Invited Paper Sessions are organized by mathematicians and designed to provide substantial mathematical content in the MAA program. Four to eight speakers are invited by the organizers to present on a designated topic for twenty-minute segments. MAA MathFest participants who come to these sessions will get the chance to hear from a diverse set of speakers on current or emerging topics in various areas of mathematics.

Invited Paper Session aligned with the Hedrick Lecture Series

New Directions in Group Theory

Group theory is a storied topic in mathematics but is constantly evolving. Speakers in this special session will touch on topics from filling area to new kinds of boundaries and dimension, making many connections from groups themselves to curves, surfaces, and cube complexes.

Organizer:
Moon Duchin, University of Chicago
Chandrika Sadanand, Bowdoin College
Corey Bregman, Tufts University
Emily Stark, Wesleyan University
Carolyn Abbott, Brandeis University

Invited Paper Session aligned with an MAA Invited Address

Mathematical Modeling of Active Matter

Colonies of bacteria in a biofilm, suspensions of self-propelled oil droplets in a surfactant solution, and actin-microtubules in the cytoskeleton are examples of active matter - collections of individual agents that consume energy to move. In such systems at the microscale, viscous flows play a crucial role, where rich fluid-swimmer and fluid-structure interactions can emerge. A wide range of dynamics has been identified, and extensive studies have been conducted through development of diverse mathematical and computational models. This session highlights recent advancements in various models in viscous flow and the progress in analytical techniques and numerical methods.

Organizer:
Lisa Fauci, Tulane University

Invited Paper Session aligned with the Gardner Lecture

Inverse Problems: The Mathematics of Seeing the Invisible

Inverse problems arise from our desire to see a hidden or distant object that we cannot access directly. But we have an indirect measurement available, where the crucial information is buried in a complicated way. An extra nuisance is ill-posedness, meaning that two quite different objects may produce almost the same data. The mathematical challenge is then to form an image of the object from the measurement using a computational algorithm, somehow made robust against measurement noise. Inverse problems appear in many applications, including medical imaging, geosciences, astronomy, nondestructive testing, antenna design and signal restoration. For example, consider a doctor who wants to know what’s going on inside her patient’s lungs. She attaches 32 electrodes around the patient’s chest, feeds harmless electric currents into the body, and measures the voltages at the electrodes. Since current flows through the body according to different conductivities of various organs, the measurements do contain information about the distribution of tissues, air and fluids inside the chest. Forming an image of a cross-section of the patient’s body is a nonlinear problem requiring techniques from many branches of mathematics. Indeed, inverse problems is a multidisciplinary field of science that constantly creates both pure and applied mathematical questions. In this session, four intriguing inverse problems are discussed, related to medical imaging, geophysics, navigation, and astronomy.

Organizer:
Samuli Siltanen, University of Helsinki, Finland

Invited Paper Session aligned with the Leitzel Lecture

Mathematics at the Edge of Change: AI in the Mathematics Classroom

This session invites the mathematics community to rethink what it means to teach and learn mathematics in an intelligent era. Generative artificial intelligence (GenAI) tools such as ChatGPT, CoPilot, and Claude are prompting new questions about how mathematics is learned, taught, and experienced. This invited session brings together educators and researchers who are exploring the role of AI across a wide range of mathematics classrooms.
Talks will highlight both the opportunities and the challenges that emerge when AI becomes part of mathematics teaching and learning. Presenters will share practical strategies for using AI to support mathematical reasoning, assessment, and creativity while maintaining the rigor and human connection that define strong mathematics instruction.

Organizer:
Angie Hodge-Zickerman, Northern Arizona University

AWM-MAA Invited Paper Session aligned with the Falconer Lecture

Bridging the Gap – Insights with Modeling

Whether it be in research or the classroom, modeling allows us to examine a variety of questions. We can use models to predict future circumstances from different dynamics, consider management, explore unobservable situations, and much more. In this session, we bring together speakers who leveraged models in a variety of situations. Furthermore, we consider how models can bridge gaps when it comes to collaborations, skill sets, topics, and more.

Organizer:
Christina J. Edholm, Scripps College

Sponsor:
Association for Women in Mathematics (AWM)

AMS-MAA Invited Paper Session aligned with the AMS-MAA Invited Address

Hidden & Broken Symmetries Across Scales: Geometry, Materials,
and Pattern Formation

Symmetry quietly organizes how patterns form: it limits what can happen and explains why certain shapes and behaviors keep appearing. This invited paper session brings together geometry and soft matter to show how symmetry, and how we intentionally break it, drives pattern formation across scales. Talks will range from geometric parameter spaces to wrinkling and buckling in thin sheets and textiles, chiral and complex fluids, and network-like transport in living systems. A common thread is how invariance, anisotropy, and heterogeneity shape morphologies, thresholds, and instabilities, using ideas from PDEs, dynamical systems, experiments, and computation. The session complements the invited address “Hidden & Broken Symmetries,” highlighting micro-to-macro links and inviting cross-pollination between pure and applied communities.

Organizers:
Laura Schaposnik, University of Illinois at Chicago
Chris Rycroft, University of Wisconsin
Yue Sun, University of Wisconsin

Invited Paper Session aligned with the Darden Lecture

Modeling Retinal Function and Disease: Computational Perspectives for Maintaining Vision

The retina is a complex neural network that transforms incoming light into neural signals that are transmitted to the brain. Understanding retinal function in normal and pathological conditions provides insights for intervening in degenerative processes and restoring vision. Mathematical modeling has been used to study diverse biological topics ranging from protein folding to cell interactions to interacting populations of humans but has only recently been used to study photoreceptor degeneration, which occurs in age-related macular degeneration (AMD) and retinitis pigmentosa (RP).  There are many different maladies that can result in blindness but the ones that result from photoreceptor degeneration pose the biggest threat as there is no cure. Computer (in silico) experiments in this area have given researchers invaluable insights to mitigate blindness and, in some cases, re-directed experimental research.  The talks in this session will present a variety of mathematical models at both the cellular and molecular level as well as the interactions and feedback mechanisms within and between these levels. Dynamical systems, optimal control, uncertainty and sensitivity analysis together with in silico experiments are used to analyze these systems of nonlinear differential equations. This work highlights the delicate balance of many aspects of the photoreceptor system including the inter-dependent and inter-connected feedback processes modulated by and affecting cone’s metabolism.

Organizer: 
Erika Tatiana Camacho, University of Texas at San Antonio

Invited Paper Session aligned with an MAA Invited Address

Computation and Illustration in Mathematical Research

Mathematicians have always drawn pictures—but visualization is more than a pedagogical tool or a way to communicate finished results. For many researchers, the process of creating images is integral to discovery itself: pictures reveal structure, suggest conjectures, and expose the flaws in our intuitions. And visualization extends beyond inherently geometric subjects—computational experiments often produce data that we interpret visually, finding patterns even when the underlying mathematics has no obvious pictorial form. This session brings together mathematicians from across the discipline who use computation and illustration as working research tools. Talks will discuss current research alongside the visual and computational methods underlying it, with a goal of learning from diverse approaches. All talks will be accessible to a broad audience.

Organizer:
Steve Trettle, University of San Francisco

MAA Invited Paper Sessions

Combinatorics and Probability

On the occasion of Peter Winkler's 80th birthday, this session will bring together mathematicians interested in some of his favorite topics, including probabilistic methods in combinatorics, random walks, percolation, Markov chains, partially ordered sets, combinatorial games, and mathematical puzzles. Speakers will include world experts in these fields, as well as some of Peter Winkler’s collaborators and former students.

Organizers:
Sergi Elizalde, Dartmouth College
Robert Dougherty-Bliss, Dartmouth College
Chris Coscia, Tufts University

Philosophy of Mathematics

The philosophy of mathematics is an interdisciplinary subject, requiring background in mathematics and philosophy. As an area of research within philosophy, it serves as a test for theories of existence, knowledge, and language, but many mathematicians have not had the chance to keep up with recent developments. The holding of a national meeting in Boston offers an opportunity to bring together many of those involved with recent developments in the philosophy of mathematics, both inside and outside the mathematical community. Many questions from a century ago remain alive in a philosophical setting, but technical results have a role to play. From the time of Zeno’s paradoxes onward, mathematicians have had to look at philosophical issues. The objective of the proposed session is not to ignore technical details but to explain how the various currents of mathematics and mathematical practice interact with philosophical issues.

Organizers:
Steven Deckelman, University of Wisconsin - Stout
Bonnie Gold, Monmouth University
Thomas Drucker, University of Wisconsin - Whitewater

Sponsor:
SIGMAA on Mathematics and Philosophy (SIGMAA POM)

Fifty Years of the Four Color Theorem

“Four Colors Suffice!” This session will address the history of the Four Color Theorem since its first proof in 1976, the current status of the theorem, and prospects for further improvements. The circumstances of the Appel-Haken proof are well documented, but the prehistory of the theorem still contains surprises, and some of the speakers will have stories from the olden days. The history since 1976 has at least four main threads: improved proofs along the original lines; some of the first great successes of computer verification; countless extensions and generalizations; and the connection of the 4CT to equivalent results in a surprising variety of areas, including algebraic combinatorics and quantum mechanics. The organizers do not expect a new human-scale proof to emerge at Mathfest, but hope never fades.

Organizers:
Walter Stromquist, Bryn Mawr College
Paul Kainen, Georgetown University

Computers and Combinatorics

The purpose of this session is to bring together mathematicians interested in using computers to discover new theorems, find counterexamples, and prove theorems in combinatorics. The 4-color theorem is the most famous classical example, but the field has seen an explosion of computer applications in recent years. The bunkbed conjecture was disproven with computational assistance, symbolic computation is regularly used to derive complicated recurrences and differential equations, and renewed interest in artificial intelligence and deep learning suggests new trends and opportunities. We plan to assemble a group of leading experts who have made contributions to graph theory, discrete geometry, combinatorial number theory, extremal combinatorics, and other areas of discrete combinatorial mathematics using computers.

Organizers:
Robert Dougherty-Bliss, Dartmouth College
William Wesley, University of California at San Diego

Fibonacci Fun!

For almost a millennium, Fibonacci numbers and related sequences have fascinated people with their remarkable properties and applications. As many of these can be proved using only elementary counting and combinatorics, and as fascinating new relations are suggested by simple numerical experiments, they're ideally suited to excite the next generation. Talks will explore these in an accessible manner, hopefully leaving each listener with an ``a-ha!'' moment as they see another remarkable connection, emphasizing possible research problems and opportunities to use in classes.

Organizers:
Art Benjamin, Harvey Mudd College
Hung Chu, Washington and Lee University
Steven Miller, Williams College

Trends in Mathematical Biology

This BIO-SIGMAA sponsored session will explore the critical role of mathematical modeling in understanding and addressing complex problems in biological systems, including ecology, epidemiology, environmental science, and medical sciences. By translating biological processes into quantitative frameworks, mathematical models enable researchers to analyze dynamics, predict outcomes, and design effective interventions for issues such as disease spread, population dynamics, and ecosystem sustainability. The session will highlight a wide range of mathematical approaches—from differential equations, stochastic processes, and network theory to agent-based modeling, dynamical systems, and data-driven computational methods. Bringing together mathematicians, biologists, and environmental scientists, this session aims to foster interdisciplinary collaboration and demonstrate how mathematics serves as a powerful lens for revealing patterns, testing hypotheses, and informing policy in the life sciences.

Organizers:
Erin Bodine, Rhodes College
Ali Campbell, University of California at Berkeley
Anne Yust, University of Pittsburgh

Sponsor:
SIGMAA on Mathematics and Computational Biology (SIGMAA BIO)