Invited Addresses

As climate change and human activities deliver new disturbance patterns to urban and ecological systems, resilience questions make us look at familiar mathematics through a new lens. Resilience is a slippery concept that has different meanings in different contexts. It is often described as the ability of a system to absorb change and disturbance while maintaining its basic structure and function. There is, therefore, an inherent interplay between transient dynamics and perturbation in resilience questions, especially when the perturbations are repeated. One way to capture this interplay is to subject the “flow” of an autonomous system of ordinary differential equations to regular “kicks” representing repeated, discrete disturbances. The resulting “flow-kick” systems occupy a surprisingly under-explored area between deterministic and stochastic dynamics. In this talk, we describe some examples in ecology and epidemiology, and some of the open questions raised.
 

It is a well known but counter-intuitive fact that even for a two dimensional linear differential equation with a globally attracting equilibrium at the origin, solutions of the differential equation may grow arbitrarily large in the short term before settling at the equilibrium in the long run. This phenomenon of transient radial amplification is called reactivity. It is especially important in resilience questions where reactivity may magnify disturbances of a system to an unhealthy level. In this talk, we describe a new framework for analyzing the radial and tangential dynamics of two-dimensional linear differential equations. We show how to recover the classical eigenvalue/eigenvector analysis for long term stability of the equilibrium, and then exploit a dual relationship between reactivity and eigenvalues to capture the transient reactivity properties of the system. To finish, we illustrate some ways this framework can provide insights into disturbance amplification via reactivity.

Mary Lou Zeeman is the Wells Johnson Professor of Mathematics at Bowdoin College. Her research is in dynamical systems with applications to biology, sustainability and resilience.She is known for collaboratively building cross-disciplinary research communities focused on the health of the planet. She helped found and co-lead the Mathematics and Climate Research Network, the Computational Sustainability Network and the SIAM Activity Group on Mathematics of Planet Earth.
 

Oswald Veblen (1880-1960) made important contributions to mathematics in America as a mathematical researcher, architect, advocate, and diplomat. Collaboration played a central role in these successful initiatives. Following Veblen’s lead, in December 2022, a group of historians of mathematics and mathematicians met for a week to organize a collaborative historical study of Veblen’s life. This talk explores some of the collaborations in Veblen’s career and some of the collaborative projects that grew out of the December workshop.

Sloan Evans Despeaux is Professor of Mathematics at Western Carolina University. She received a B.A. from Francis Marion University, M.S. from Florida State University, and a Ph.D. from the University of Virginia, where she worked under the supervision of Karen Parshall. Her research interests center on the history of mathematics (especially the mathematics, mathematicians, and scientific journals in nineteenth-century Britain, and more recently, early twentieth-century America). She is secretary of the International Commission of the History of Mathematics, chair of the AMS HMATH Editorial Committee, and deputy editor of the American Mathematical Monthly. She is a Project NeXT Forest Dot (2002) and co-directs the NC Network of Math Teachers’ Circles.

 

Music is full of mathematics – from sums of trigonometric sound waves that comprise audio recordings to transitions between melody notes, between chords, and between onsets in a rhythmic pattern. A variety of mathematical tools (including calculus, linear algebra, number theory and combinatorics) are available for both musical analysis and generation. In this talk we discuss:

• how patterns and transformations play a significant role in musical aesthetics,
• why we are drawn to the repetitive nature of the blues,
• why the bridge to I Want to Hold Your Hand is so mathematically perfect,
• what statistics and machine learning can say about music authentication, and
• how Fourier transforms can unravel a few musical mysteries surrounding A Hard Day’s Night.

Music is full of mathematics – from sums of trigonometric sound waves that comprise audio recordings to transitions between melody notes, between chords, and between onsets in a rhythmic pattern. A variety of mathematical tools (including calculus, linear algebra, number theory and combinatorics) are available for both musical analysis and generation. In this talk we discuss:

 

Mathematics has played a prominent role in the pandemic, and mathematical concepts have been in the press throughout, from “flatten the curve” to “herd immunity” to “Rt” and beyond. Mathematical models have also been used by decision-makers to forecast the numbers of infections and cases, project health care demand, and envision longer-term pandemic trajectories. But one of the driving features of the pandemic has been evolution: the virus has changed, increasing its transmissibility, changing its severity (both up and down) and evading our immunity. These changes have posed huge challenges for pandemic control.

In this talk, I will describe the challenges and opportunities that this brings to mathematicians.

The capacity to read the genomes or large numbers of viruses offers a lot of information about how the virus spreads and evolves. But there is a real gap between genetic sequences and interpretable information that can be used to understand dynamics, make projections and support decision-making. I will describe how new mathematical tools help fill this gap, using a combination of discrete structures, estimation and dynamic modelling. Mathematical innovations offer new ways to describe and summarize the information in genetic data, new methods to use those data to learn how pathogens move from person to person and around the world, and new ways to learn where the highest levels of transmission are occurring. I will conclude by outlining ongoing modelling challenges in the world of evolving infectious diseases.

My work is at the interface of mathematics and the epidemiology and evolution of pathogens. I hold a Canada 150 Research Chair in Mathematics for Evolution, Infection and Public Health. In my group we develop mathematical tools connecting sequence data to the ecology and evolution of infections. I also have a long-standing interest on the dynamics of diverse interacting pathogens. For example, how does the interplay between co-infection, competition and selection drive the development of antimicrobial resistance? To answer these questions, my group is building new approaches to analyzing and comparing phylogenetic trees derived from sequence data, studying tree space and branching processes, and developing ecological and epidemiological models with diversity in mind.

The speaker will discuss a very simple but popular random walk description of communication in a social network known as a consensus model. An individual in the network as represented by a vertex and is connected by edges to other vertices representing members with whom the individual communicates. Suppose one seeks to spread a message throughout the entire network by initially telling just a few members. Given constraints on the cardinality, what subset of nodes should be selected so the message spreads to the rest of the network at the fastest rate? We will describe an approach to this problem that uses a combination of discrete optimization and the mixing theory of Markov chains to identify optimal and close to optimal subsets.

Fern Hunt is scientist emeritus and mathematician at the National Institute of Standards and Technology (NIST) in Gaithersburg Maryland. Dr. Hunt received an A.B. degree in Mathematics from Bryn Mawr College and an M.S. and PhD degree in Mathematics from Courant Institute of Mathematical Sciences, New York University.

Hunt’s career has been in academia and government. She taught at City College of NY, University of Utah and Howard University before joining the government at NIST. Dr. Hunt has received research support from the National Science Foundation and NIST and has given invited addresses at meetings of the AMS and SIAM and the MAA. Hunt has received awards for her research and service to the mathematics community. Among them the Arthur Flemming Award for Outstanding Federal Service in Science, and was given special honors by the Chicago Museum of Science and Industry. For her research and service to the mathematical community Dr. Hunt was named a Fellow of the Association for Women and a Fellow of the American Mathematical Society.

Really think about that: nobody plans to fail. Nobody! And yet, not only do many students drop out of STEM, but students from marginalized communities (especially Black, Latino, Indigenous, and other marginalized racial groups) switch out of STEM or drop out at especially high rates. We often find ourselves thinking oppositionally to our students, where if only they tried harder or communicated better with us or whatever else, we could give them a better grade.

I want to shift that perspective to one of finding productive and workable solutions. I'll explore what factors go into the educations of young students, especially those in STEM majors. What kind of preparation and experiences have they had before college? What expectations do they have? What are academic factors and non-academic factors that contribute to leaving, and what solutions can we implement that will give them the tools and resources, and above all else be welcoming, so that they can succeed? Some tools are easy to do, and some will be more of a lift, but I hope that everyone comes away more prepared to effectively support students from all backgrounds.

Dan Zaharopol is the CEO of the Art of Problem Solving Initiative, Inc., where he founded and runs the Bridge to Enter Advanced Mathematics (BEAM) program. BEAM creates pathways for students from low-income and historically marginalized communities to become scientists, mathematicians, engineers, and computer scientists. Its work has been featured in the New York Times, Education Week, and the Atlantic Monthly, among others.

Dan loves math and helping others to love math. He's a product of STEM pathways himself: he received his undergraduate degree in math from MIT and masters' degrees in both mathematics and teaching mathematics from the University of Illinois. Prior to BEAM, he co-founded and served as the first CEO of Learning Unlimited.

In this talk I will describe the question that has motivated my recent work in Geometry Measure Theory. We will explore whether the behavior of a measure on balls in different metrics provides information about the structure of the support of the measure. Along the way we will see how concepts learned in calculus play an important role in this area of mathematics.

Tatiana Toro joined the Department of Mathematics at University of Washington in 1996. She is currently the Craig McKibben & Sarah Merner Professor in Mathematics. Her primary research interest lies in the interface of Partial Differential Equations, Harmonic Analysis and Geometric Measure Theory. She earned her PhD from the Stanford University under the supervision of Leon Simon (1992) and received her BS equivalent from the Universidad Nacional de Colombia, Bogota, Colombia (1986). She was a visiting member at the Institute for Advanced Study in Princeton, NJ (1992–1993). She was a Morrey Jr. Assistant Professor, University of California at Berkeley (1993-1994) and an Assistant Professor at the University of Chicago (1994-1996).

Her honors and awards include Sloan Fellowship (1998–2002), Guggenheim Fellowship (2015–2016), Simons Foundation Fellowship (2012-2013 & 2019-2020). She was an invited session speaker to the International Congress of Mathematicians in 2010 in Hyderabad, India. She is a fellow of the American Mathematical Society (AMS), a member of the American Academy of Arts and Sciences and of the Academia Colombiana de Ciencias Exactas, Físicas y Naturales. Toro is the recipient of the 2020 Blackwell-Tapia Prize and of the 2019 Landolt.

Distinguished Graduate Mentor Award from the University of Washington. Her research has been continuously supported by the National Science Foundation since 1994.

Toro served on the Board of Trustees of the Institute of Pure and Applied Mathematics (IPAM) and on the Board of Directors of the Pacific Institute for the Mathematical Sciences (PIMS). She currently serves on the Board of Directors of BIRS. She has played a leading role in the organization of the Latinx in the Mathematical Sciences conferences at IPAM (2015 & 2018).

A permutation is a list where order matters. Despite this humble definition, permutations offer a wealth of beautiful mathematics that can be applied across scientific disciplines. Starting simply, with lists of numbers, we'll discuss how smaller permutations can be embedded into larger permutations along with a host of interesting counting problems with connections not just to mathematics, but to computer science, chemistry, and more.

Lara Pudwell is a Professor of Mathematics and Statistics at Valparaiso University. She earned her undergraduate degrees (BS in mathematics, BA in computer science) from Valparaiso in 2003 and a Ph.D. in mathematics from Rutgers University in 2008. Her work in the classroom has been recognized with the 2014 Henry L. Alder Award for Distinguished Teaching from the MAA and the 2021-2022 Valparaiso University Excellence in Teaching Award. Outside of the classroom, she is a past Chair of the Indiana Section of the MAA and she has served for 11 years on the steering committee of the International Conference on Permutation Patterns. She is a coauthor of A Mathematician's Practical Guide to Mentoring Undergraduate Research (MAA Press, 2019) and spent a decade directing the Valparaiso Experience in Research by Undergraduate Mathematicians (VERUM) program. She is also the Executive Director of MathPath, a national residential summer camp for middle schoolers who love mathematics.

Mathematical modeling is a vibrant area of mathematical research that continues to expand as modelers find new ways of using mathematics to investigate a variety of phenomena. I will describe current research in the area of biological fluid dynamics, for which we have developed mathematical models and computational methods that advance our understanding of the observed swimming and feeding patterns of microorganisms. The presentation will focus on choanoflagellates, which are organisms that wave their flagellum to propel themselves or to create fluid currents that bring nutrients toward them. This work is in collaboration with experimental biologists, which allows for experimental data to be included in the models and for model results to suggest new experiments. Upon reflection on the process undertaken throughout our research, we find that the modeling process is essentially the same as the process experienced by students learning about modeling. In the last decade, we have seen a sharp increase in mathematics education research related to all aspects of modeling, including determining effective ways of teaching it and ways of preparing undergraduate students who plan to become teachers or to use mathematics professionally. The final part of the presentation will describe research on teaching mathematical modeling, including using modeling to learn new mathematical concepts or reinforce concepts learned in other courses. Our approach places emphasis on pursuing student-generated ideas for models rather than on using previously established models. This work is in collaboration with mathematics educators.

Ricardo Cortez was born in New York City. At the age of 4, his family relocated to San Salvador, El Salvador, where he grew up. He returned to the United States to go to college at Arizona State University where he received bachelor’s degrees in mathematics and in mechanical engineering. He earned a Ph.D. in applied mathematics from the University of California at Berkeley in 1995 where he received the Bernard Friedman Award for outstanding dissertation research. He then went to the Courant Institute at New York University as a National Science Foundation postdoctoral fellow and Instructor. In 1998, he joined the faculty at Tulane University. Early in his career he received a Career Enhancement Fellowship for Junior Faculty from Underrepresented Groups from the Woodrow Wilson National Fellowship Foundation and now Ricardo is the Pendergraft William Larkin Duren Professor of Mathematics and Director of the Center for Computational Science. ‍ In recognition for his research in fluid dynamics and mathematical modeling, Ricardo has been elected Fellow of SIAM and the AMS. For his mentoring work, he has been honored with the SACNAS Distinguished Undergraduate Institution Mentor award and the SACNAS Presidential award. He was the 2012 recipient of the Blackwell-Tapia prize for significant contributions to research and for his work to increase opportunities for students from underrepresented minority groups.

In 1852, a math student posed a deceptively simple-sounding question: if you want to color a map so that bordering regions always have different colors, how many colors do you need? This opened a rabbit hole that has kept mathematicians, computer scientists, and philosophers occupied for over a century, igniting a fundamental debate about how we know what is true. The central result of this exploration is the Four-Color Theorem, which covers every map of our world.

Along the way, topological explorers found a collection of worlds more complex than our own, worlds where aspiring map makers need many more than four colors. We will take a guided tour of these worlds through contemporary artists’ renditions in yarn, beads, ceramics, paper, and other media. The journey features visual and conceptual delights stretching from the nineteenth century up to now.

Susan Goldstine received her A.B. in Mathematics and French from Amherst College and her Ph.D. in Mathematics from Harvard University. For over a decade, her artworks have appeared in mathematical art exhibits across the US and around the world. Her art and research center around handcrafts, particularly knitting, crochet, and beadwork, and their connections to various mathematical fields, including abstract algebra, combinatorics, and topology. The 2014 book Crafting Conundrums: Puzzles and Patterns for the Bead Crochet Artist, which she cowrote with computer scientist and artist Dr. Ellie Baker, collects their extensive research on the mathematics of bead crochet.

Susan is Professor of Mathematics at St. Mary’s College of Maryland, where she has been on the faculty since 2004, a member of the Bridges Organization Board of Directors, co-organizer of the Bridges Math + Fashion show, and an Associate Editor for the Journal of Mathematics and the Arts. Her guiding principle is that a professor’s office can never have too many toys.

In this talk, I will discuss different examples and contexts of the word “difference.” First, I will explain how different kinds of difference quotients known as nonstandard finite differences are used to approximate the derivatives that appear in differential equations as a solution technique. Second, I will provide some ways different aspects of my identity (may) have affected my career trajectory. Third, I will present comments on how the mathematics community treats “difference” and provide suggestions for how the future for other mathematicians who differ from the norm can be different from how we were treated in the past.

Ron Buckmire is Professor of Mathematics at Occidental College (Oxy) in Los Angeles, California. He holds mathematics degrees (Ph.D., M.Sc. and B.Sc.) from Rensselaer Polytechnic Institute in Troy, NY. He has been on the Oxy faculty since 1994, beginning as Minority Postdoctoral Scholar-in-Residence and eventually serving as chair of the mathematics department twice (2005-2010 and 2015-2016), achieving the rank of Full Professor in 2014 and was Associate Dean for Curricular Affairs and Director of the Core Program from 2018 to 2022. He was an employee of the United States National Science Foundation (NSF) from 2011-2013 and 2016-2018. At NSF, he was a Lead Program Director in the Division of Undergraduate Education (DUE) where he headed the S-STEM program and was responsible for managing DUE’s award portfolio promoting excellence in undergraduate mathematics education throughout the United States.

He is the co-editor of Improving Applied Mathematics Education (Springer Nature, 2021) and has published peer-reviewed articles in an eclectic collection of peer-reviewed journals such as Data, Notices of the American Mathematical Society, Numerical Methods for Partial Differential Equations, IMA Journal of Management Mathematics, Works and Days and the Albany Law Review. His research is in numerical analysis, ordinary differential equations, the scholarship of teaching and learning and data science. He is a passionate advocate for broadening the participation of historically excluded groups (especially LGBTQ+ individuals and racial/ethnic minorities) in mathematics and other STEM disciplines. He serves and has served the broader mathematics community in several capacities, such as Vice-President for Equity, Diversity and Inclusion (EDI) at SIAM, Chair of the AMS Committee on EDI, Chair of MSRI’s BPAC, member of BIRS’ EDI board and ICERM’s board of trustees. He is a co-founder and board member of Spectra, the association for LGBTQ+ mathematicians and their allies.

A Platonic solid is a polyhedron with the following properties: all its faces are congruent regular polygons, and the number of polygons meeting at each vertex is the same. Book XIII of Euclid’s elements contains a proof that there are exactly five such solids, namely, the tetrahedron, cube, octahedron, dodecahedron, and (the MAA logo) icosahedron. During our hour together we will make origami models of these solids, talk about Euler’s formula for convex polyhedra, and use it to prove that these are the only five Platonic solids.

Kevin Knudson is Professor of Mathematics at the University of Florida, where he currently serves as Chair of the Department of Mathematics. An algebraic topologist by training, his current research interests lie in the field of topological data analysis with a particular focus on discrete Morse theory. Knudson serves on the editorial board of Math Horizons and produces, with freelance writer Evelyn Lamb, the My Favorite Theorem podcast. In his spare time he enjoys cooking, kayaking, yoga, and playing the guitar (poorly, but hey, he didn’t take it up until his mid-40s).

Reflection is an important practice to make sense of and grow from any experience—big or small. Whether attending a meeting, teaching a class, writing an article, leading an organization, or adapting to a pandemic, there are lessons to be learned. For this talk, I take stock of some important lessons inspired by a life in combinatorics.

Dr. Jennifer Quinn is a professor of mathematics at the University of Washington Tacoma. She earned her BA, MS, and PhD from Williams College, the University of Illinois at Chicago, and the University of Wisconsin, respectively. Her first academic position was at Occidental College, where she rose through the ranks to full professor and chaired the department. At UW Tacoma for the past 15 years, she has helped build a mathematics curriculum on the expanding campus. Jenny has held many positions of national leadership in mathematics including Executive Director of the Association for Women in Mathematics, co-editor of MAA’s Math Horizons, and several positions on the MAA Board of Directors (and its predecessor, the Executive Council). She received an MAA Haimo Award for Distinguished College or University Teaching and a Beckenbach Book award for Proofs That Really Count: The Art of Combinatorial Proof, co-authored with Arthur Benjamin. As a combinatorial scholar, Jenny thinks that beautiful proofs are as much art as science. Simplicity, elegance, transparency, and fun should be the driving principles. As President of MAA 2021-22, Jenny worked to do what was needed when it was needed to keep MAA strong and build community during pandemic isolation. Serving as President was a highlight of her professional career.