Interdisciplinary scholarship in mathematics and gender studies as well as the scholarship of teaching and learning have inspired a broad variety of published articles, books, plenary addresses, special issues of *PRIMUS* and more, for example, the educational website SimpsonsMath.com created with Andrew Nestler. *Library Journal* named the three-volume *Encyclopedia of Mathematics & Society* co-edited with Jill Thomley a “Best Reference 2011.” Plenary addresses have wide-ranging topics including π-day with *The Simpsons* and *Futurama*, the geometry of the earth and universe, how and why the Association for Women in Mathematics (AWM) was founded and is still needed today, mathematical identities: representing the underrepresented, mathematical morsels from *The Simpsons* and *Futurama*, popular culture and mathematics: gender, race and more, and Rubik's cube games on spheres.

Investigating connections between mathematics and society, Greenwald has won awards for teaching, scholarship and service. These include an MAA Henry L. Alder Award for Distinguished Teaching by a Beginning College or University Mathematics Faculty Member, an AWM Service Award, and College of Arts and Sciences Outstanding Teacher of the Year. As an AWM Fellow, Greenwald was cited for “creative and effective efforts to spark interest in mathematics among young people, especially girls… extensive contributions to advancing women in mathematics through writing, lectures and working with professional societies… and mentorship of students.” Greenwald’s Erdős-Bacon number is six, seven or infinity, depending on what and how we count. For instance, the interactive mathematics lecture “Bite My Shiny Metal X” has been distributed on approximately one million DVDs worldwide as a 25-minute extra for the *Futurama* movie *Bender's Big Score* and is listed as “Mind-bending.” Greenwald has spoken about the impacts of scientific popular culture representations on NPR's *Science Friday* and all over the country.

Harvey Mudd College

**Bio:** Dr. Talithia Williams is a host of the PBS series *NOVA Wonders*, a groundbreaking professor, popular TED speaker, inspiring author and passionate STEM/STEAM advocate. She has made it her life's work to get people of all ages and backgrounds excited about the bold possibilities of a STEM education and to “STEMpower” women and minorities to enter these professions. Her latest book, *Power in Numbers: The Rebel Women of Mathematics* reflects Williams’ passion to re-brand the field of mathematics as anything but dry, technical or male-dominated. Renowned for her popular TED Talk, “Own Your Body’s Data,” she advocates for all of us to deploy data as a way of taking charge of our own health. A vibrant, engaging and energizing speaker, Dr. Williams demystifies data, statistics, probabilities and the mathematical process in amusing and insightful ways. She also passionately champions the contributions of scientists, technologists, engineers and mathematicians and their vital role in transforming our future.

Dr. Williams is Associate Dean for Faculty Development and Diversity and Associate Professor of Mathematics at Harvey Mudd College, where she develops statistical models which emphasize the spatial and temporal structure of data, applying them to real world problems. Focused on data analytics, mathematics, statistical modeling and STEM outreach, she is the first African-American woman to achieve tenure at the college. She hosts *NOVA Wonders*, a PBS mini-series that explores the biggest questions on the frontiers of science. The *Los Angeles Times* praised the show for sending the message “that scientists come in a range of ages, genders, colors and hairstyles.” She also appeared in NOVA’s Prediction by the Numbers, a series exploring the history of probabilities and gambling which Forbes called, “an entertaining, fun piece that conveys her knowledgeable and deep interest in this predictive method.” In addition to her teaching and television work, she has partnered with the World Health Organization in developing a cataract model used to predict the cataract surgical rate for countries in Africa. Her professional experiences include research appointments at NASA’s Jet Propulsion Laboratory, NASA’s Johnson Space Center, and the National Security Agency.

An exceptional communicator and gifted teacher, Dr. Williams won the Mathematical Association of America’s Henry L. Alder Award for distinguished teaching. She also developed a 24-part college level lecture series, "Learning Statistics: Concepts and Applications in R", for *The Great Courses*, an online platform for lifelong learners. Dr. Williams earned a bachelor’s degree in mathematics from Spelman College, a master’s degree in mathematics from Howard University and a PhD in statistics from Rice University. In 2019, she received an honorary doctorate from Fielding Graduate University for her "substantial impact on higher education" and for "championing the development of women in the STEM professions."

Described by audiences as engaging, relevant, funny, accessible, and a joy to work with, Dr. Williams captivates and inspires with her contagious enthusiasm for STEM in general and math in particular. Applying the data-driven approach made famous in her TED talk to a range of subjects, she takes sophisticated numerical concepts and makes them understandable to a wide audience, debunking perceptions with an energizing call to “show me the data!”

View the list of past Pólya Lecturers

### MAA AWM Speakers

###### Catherine Hsu

**Bio:** Catherine Hsu is an Assistant Professor in the Department of Mathematics and Statistics at Swarthmore College. Her mathematical interests began as a penchant for logic puzzles and problem solving and grew into a love of abstract algebra and Galois theory while she was an undergraduate student at Rice University. Her research is now primarily in algebraic number theory, including projects related to modular forms and Apollonian circle packings. She also enjoys thinking about mathematical exposition, pedagogy, and unnecessarily complicated strategies for the card game Hanabi.

Prior to joining Swarthmore in the fall of 2020, Hsu was a Heilbronn Research Fellow at the University of Bristol as well as an AAUW American Dissertation Fellow and a Doctoral Research Fellow at the University of Oregon. As a junior researcher, she has greatly enjoyed traveling and speaking at conferences around the world and is looking forward to meeting new mathematicians as part of the MAA-AWM Lecturer program.

**Topics include:**

__Prime Components in Apollonian packings__

An Apollonian circle packing is a fractal arrangement formed by repeatedly inscribing circles into the interstices in a Descartes configuration of four mutually tangent circles. The curvatures of the circles in such a packing are often integers, and so it is natural to ask questions about their arithmetic properties. For example, it is known by work of Bourgain-Fuchs that a positive fraction of integers appear as curvatures in any integral Apollonian circle packing. In this talk, we investigate the arithmetic properties of the collection of integers appearing in “thickened prime components'' of Apollonian circle packings.

__Projective and Non-Abelian SET__

Mathematicians love SET. On the surface, this classic game is a con test of pattern recognition, but it also presents an interesting way to visualize the geometry of a torus over a finite field. In this talk, we will discuss some of the mathematics connected to SET and then explore several new versions of the game, including one arising from projective geometry and one arising from non-abelian groups. In particular, we will see how these non-abelian variations on SET can give intuitive visualizations of abstract group structures.

__Small Eisenstein Congruences and Explicit Non-Gorenstein __*R* = T

In his seminal work on modular curves and the Eisenstein ideal, Mazur studied the existence of congruences between certain Eisenstein series and new forms, proving that Eisenstein ideals associated to weight 2 cusp forms of prime level are locally principal. In this talk, we’ll explore generalizations of Mazur’s work to squarefree level, focusing on some work in progress, joint with Preston Wake and Carl Wang-Erickson, that establishes a computable algebraic criterion for having *R* = T in a certain non-Gorenstein setting.

###### Anastasia Chavez

**Bio:** Anastasia Chavez is an Assistant Professor of Mathematics at Saint Mary’s College of California. Born and raised in California, she transferred from the Santa Rosa Junior College and earned a bachelors in applied mathematics and masters in mathematics from San Francisco State University. After earning her Ph.D. in enumerative and algebraic combinatorics with an emphasis in matroid theory from the University of California, Berkeley, Anastasia was a Huneke Fellow at the Mathematical Sciences Research Institute and Presidents’ Postdoctoral Fellow, NSF Mathematical Sciences Research Postdoctoral Fellow, and Krener Assistant professor at the University of California, Davis.

**Topics include:**

__Matroids, Positroids, and Beyond!__

Matroids are a fundamental combinatorial object with connections to many areas of mathematics: algebraic geometry, cluster algebra, coding theory, polytopes, physics ... just to name a few. Introduced in the 1930’s, Whitney defined matroids with the desire to abstract linear and graphical dependence. In fact, every graph is associated with a matroid (called *graphical*) and from every vector configuration a *realizable (sometimes called representable)* matroid exists. It has been shown that most matroids are neither graphical or realizable, making these two matroid properties rare and highly desired.

A particularly well-behaved family of representable matroids, called positroids, was introduced by Postnikov and shown to have deep connections to the totally nonnegative Grassmannian and particle physics. Moreover, he described several combinatorial objects in bijection with positroids that compactly ecodes matroidal data and have been shown to characterize many matroidal properties.

With just a few definitions and examples revealing their connections to a variety of fields, you too can begin searching for the matroids living among us.

__On the Lattice and Vector Spaces of Cycles of an Undirected Graph__

It is well known that cycles in a graph exhibit a rich structure that play a powerful role in many applications. Cycles on graphs, oriented or unoriented, can also lead to deceivingly simple open questions. For example, the Cycle Double Cover Conjecture claims that there is a family of cycles such that every edge of a bridgeless graph is contained in exactly two cycles.

One can consider a linear-algebraic view and consider every cycle as an indicator vector. This translates graphical questions into algebraic ones and leads to structural questions about the cone, lattice, and cycle spaces over some field. This linear algebraic perspective has been applied historically to model combinatorial problems on directed graphs with great success (in some textbooks), whereas the undirected edge case less so. We will explore this algebraic perspective and the distinctions between directed and undirected graphs on the cycle spaces generated by linear combinations of the 0/1-incidence vectors of cycles.

###### Kara Djima

**Bio: **Dr. Karamatou Yacoubou Djima is an applied mathematician and an Assistant Professor of Mathematics at Amherst College. Before moving to Amherst, she spent a year at Swarthmore College as a visiting postdoctoral fellow. She received both her Ph.D. and MSc in Applied Mathematics & Statistics and Scientific Computing from the University of Maryland in College Park. Dr. Yacoubou Djima’s current research interests lie at the intersection of applied harmonic analysis and machine learning. Her past and ongoing projects include novel spectral graph methods, early diagnosis of autism spectrum disorder using features present in placenta images, and motion detection in animated images for Pixar.

**Topics include:**

__Heuristic Framework for Multi-Scale Testing of the Multi-Manifold Hypothesis__

Global linear models often overestimate the number of parameters required to analyze or efficiently represent datasets, for example when a data set in sampled from a manifold of lower dimension than the ambient space. The manifold hypothesis consists in asking whether data lies on or near a d-dimensional manifold or is sampled from a distribution supported on a manifold. In this talk, we outline a heuristic framework for a hypothesis test suitable for computation and empirical data analysis. We consider two datasets made of multiple manifolds and test our manifold hypothesis on a set of spline-interpolated manifolds constructed based variance-based intrinsic dimensions computed from the data. This is joint work with Patricia Medina, Linda Ness and Melanie Weber.

__A brief tour of applied harmonic analysis: from Fourier series to machine learning__

I will discuss how the field of Harmonic Analysis has tackled the analysis of data, starting from the year 1807, when Joseph Fourier asserted that all functions can be represented by a trigonometric series, to these days with our obsession with deep learning algorithms. We start by deriving the coefficients in Fourier series and doing so, get some insights into functional analysis, the linear algebra of functions. From there, we establish parallels with the relatively recent field of Harmonic Analysis on graphs and Deep Learning techniques. We will also look at some interesting applications, including analyzing images placenta vascular networks for autism detection.

###### Marissa Loving

**Bio:** Marissa Kawehi Loving is an NSF Postdoctoral Research Fellow and Visiting Assistant Professor in the School of Math at Georgia Tech. She graduated with her PhD in mathematics in August 2019 from the University of Illinois at Urbana-Champaign where she was supported by an NSF Graduate Research Fellowship and an Illinois Graduate College Distinguished Fellowship. Marissa was born and raised in Hawai'i where she completed her B.S. in Computer Science and B.A. in Mathematics at the University of Hawai'i at Hilo. She is the first Native Hawaiian woman to earn a PhD in mathematics. Her research interests are in geometry/topology, especially mapping class groups of surfaces (of both finite and infinite type). Marissa is also deeply invested in making the mathematics community a more equitable place. Some of her work includes mentoring undergraduate research (through programs such as Summer@ICERM, MSRI-UP, and the Georgia Tech School of Math’s REU) and co-organizing initiatives like SUBgroups and paraDIGMS.

**Topics include:**

__Symmetries of Surfaces__

I will give a gentle introduction to surfaces (of both finite and infinite-type) and their associated mapping class groups. I will then discuss some of the different areas of mathematics that naturally arise in the study of surfaces and the mapping class group, from geometry and dynamics to algebra, combinatorics and number theory. Along the way we will see how these different perspectives often come together in beautiful ways.

__Surfaces: BIG and small__

As a geometric group theorist, my favorite type of manifold is a surface and my favorite way to study surfaces is by considering the mapping class group, which is the collection of symmetries of a surface. In this talk, we will think bigger than your average low-dimensional topologist and consider surfaces of infinite type and their associated “big” mapping class groups.

__Where do I belong? Creating space in the math community__

Who belongs in mathematics? Who is given the resources they need to flourish mathematically? Who is undermined, sidelined, and excluded by both their peers and seniors? I will address these questions from the perspective of my own personal mathematical journey. I will also share some of the programs and spaces I have helped create in my quest to make the mathematics community into a place where folks from historically underrepresented groups (particularly women of color) can feel safe, seen, and free to devote their energy to their work. If you have ever felt like you don’t belong or worried that you have made others feel that way, this talk is for you.

### MAA NAM Speakers

###### Jose Perea

**Bio:** Jose Perea holds a Ph.D. in Mathematics from Stanford University (2011) and a B.Sc. in Mathematics from Universidad del Valle, Colombia (Summa cum laude and Valedictorian, 2006). He was a visiting assistant professor in the department of Mathematics at Duke University from 2011 to 2015, and a member of the Institute for Mathematics and its Applications (IMA) at the University of Minnesota during the Fall of 2014. In August of 2015 he joined Michigan State University as an Assistant Professor with joint appointments in the department of Computational Mathematics, Science & Engineering (CMSE), and the department of Mathematics. He is the recipient of a 2020 NSF CAREER award, a 2020 honoree of Lathisms during Hispanic heritage month, a 2018 honoree of Mathematically Gifted and Black during black history month, and recognized as being in the top 5% of teachers at Duke University (2013).

**Topics Include:**

__The Underlying Topology of Data__

Topology, and particularly algebraic topology, seeks to develop computable invariants to quantify the shape of abstract spaces. This talk will be about how such invariants can be used to analyze scientific data sets, in tasks like time series analysis, semi-supervised learning and dimensionality reduction. I will use several examples to illustrate real applications of these ideas.

###### Haydee Lindo

**Bio:** Dr. Haydee Lindo is an assistant professor of mathematics at Harvey Mudd College. Dr. Lindo is from Jamaica and earned her BAs in mathematics and political science. She received her Ph.D. in mathematics from the University of Utah and was previously a Gaius Charles Bolin Fellow and, later, an assistant professor of mathematics & statistics at Williams College. Dr. Lindo is a commutative algebraist with research interests in homological algebra and representation theory. She focuses on the development and application of the theory of trace modules over commutative rings.

**Topics Include:**

__Introduction to trace ideals and centers of endomorphism rings__

In many branches of mathematics, the full set of "functions" between two objects exhibits remarkable structure; it often forms a group and in some special cases it forms a ring. In this talk, we will discuss this phenomenon in Commutative Algebra. In particular, we will talk about the endomorphism ring formed by the homomorphisms from a module to itself by first looking at commuting square matrices with real entries. The well-known trace map on matrices can be generalized to a map on any module over a commutative ring. The image of such a map is a trace ideal. I'll introduce the trace ideal and explain its role in the question "What properties of a module does its endomorphism ring detect?"

__Stable Trace Ideals and Arf Rings__

In this talk we will explore the intersection of notions of an ideal being “trace” and an ideal being “stable” that is, ideals that map to themselves under all homomorphisms to the base ring and ideals that isomorphic to their endomorphism rings. Following Lipman’s seminal work exploiting the nice properties of stable ideals to study Arf rings, we apply our results, incorporating the modern theory of trace ideals, to show that Arf rings enjoy even more geometric and homological properties than previously known. This is joint work with Dr. Hailong Dao.

###### Talea Mayo

**Bio:** Talea Mayo is a computational mathematician with expertise in the development and application of numerical hydrodynamic models for coastal hazards. She specializes in hurricane storm surge modeling, including their use for the investigation of climate change impacts on coastal flood risk. She also has expertise in statistical data assimilation methods for state and parameter estimation. She has recently expanded her work to include coastal erosion and the impacts of sustainable resilience efforts. She earned her B.S. in Mathematics from Grambling State University, and her M.S. and Ph.D. in Computational and Applied Mathematics from The University of Texas at Austin. She is currently an Assistant Professor in the Department of Mathematics at Emory University, and was recently awarded the Early-Career Research Fellowship by the National Academies of Sciences Gulf Research Program and the Early Career Faculty Innovator Award by the National Center for Atmospheric Research. She is a fierce advocate of accessible, inclusive science and education of all people, and spends her free time chasing marathon PRs and toddlers.

**Topics include:**

__Mathematics applied: the use of computational models to understand climate change impacts to storm surge risk__

It is widely accepted that climate change will cause global mean sea level rise, increasing coastal flood risk in many places. However, climate change also has significant implications for tropical cyclone climatology. Specifically, hurricane intensity, size, and translation speed are all expected to intensify in the future, and each of these influences storm surge generation and propagation. In this talk, I will discuss probabilistic and deterministic numerical modeling approaches we have taken to understanding what this means for coastal flooding from storm surges.

__Data meets model: how observations are used to improve prediction and simulation of hurricane storm surges__

Coastal ocean models are used for a variety of applications, including simulation of tides and hurricane storm surges. These models numerically solve the shallow water equations, which assume large horizontal length scales relative to the vertical length scales, and allow depth integration of the Navier-Stokes equations. The inherent uncertainties in coastal ocean models are a result of many factors, including this modeling assumption, numerical discretization of the resulting equations, and uncertain model inputs and parameters. In this talk, I will discuss how we have used statistical data assimilation methods for state and parameter estimation to quantify and reduce model uncertainties.

__Theories of evolution: how my research program and I have transformed through my career in academia__

I began my career as a criminal justice student in hopes of becoming a lawyer, but when I realized I had already fulfilled all the math requirements, I quickly changed my major to mathematics. Mathematics provided the foundation for me to participate in multiple interdisciplinary summer research opportunities, and living in Louisiana during Hurricane Katrina solidified my interest in using math as a tool for solving real world problems. I chose an interdisciplinary program for my graduate studies, and gained expertise in numerical storm surge modeling. Upon earning my PhD, I learned to use storm surge models for coastal engineering and climate change applications as a postdoctoral researcher. I expanded my research program to include wave energy and coastal erosion when I became a tenure track faculty member. In this talk, I’ll discuss my research program, my path to becoming part of the 1% of faculty who are black women, and my efforts to improve this statistic through outreach and education.

Questions about Section Lecturers? | email MAA Communities at Communities@maa.org