Earle Raymond Hedrick Lecture Series
Algebra Over Finite Fields
Karen Smith, University of Michigan
Hedrick Lecture 1
Wednesday, August 5, 9:30 AM - 10:20 AM, Marriott Wardman Park, Salon 2/3
Starting with a little trick I learned in third grade to check my multiplication homework, I'll share my fascination with algebra as it grew through middle school, high school, college and eventually led to research in characteristic p rings. Along the way, I'll point out the importance of many mentors and teachers who led me to eventually pursue my career in mathematics.
Hedrick Lecture 2
Friday, August 7, 9:30 AM - 10:20 AM, Marriott Wardman Park, Salon 2/3
In the second talk, I will explain how doing algebra over finite fields can deepen our understanding of geometry. Specifically, I'll discuss how understanding solutions to polynomials over finite fields can help understand the geometry of algebraic varieties defined by real or complex polynomials. Miraculously, rings of characteristic p have some very special properties that can be powerful tools in analyzing them, often replacing tools like integration for real manifolds.
Hedrick Lecture 3
Saturday, August 8, 9:30 AM - 10:20 AM, Marriott Wardman Park, Salon 2/3
In the third talk, I will explain some of these recent tools in “characteristic p” algebra---specifically Frobenius splitting and related tools--- which have made an impact on different areas of math, including the minimal model program for complex algebraic varieties and cluster algebras in combinatorics/representation theory. Some of this work is joint work with my PhD students and post-docs.
MAA Centennial Lecture 1
Replicators, Transformers, and Robot Swarms: Science Fiction through Geometric Algorithms
Wednesday, August 5, 8:20 AM - 9:20 AM, Marriott Wardman Park, Salon 2/3
Erik Demaine, Massachusetts Institute of Technology
Science fiction is a great inspiration for science. How can we build reconfigurable robots like Transformers or Terminator 2? How can we build Star Trek-style replicators that duplicate or mass-produce a given shape at the nano scale? How can we orchestrate the motion of a large swarm of robots? Recently we've been exploring possible answers to these questions through computational geometry, in the settings of reconfigurable robots (both modular and folding robots that can become any possible shape), robot swarms (which may be so small and simple that they have no identity), and self-assembly (building computers and replicators out of DNA tiles).
MAA Centennial Lecture 2
Network Science: From the Online World to Cancer Genomics
Wednesday, August 5, 10:30 AM - 11:20 AM, Marriott Wardman Park, Salon 2/3
Jennifer Chayes, Microsoft Research
Everywhere we turn these days, we find that networks can be used to describe relevant interactions. In the high tech world, we see the Internet, the World Wide Web, mobile phone networks, and a variety of online social networks. In economics, we are increasingly experiencing both the positive and negative effects of a global networked economy. In epidemiology, we find disease spreading over our ever-growing social networks, complicated by mutation of the disease agents. In biomedical research, we are beginning to understand the structure of gene regulatory networks, with the prospect of using this understanding to manage many human diseases. In this talk, I look quite generally at some of the models we are using to describe these networks, processes we are studying on the networks, algorithms we have devised for the networks, and finally, methods we are developing to indirectly infer network structure from measured data. I'll discuss in some detail particular applications to cancer genomics, applying network algorithms to suggest possible drug targets for certain kinds of cancer.
MAA Centennial Lecture 3
Mathematics for Art Investigation
Thursday, August 6, 8:30 AM - 9:20 AM, Marriott Wardman Park, Salon 2/3
Ingrid Daubechies, Duke University
Mathematical tools for image analysis increasingly play a role in helping art historians and art conservators assess the state of conservation of paintings, and probe into the secrets of their history. The talk will review several case studies, Van Gogh, Gauguin, Van Eyck among others.
MAA Centennial Lecture 4
The Role and Function of Mathematical Models in Interdisciplinary Mentorship through Research: Lessons from the World of Epidemics
Thursday, August 6, 10:30 AM - 11:20 AM, Marriott Wardman Park, Salon 2/3
Carlos Castillo-Chavez, Arizona State University
We live in an interconnected world in which seeking solutions to societal problems no longer makes sense within the confines of single-discipline organized institutions. The nation’s ability to train 21st century scientists depends on systems of learning and thinking that are naturally embedded within interdisciplinary educational research/mentorship models. The use of multiple modes of doing science including the systematic use of computer experiments and data science (Big Data) must be at the heart of a modern 21st Century STEM education.
As Steve Strogatz observes “… cancer will not be cured by biologists working alone. Its solution will require a melding of both great discoveries of 1953 [Fermi-Pasta-Ulam introduction of the computer experiment and Watson & Creek discovery of the chemical structure of DNA]. Many cancers, perhaps most of them, involve the derangement of biochemical networks that choreograph the activity of thousands of genes and proteins. As Fermi and his colleagues taught us, a complex system like this can't be understood merely by cataloging its parts and the rules governing their interactions. The nonlinear logic of cancer will be fathomed only through the collaborative efforts of molecular biologists — the heirs to Dr. Watson and Dr. Crick —and mathematicians who specialize in complex systems — the heirs to Fermi, Pasta and Ulam.”
In this lecture, I will highlight (1) the role that interdisciplinary research challenges has played in shaping the training and mentorship of students from high school to the postdoctoral level and (2) the impact that has had on my own research program. The discussion will be centered on questions that arise in the study of disease dynamics (Ebola and Influenza) across levels of organization and over multiple spatiotemporal scales.
The examples used are the result of the research carried out with a myriad of collaborators (undergraduate, graduate, postdoctoral students and colleagues) over the past three decades.
MAA Centennial Lecture 5
CSHPM Kenneth O. May Lecture
"We Are Evidently on the Verge of Important Steps Forward": The American Mathematical Community, 1915-1950
Friday, August 7, 10:30 AM - 11:20 AM, Marriott Wardman Park, Salon 2/3
Karen Parshall, University of Virginia
The American mathematical community experienced remarkable changes over the course of the thirty-five years from the founding of the Mathematical Association of America (MAA) in 1915 to the establishment of the National Science Foundation in 1950. The first fifteen years witnessed not only the evolution of the MAA with its emphasis on the promotion of mathematics teaching but also the “corporatization” and “capitalization” of the American Mathematical Society as mathematicians worked to raise money in support of research-level mathematics. The next decade, one characterized by the stock market crash and Depression, almost paradoxically saw the building of mathematics departments nationwide and the absorption into those departments of European mathematical refugees. Finally, the 1940s witnessed the mobilization of America’s mathematicians in the war effort and their subsequent efforts to insure that mathematics was supported as the Federal government began to open its coffers in the war’s immediate aftermath. This talk will explore this period of optimism in which the American mathematical community sensed, as Roland Richardson put it, “we are evidently on the verge of important steps forward.”
MAA Centennial Lecture 6
Recent Results Toward the Birch and Swinnerton-Dyer Conjecture
Saturday, August 8, 10:30 AM - 11:20 AM, Marriott Wardman Park, Salon 2/3
Manjul Bhargava, Princeton University
Over the past half-century, the Birch and Swinnerton-Dyer Conjecture has become one of the most notoriously difficult unsolved problems in mathematics, and has been listed as one of the seven million-dollar "Millennium Prize Problems" of the Clay Mathematics Institute. In this talk, we describe the problem in elementary terms, and the surprising and beautiful ways in which it is related to several well-known open problems in number theory. Despite the difficulties in solving it, there is actually quite a bit known now towards the conjecture. We will give a survey of what is known – including several recent advances – and, finally, what remains to be done!
AMS-MAA Joint Invited Address
The Arithmetic of the Spheres
Thursday, August 6, 9:30 AM - 10:20 AM, Marriott Wardman Park, Salon 2/3
Jeffrey Lagarias, University of Michigan
Beginning with historical remarks on the harmony of the spheres, this talk tours two topics at the interface of number theory and dynamical systems. The first concerns the Farey tree, Ford circles and the Minkowski question-mark function. The second concerns Farey fractions, radix expansions and the Riemann zeta function.
MAA James R. C. Leitzel Lecture
Calculus at Crisis
Saturday, August 8, 8:30 AM - 9:20 AM, Marriott Wardman Park, Salon 2/3
David Bressoud, Macalester College
The predominance of calculus in high school, recognition of the importance of modeling dynamical systems—especially in the biosciences, and existence of sophisticated online resources have changed what students need from college calculus. Despite recent insights into what it means to understand calculus and how students achieve this knowledge, failure rates are unacceptably high, and passing is no guarantee of ability to use the ideas of calculus. Together, these forces confront departments with a series of decision points around what to teach and how to teach it.
AWM-MAA Etta Z. Falconer Lecture
"A Multiplicity All At Once": Mathematics for Everyone, Everywhere
Friday, August 7, 8:30 AM - 9:20 AM, Marriott Wardman Park, Salon 2/3
Erica Walker, Columbia University
What does it mean to learn mathematics? What does it mean to say that some people are “math people”? In this talk, I draw upon 20 years of research and teaching to describe multiple contexts for mathematics learning and socialization across the lifespan. I share findings from studies with elementary students, high school youth, teachers, and mathematicians to describe how they engage in mathematical practice, develop mathematics identities, and craft meaningful spaces for rich mathematics learning. I discuss implications of this work for reframing teaching and learning, both within and outside of schools, to better foster people's success, interest, and creativity in mathematics.
MAA Chan Stanek Lecture for Students
Seventy-Five Years of MAA Mathematics Competitions
Wednesday, August 5, 1:00 PM - 1:50 PM, Marriott Wardman Park, Salon 2/3
Joseph Gallian, University of Minnesota Duluth
In this talk we provide facts, statistics, oddities, curiosities, videos, and trivia questions about the mathematics competitions that the MAA has sponsored for 75 years.
Pi Mu Epsilon J. Sutherland Frame Lecture
G-sharp, A-flat, and the Euclidean Algorithm
Friday, August 7, 8:00 PM - 8:50 PM, Marriott Wardman Park, Salon 2/3
Noam Elkies, Harvard University
Why does Western music almost universally use the same repeating pattern of 7+5 notes seen in the piano's white and black keys, and why does each of these notes (especially the black ones, like G-sharp / A-flat) get more than one name? Using a piano, the audience's voices, and more traditional lecture materials, I'll outline how music, physics, and mathematics converged to produce this structure, including an overlap between one thread of music history and the first few steps of the Euclidean algorithm applied to the logarithms of 2 and 3.
NAM David Harold Blackwell Lecture
Mathematics, Mathematicians, Mathematics Education and Equity: Challenges and Opportunities
Friday, August 7, 1:00 PM - 1:50 PM, Marriott Wardman Park, Salon 2/3
Terrence Blackman, The University of Denver
African Americans have a long and honorable tradition of doing Mathematics and Mathematics Education in the African American community. In this talk, from a perspective of excellence and equity, I will address the critical necessity of engagement in Mathematics Education, by all mathematicians and in particular, African American mathematicians. In so doing, I will describe some of the challenges and opportunities for undergraduates considering careers in the mathematical sciences.