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Invited Paper Sessions

The Serious Side of Recreational Mathematics

Friday, August 2, 1:30 p.m. - 4:20 p.m., Duke Energy Convention Center, Room 200


Recreational mathematics covers a wide variety of themes: card tricks, board games, puzzles, origami, and art are just a few. The use of “recreational” gives the impression that research in these topics is more of a pastime than an investigation with depth to it. However, when you look below the surface, there is a surprising amount of complexity to the subjects being studied. This invited paper session will include experts in the many topics in recreational math showing how starting with a fun puzzle, game, or story can take one on a trip to deep mathematics.

Our goal is to show the myriad of topics gathered underneath the recreational umbrella rather than highlight one topic. The gamut of this runs from the combinatorial questions in designing unique puzzles and using origami in designing robots, to the powerful logic in Knights and Knaves puzzles, the geometric structures hidden in the game SET, and using number theory to create new tricks with playing cards.

Robert Vallin, Lamar University

Sponsor: SIGMAA on Recreational Mathematics

Art Benjamin, Harvey Mudd
James Sellers, Penn State University
Liz McMahon, Lafayette College
Steve Butler, Iowa State University
Bob Bosch, Oberlin College


Cryptography and the Mathematics Behind It

Thursday, August 1, 1:30 p.m. -4:20 p.m., Duke Energy Convention Center, Room 205


The security of our voting, banking, and military systems, the infrastructure of modern day society, and democracy itself rely on cryptography, to ensure privacy and allow secure and authenticated communication. Public key cryptography is based on mathematics, especially number theory and algebraic geometry. Recent proposals to solve long-standing important problems in the field of computer security use the geometry of numbers and the theory of lattices. Other mathematical ingredients found in modern day cryptography include factorization of numbers, discrete logarithms, and the theory of elliptic curves. Current research includes the area of fully homomorphic encryption and the search for cryptographically useful multilinear maps.

This session will have expository talks aimed at a general mathematical audience and will be suitable for both students and faculty.

Alice Silverberg, University of California, Irvine

Jingtai Ding, University of Cincinnati
David Jao, University of Waterloo
Kumar Murty, University of Toronto
Steven J Miller, Williams College
Adriana Salerno, Bates College


The Mathematics of Uncertainty

Friday, August 2, 10:10 a.m. - 12:00 p.m., Duke Energy Convention Center, Room 200


We encounter uncertainty everywhere, at all levels of our consciousness, in almost every one of our endeavors. Even things of which we are certain: the sun will rise tomorrow, our current existence has a finite time span, are subject to imprecision. How has mathematics helped us understand uncertainty and unpredictability? How can we use use quantitative tools to make decisions under incomplete information or cognitive limitations?

In this session we will present mathematical tools and results from probability, dynamical systems and ergodic theory that give insight into these questions.

Ami Radunskaya, Pomona College

Potential Speakers:
Kim Ayers, Pomona College
Sarah Bryant, Dickinson College
Peter Hinow, University of Wisconsin, Milwaukee
Joshua Sack, California State University, Long Beach


Equity and Justice in the Context of Inquiry

Thursday, August 1, 1:30 p.m. - 4:20 p.m., Duke Energy Convention Center, Room 200


Research is indicating that inquiry pedagogies have the potential to offer rich learning experiences that address some of the ways in which the collegiate mathematics education systematically under-serves some populations. And yet, we also know that elements of these environments, if implemented without care, can contribute to the alienation of exactly the students instructors are hoping to support. For example, being asked to talk in class can trigger stereotype threat for students of color, and unstructured discussions may create spaces in which privileged voices dominate. In addition to implementation issues, as researchers we must develop and apply methods that allow us to see the experiences of marginalized students even when these experiences can be hidden by averages or statistical methods.

While inquiry pedagogies and equity research have great potential for interconnections, combining them as pre-existing perspectives can miss key issues. Inquiry in general might have potential for equity, but colorblind approaches to this framing of the classroom will hide the different meanings made by students in those classrooms and cannot address the pervasive issue that students of color are disproportionately tracked out of some mathematical spaces and into others. Similarly, to the extent that some equity research has had to use instructor-centered pedagogies as a backdrop, different assumptions in inquiry pedagogies might produce significantly different observations. As a result, equity and inquiry must be theorized and researched together in order to engage these emergent questions about using inquiry to rehumanize mathematics and offer justice for all students. The scholars in this session have all contributed to this ongoing research agenda; this session will put their work in direct conversation in support of extending this research agenda.

Brian Katz, Augustana College

Potential Speakers:
Sandra Laursen, University of Colorado Boulder
Chris Rasmussen, San Diego State University
Stacy Brown, CalPoly Pomona
Rochelle Gutierrez, University of Illinois
Jessica Ellis Hagman, Colorado State University
Estrella Johnson, Virginia Tech
Christine Andrews-Larson, Florida State University
Gail Tang, University of LaVerne
Emily Cilli-Turner, University of Washington Tacoma
Aditya Adiredja, University of Arizona
Robin Wilson, CalPoly Pomona
Brian Katz, Augustana College


Mathematical Diversity in Mathematical Biology

Friday, August 2, 1:30 p.m. - 5:20 p.m., Duke Energy Convention Center, Room 205


In this session, Project NExT'rs from the 2018 cohort will showcase the diversity of mathematics used in better understanding biological systems. This session is designed specifically for an under-graduate audience.

Mathematical biology is grab-bag description for using mathematical techniques to understand biological phenomena. The mathematics applied to study biology is not restricted to a particular sub-discipline of mathematics, but rather is as diverse as the biological systems studied themselves. It requires a blend of existing and contemporary mathematics and fosters wide spread collaboration between not only mathematicians, but also biologists and biomedical scientists. This session will showcase a diverse range of mathematical techniques being applied to a variety of biology systems, from molecular biology and physiology to organismal biology across all length scales of life. Mathematics has been called `biology's next microscope, only better' and to complement that `biology is mathematics' next physics, only better' (J.E. Cohen 2004). This session is designed to be accessible for undergraduate students; we will introduce and discuss how mathematics can contribute to new understanding of biological and biomedical phenomena. Theory and concepts from dynamical systems, optimal control, partial differential equations, numerical analysis, geometry, combinatorics, probability theory, and other areas will be discussed in conjunction with searching for biological insight for problems stemming from cancer biology, epidemiology, psychology, ecology, phylogenetics, organismal biology, personalized medicine, and biomechanics.

Nicholas A. Battista, The College of New Jersey
Rebecca Everett, Haverford College

Brittany Stephenson, Lewis University
Reginald McGee, College of the Holy Cross
Rebecca Everett, Haverford College
Forest Mannan, Colorado School of Mines
Diana Schepens, Whitworth University
Amy Buchmann, University of San Diego
Amy Veprauskas, University of Louisiana at Lafayette
Garner Cochran, Berry College


Commutative Algebra

Saturday, August 3, 9:00 a..m. - 11:50 a.m., Duke Energy Convention Center, Room 200


Commutative algebra is central discipline at the intersection of algebraic geometry, number theory, and many other areas. Many of the foundations were laid by Emmy Noether and modern commutative algebra combines techniques from computational symbolic algebra, combinatorics, graph theory, and homological and homotopical algebra. This session will have expository talks on many flavors of commutative algebra with a broad appeal towards the subjects natural influence. The talks will be aimed at a general mathematical audience, will be suitable for both students and faculty, and will hope to expose participants to the rich tapestry of current and classic results available.

Irena Swanson, Reed College
Lance Miller, University of Arkansas, Fayetteville