. We rely on mathematics in our efforts to establish an accurate historical record, and to ensure that when we speak truth to power, that truth can stand up to adversarial environments. Through a series of case studies from HRDAG’s work over the years, we’ll explore the types of math problems that arise in our work and see examples of rigorous analysis used to hold the powerful to account.

Name: Victor Bankston, Tulane University

Title: Nonlocal games on Pauli measurements 

Abstract: Nonlocal games (or 2-prover, 1 round multiprover interactive protocols) are well-studied in communication complexity. The Pauli (Stabilizer) measurements are a natural class of measurements from quantum information. We will present a series of games based on these measurements and describe upper bounds on their best strategies via graph expansion. The games exhibit a specific task where quantum technologies can achieve a goal that cannot be replicated using only classical resources.

Name: Yuwei Bao

Title: Bayesian Coalescent-Based Model for Inferring Population Dynamics

Abstract: Coalescent-based inference methods are essential in estimating population genetic parameters directly from gene sequence data under a variety of scenarios. In the last two decades, there have been several non-parametric expansions of the coalescent model for more flexible treatment towards demographic changes. The Bayesian Skygrid model is currently the most popular nonparametric coalescent model that discretizes continuous effective population size changes over an array of predefined time epochs. The effective population size in an epoch is constant and represented by a single parameter. Therefore, the change points of the effective population size parameters introduce discontinuities with respect to time and cause difficulties in the application of dynamic-integration-based samplers such as the Hamiltonian Monte Carlo method.  In this talk, we introduce the original Skygrid coalescent prior, demonstrate the aforementioned discontinuities and introduce our preliminary thoughts on solving them with a new smoothed version of the Skygrid coalescent prior.

Name: Dana Ferranti

Title: Regularized Stokeslet Surfaces

Abstract: The incompressible Stokes equations describe fluid motion where viscous forces dominate inertial forces. The Method of Regularized Stokeslets (MRS), introduced in 2001, is a popular numerical method for simulating flows generated by forces on the surfaces of bodies immersed in the flow. The accuracy of the method relies on a numerical parameter, \epsilon, which desingularizes the integration kernel but introduces error. The latter are smallest when \epsilon is chosen on the order of the discretization size used on the surfaces. In this talk, we introduce an extension of MRS called the Method of Regularized Stokeslet Surfaces which alleviates this coupling by using a continuum of forces over a surface and allows the use of smaller values of \epsilon without affecting the error. An overview of the method and numerical results will be presented. 

Name: JJ Hoo, Texas Tech University

Title: Mathematical Pedagogy - An Introduction into Learning How to Learn

Abstract: This short talk is designed around discussing my personal views on how Mathematics should be taught and learned. Across many institutions of higher learning, Mathematics is often found to be a difficult field in which one can find immersion, but much of this comes down to learning a proper way to study Mathematics, as opposed to the content provided by courses in Mathematics. This talk will include a brief overview into my thoughts and opinion, along with some examples of techniques students can employ to enrich their journey through the world of Mathematics.

Name: Megan Peltier, Florida State University

Title: A Proposed Mathematical Model to Understand Rhizobium Legume Symbiosis

Abstract: The interaction between rhizobia and legume plants has been widely studied as a symbiotic relationship. In a successful symbiosis, these bacteria can perform nitrogen fixation to provide the plant with an essential nitrogen source. All the while, the bacteria can thrive on nutrients from the plant. However, much is still unknown about the effects of parasitic bacterial strains that do not have the capability to provide nitrogen to the legume. This talk will focus on introducing a mathematical model to further understand the dynamics of different bacterial strains inside the root nodule environment. Further, we hope to eventually understand how the specific rhizobium-legume symbiosis is impacted by a mutant bacterial strain. To do so, we will discuss the preliminary model predictions.

Name: Susan Rogowski, Florida State University

Title: Recovering the Growth Rate of Bacteria Using Data Assimilation

Abstract: It is a common problem in biomathematics that, given a noisy set of observations or data, one must estimate parameters for some mathematical model. Here, we consider the scenario of predicting the growth rate of a bacteria population from noisy data. Using the logistic growth equation as a simple model, we develop an algoristhm to dynamically learn the growth rate from the given noisy data. Under proper assuptions, and in the case of noise free data, we provide an analytical proof of convergence of our algorithm to the correct rate of growth. We support our analysis by demonstrating computationally the convergence of the algorithm, including the case of noisy observations. Lastly, we will discuss expanding this algorithm when bacteria growth is modeled in a two-tank chemostat model.

Name: Benjamin Stager

Title: An Analytical Method for the One-Dimensional Cubic Bousinnesq Equation

Abstract: The Cubic Boussinesq Equation derives from a class of nonlinear wave equations. Often, these systems are typically challenging to analytically solve. In this paper we outline the 'tanh method', implementing a hyperbolic tangent function to simplify the complex, nonlinear, fourth-ordered nature of this partial differential equation. By shifting the temporal domain using tanh, we are able to derive a simple, closed-form solution to the Boussinesq equation.

Name: Dayton Syme, Florida State University

Title: Modeling the Immune Response to Immunotherapy and Triple Negative Breast Cancer in Mice

Abstract: Triple negative breast cancer is particularly lethal and difficult to treat due to its aggressive and resistant biology. Recent tumor treatment options incorporate immune checkpoint inhibitors (ICI) in aiding a patient's immune response and have shown varied levels of success. Our talk details an immune response model of CD4+ and CD8+ cells to breast cancer in mice while being treated by two ICI drugs (either in combination or separately). Our model consists of a system of ordinary differential equations reflecting quantification of the immune and tumor response. 

The immune response activity is defined directly from state-of-the-art positron emission tomography (PET) image data that provide the distribution of CD4+ or CD8+ cells in the organism. Our model is parameterized from this novel longitudinal data alongside tumor volume measurements from the same experiments. With our optimized parameter set, we will discuss the effects of the ICI treatments on tumor-initiated inflammation and compare our results between combination and single ICI therapy.

The talk is joint with Yun Lu, Anna G. Sorace, and Nicholas G. Cogan.

Name: Melanie Tian

Title: A Combinatorial Proof for the Aftermath of a Party

Abstract: Consider a party sufficiently intense such that at one moment everyone suddenly leaves grabbing a random Tulane ID card. Given that there is no fake ID, what is the expected number of people who grab their own ID? This problem is usually phrased as the average number of fixed points in a random permutation and is usually solved by linearity of expectation. Here we present a proof which is mostly just messing with combinatorial identities. Note that even though the paper appears on the College Mathematics Journal, everything is done with pre-calculus methods. 

One of the main goals of Math For All is to create a welcoming environment for all participants. We wish for every participant to feel welcome, included, and safe at our conference.  For that reason, we ask you to be mindful of your words and actions when communicating with others. We all have a bias and make mistakes. With an open mind and a willingness to apologize, we can create a safe space for everybody. 

If there is a situation during the conference that makes you feel unwelcome, we ask you to please talk to one of the organizers so we can help you as best as we can. 

We acknowledge and pay tribute to the original inhabitants of this land. The city of New Orleans is a continuation of an indigenous trade hub on the Mississippi River, know for thousands of years as Bulbancha. Native peoples have lived on this land since time immemorial, and the resilient voices of Native Americans remain an inseparable part of our local culture. With gratitude and honor, we acknowledge the indigenous nations that have lived and continue to thrive here.