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Invited Addresses, Sessions, and Other ActivitiesBelow are some selected events from the wide variety of activities at the meeting:
The Genome Project for Three-Manifolds - MAA Invited Address by Jeffrey Brock (Brown University) It is now widely accepted within the mathematical community that the
Poincaré Conjecture and Thurston's Geometrization Conjecture
are no longer conjectures, but actual theorems, thanks to the seminal
ideas of Richard Hamilton, which were recently taken to their ultimate
conclusion by Grigory Perelman. The proof of these results settles
questions that drove much of the research in three-manifold topology
during the twentieth century. What's next for this field? Jeffrey
Brock of Brown University explored this question in his MAA Invited
Address. The proof of the
Geometrization Conjecture established (loosely speaking) that all
three-manifolds admit one of eight geometric structures. But the mere
existence of these structures tells us nothing about the geometric
properties of three-manifolds. If one thinks like a biologist, Brock
proposed, one might ask, How does the topology of a three-manifold
determine its geometry? Can one do "topological genomics" and create
a taxonomy of three-manifolds? What kind of data could serve as the
"DNA" of three-manifolds? Thurston showed that "most" three-manifolds
admit a hyperbolic geometric structure, and Mostow rigidity shows that
this structure is unique. But these results give no effective
information about the nature of the hyperbolic structure on any given
three-manifold. Work of Brock, Richard Canary, and Yair Minsky shows
that the nature of a hyperbolic structure on a three-manifold is
uniquely determined by its "end invariants" (end invariants are
analogous to simple closed curves on surfaces). Brock called end
invariants the DNA that determines the manifolds' geometric
morphology. Brock also described similar efforts to use Heergaard
splittings to produce geometric models for hyperbolic three-manifolds.
Just as DNA is thought to provide a Rosetta Stone for the nature of
living creatures, the work discussed in Brock's lecture might one day
provide a Rosetta Stone for three-manifolds. Statistics for Smart People Who Don't Know Anything About Statistics - AMS-MAA Invited Address by Persi Diaconis (Stanford University)
Automorphisms of Free Groups, Outer Space, and Beyond - Association for Women in Mathematics Emmy Noether Lecture by Karen Vogtmann (Cornell University) On a background of the night sky, Karen Vogtmann happily displayed a stunning picture of the non-astronomical Outer Space for n = 2 embedded in infinite projective space. This Outer Space is one on which Out(F2) acts in symmetric fashion, much as D6 acts on a six-pointed star. As motivation for studying automorphisms of free groups, connections were drawn between their actions on Outer Space, mapping class groups actions on Teichmuller Space, and arithmetic groups actions on homogeneous space. The homology of Out(Fn) has also shed light on symplectic Lie Algebras. In Vogtmann’s area of study, geometric group theory, groups are examined in tandem with the spaces on which they act. Geometric and topological information about the space provides insight into the structure of the group and visa versa. Colorful diagrams illustrated the "spine" of outer space, a deformation retract with desirable properties. And a close-up of Outer Space showed a collection of graphs with labels, each associated with a simplex. One moves through the space by contracting edges and altering the labels to obtain nearby graphs. Detailed explanations with pictures are available in Vogtmann's survey paper
of the same title as the talk at. This talk continued the 28-year-old tradition of honoring outstanding women mathematicians by inviting them to give an expository lecture.
Barcodes: The Persistent Topology of Data - AMS Current Events Bulletin by Robert Ghrist (University of Illinois)
For a more impressive example, data points from a large sample of grayscale digital pictures of natural imagery were combed through in hopes of finding natural patterns or structure. By selecting small 3x3 grids of pixels to analyze, persistent homology was revealed in three "loops" (generators of the first homology group) inside the resulting nine-dimensional space. These loops passed through data points in such a way as to suggest that nature exhibits a preference for certain visual arrangements. Furthermore the higher homology indicated a way to embed a Klein Bottle into the space of pixilated images, thus the picture of the Klein bottle atop a barcode. For pictures from this talk, and for text and images from the other three talks in the session, refer to the Current Events Bulletin
booklet.
Why “Mathematicians of the African Diaspora”? - National Association of Mathematicians Cox-Talbot Address by Scott W. Williams (University at Buffalo, SUNY) Scott Williams spoke at the NAM banquet concerning his website Mathematicians of the African Diaspora (M.A.D.), hosted by SUNY Buffalo. Williams created the site in the 90’s, after years of struggling to find and maintain connections amongst mathematicians with African heritage. In one story, Dr. Williams told of his hiring at SUNY Buffalo, and how surprised he was to see in the headlines of the local paper that "one of the top three black mathematicians was hired." The other two were not mentioned, and he was not sure who they were supposed to be anyway. In an effort to create a nationwide community of black mathematicians, M.A.D. provides information on upcoming conferences, listings of new Ph.D.’s and working mathematicians, and relevant statistics. Williams stressed the site’s role in inspiring black youth to look past typical stereotypes and view mathematics as a natural choice of study. During Black History Month, he receives thousands of emails and hits as students search for events such as the hiring of the first African-American mathematics professor (in 1849). Other links lead to biographies of mathematicians who succeeded despite racial prejudice, and excerpts from the ancient history of mathematics in Africa. Many audience members expressed an appreciation for the site and interest in continuing it in the future.
Math Circles and Similar Programs for Students and Teachers - AMS-MAA Special Session Math circles are informal get-togethers, often held on Saturdays, that provide a forum for schoolchildren to explore mathematics. Generally led by mathematicians, math circles emphasize play and discovery rather than the "cover the material" approach of most school mathematics classrooms. The wide variety of math circles now in existence in the United States was on display in this special session. One of the session organizers, Hugo Rossi of the Mathematical Sciences Research Institute (MSRI) in Berkeley, said that when MSRI began to get involved with math circles in 1997, there was only one, started in 1994 by Robert and Ellen Kaplan in Cambridge, Massachusetts. Rossi said that today MSRI knows of about 30 math circles in the United States. Among the speakers at the special session were those two pioneers, the Kaplans, whose math circle nowadays has 10 teachers and around 120 students. They do no advertising; people hear about the circle through word of mouth. The Kaplans' approach dispenses entirely with competition: As Ellen Kaplan put it, they do not want a room full of kids with one winner and a bunch of losers. The Kaplans also want to break the "myth" that math is only for the talented, asserting that talent is no more needed for kids to do math than it is for kids to learn to read. As Ellen Kaplan put it, "Curiosity is passport enough to the republic of math." Presentations by others who
lead math circles show that not everyone hews to the Kaplan approach,
with some circles making competition central to the way they operate.
Inevitably, many math circles cater to elite kids---those whose
parents, as session speaker Paul Zeitz of the University of San
Francisco put it, spend their evenings surfing the web in search of
enrichment activities for their kids. Zeitz launched the San
Francisco Math Circle to reach those without such advantages. This
circle has to operate rather differently from other circles; for
example, it relies on teachers, rather than parents, to bring the students
to circle meetings. The meetings take place after school, rather
than on Saturdays, so there is not as much time as in other math
circles. Nevertheless, within these constraints the San Francisco
Math Circle has been successful in reaching many students who would
otherwise never have this kind of exposure to mathematics.
At the Joint Meetings Project NExT (New Experiences in Teaching) also conducted its own seminars. Project NExT is a program of the MAA for math faculty starting their first or second year of teaching. The program addresses all aspects of an academic career, including improving the teaching and learning of mathematics, engaging in research and scholarship, and participating in professional activities. It also provides the participants with a network of peers and mentors as they assume these responsibilities.
Mathematics and the Geometry of Voting - an MAA Minicourse by Donald Saari (University of California, Irvine)
Throughout the course, audience participation was high, and questions ranged from the philosophical "Is there such thing then as the will of the voters?" to the more mathematical "What is the significance of the eigenvalues of that matrix?" All questions were met with answers, stories, or enthusiastic encouragement to pursue research. Mathematicians’ collaborations with social scientists will undoubtedly increase in other areas, as it has in voting theory.
Using Origami in Undergraduate Math Classes - an MAA Minicourse organized by Thomas C. Hull (Merrimack College)
--- Brie Finegold, 2006 AMS-AAAS Media Fellow The Aftermath of Katrina Fifteen hundred people died in connection with Hurricane Katrina, which hit New Orleans in the fall of 2005, and 80 percent of the city's population was displaced. The Joint Meetings were held at a time when much of New Orleans was still recovering from the devastation. The JMM took place in two hotels in downtown New Orleans, next to the French Quarter, a part of the city that emerged largely unscathed in the hurricane. But some mathematicians ventured out to other areas that had been hard hit and returned with tales of eerily deserted neighborhoods devoid of any living creatures, where power lines were still down and reconstruction had not yet begun. The JMM included a session called "Katrina and Its Aftermath: Institutional Survival in New Orleans since the Storm," organized by Jim E. Hoste of Pitzer College and sponsored by the AMS Committee on the Profession, which Hoste chairs. The session brought together four speakers from area universities, who described how their institutions have fared. The speakers were Kenneth Holladay of the University of New Orleans, Morris Kalka of Tulane University, Vlajko L. Kocic of Xavier University of New Orleans, and Katarzyna Saxton of Loyola University New Orleans. Due to losses incurred during the storm, the universities underwent major reorganizations that brought large cuts in staff and the elimination of whole departments. As Holladay explained, the losses of the University of New Orleans were so great that it applied to the state government for an allowance to declare a state of financial exigency; the allowance was granted after the second application. The declaration of financial exigency permitted the university to eliminate tenure, paving the way for faculty to be fired. A combination of firings, early retirements, and voluntary departures has reduced the faculty by about 100 people. Because enrollments have fallen so sharply, these faculty are not being replaced. Although Loyola University had less damage and thus did not declare financial exigency, the university administration instituted a reorganization that entailed the firing of tenured faculty. In the turmoil that followed, the faculty of the College of Arts and Sciences took a vote of no confidence in the provost and president. Saxton said that the American Association of University Professors formed a special committee to investigate the treatment of faculty at universities in New Orleans, including Loyola and Tulane. Kalka spoke of huge financial losses at Tulane, which also underwent a painful restructuring that entailed large staff cuts and the elimination of departments and graduate programs. However, the Tulane mathematics department fared relatively well and was not cut in the restructuring. Xavier is a Catholic, historically black university, and it sustained enormous damage during the storm. Kocic reported that the mathematics department faculty fell from 16 pre-Katrina to 8 today. The size of the student body is 70 percent of what it was before the storm. Kocic said the mathematics department is struggling with a low number of students. "Katrina changed a lot of things, and we don't know where we are heading," he said. In the question period at the end of the session, there were complaints---in particular from Lee Lorch of York University and Abdulalim Shabazz of Lincoln University---that insufficient attention has been paid to the plight of mathematicians at historically black institutions in the areas hit by Katrina. On a more optimistic note, the JMM held a raffle and T-shirt sale and
raised a total of US$10,000 for a local relief charity. Individual
mathematicians also showed generosity in making personal donations.
One especially noteworthy example is Jennifer Quinn, executive
director of the Association for Women in Mathematics, who received the
MAA's Haimo Award for Distinguished College or University Teaching of
Mathematics. The award came with a cash prize of US$1000, which
Quinn donated to the New Orleans Area Habitat for Humanity. One factor in the large turnout (the largest ever, at over 5200
registrants) was a big surge in the number of students attending. AMS
Director of Meetings Diane Saxe asked her staff to prepare statistics
about the number of student attendees and found that there was a 33
percent increase between the Baltimore JMM in 2003 and the New Orleans
JMM in 2007. In fact, students accounted for nearly a quarter of
registrants in New Orleans. About half of the graduate students in
New Orleans took part in the Employment Register. The strong
attendance by undergraduates is likely due to the increasing number of
these students involved in research. Darren Narayan, Carl Lutzer,
Bernard Brooks, and Tamas Wiandt, all of the University of Rochester,
together with Michael Fisher of California State University in Fresno,
organized an AMS-MAA-SIAM special session that provided a venue for
undergraduates to present their research. The organizers had so many
takers that they requested and then filled an extra day for the
session.
Puzzling at the Student Hospitality Center
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