MAA Invited Paper Sessions Descriptions
The Unreasonable Effectiveness of Modern Mathematics, organized by Andrew Conner and Ellen Kirkman, Wake Forest University; Wednesday morning. The session will demonstrate that abstract mathematics continues to provide tools for use outside of mathematics. Speakers include Robert Ghrist, University of Pennsylvania, on topology; Daniel Nakano, University of Georgia, on representation theory; Alice Silverberg, University of California Irvine, on number theory; and Bernd Sturmfels, University of California Berkeley, on algebraic geometry, combinatorics, and commutative algebra.
The Continuing Influence of Paul Erdős in Number Theory, organized by Paul Pollack, University of Georgia, and Carl Pomerance, Dartmouth College; Friday morning. For the better part of the twentieth century, Paul Erdo˝s stood as a leading figure in number theory. This session brings together experts from that area to discuss the impact of Erdo˝s's work on modern research. Speakers include Michael Filaseta, University of South Carolina; Ron Graham, University of California, San Diego; Mits Kobayashi, Cal Poly Pomona; Florian Luca, National Autonomous University of Mexico; Melvyn Nathanson, City University of New York; and Andrew Granville, University of Montreal.
Uniform Distribution, Discrepancy, and Related Fields, organized by Dmitriy Bilyk, University of Minnesota, and Jill Pipher, Brown University; Friday afternoon. How well can one approximate various continuous geometric objects by discrete sets of points and how big are the inevitable errors? Different manifestations of this question, which lies at the interface of number theory, probability, approximation theory, combinatorics, analysis, and geometry, will be discussed from various points of view. Speakers include Art Owen, Stanford University; Michael Lacey, Georgia Institute of Technology; Ed Saff, Vanderbilt University; and Vladimir Temlyakov, University of South Carolina.
Graphs Don’t Have to Lie Flat: The Shape of Topological Graph Theory, organized by sarah-marie belcastro, Sarah Lawrence College, and Mark Ellingham, Vanderbilt University; Thursday morning. Topological graph theory is the study of graphs drawn on topological surfaces, usually (but not always!) so that no edges cross. The field is concerned with most of the same topics as ordinary graph theory as well as questions that arise from encoding the embedding of a graph in a surface. Speakers include Mark Ellingham, Vanderbilt University; Joan Hutchinson, Macalester College; Jo Ellis-Monaghan, St. Michael’s College; and Michael Pelsmajer, Illinois Institute of Technology.
Mathematics and Effective Thinking, organized by Michael Starbird, University of Texas Austin; Thursday, morning and afternoon. Mathematics classes can and do influence students’ thinking well beyond the mathematical content. Mathematics classes can help students in all parts of their lives by helping them to think effectively—that is, being innovative problem-solvers, insightful and clear-minded, intellectually curious, able to ask illuminating questions, and confident and competent to reason through complex issues. These habits of mind can be fostered and developed systematically through mathematical experiences. This session focuses on how the mathematical curriculum and strategies of instruction can intentionally help students to learn to think effectively throughout their lives. Speakers include Deborah Bergstrand, Swarthmore College; David Bressoud, Macalester College; Edward Burger, Southwestern University; Jodi Cotton, Westchester Community College; Sandra Laursen, University of Colorado Boulder; Michael Pearson, Mathematical Association of America; Carol Schumacher, Kenyon College; Katherine Socha, Math for America; Francis Su, Harvey Mudd College; Stan Yoshinobu, California State University Dominguez Hills; and Paul Zorn, St. Olaf College.
Six Crash Courses on Mapping Class Groups, organized by Benson Farb, University of Chicago, and Dan Margalit, Georgia Institute of Technology; Friday morning and Saturday afternoon. The mapping class group is the group of homotopy classes of homeomorphisms of a surface. It was first studied by Dehn in the 1920s. The mapping class group is important because it connects in deeps ways to many areas of mathematics, including low-dimensional topology, algebraic geometry, dynamics, geometric group theory, and representation theory. The goal of this session is to give an introduction and overview of the theory of mapping class groups for the non-expert. There will be six (mostly) self-contained expository lectures, starting from the basic definitions, examples, and theorems, moving to the connections with surface bundles, and culminating in more recent developments, including the Nielsen-Thurston classification of elements of the mapping class group, which is analogous to Jordan Canonical Form. In the final lecture, we will discuss some of the many open directions in this very active and diverse area of research.