The department has had another active year hosting research conferences. This is a great way to show off Athens and the UGA Mathematics Department to the international mathematics community. The intensity of mathematical energy vibrating through the halls of Boyd during these conferences is palpable. What a great experience for our students and faculty!
Georgia Topology Conference
May 18-22, 2011
2011 was the fiftieth anniversary of the first Georgia Topology Conference held (not surprisingly) in 1961. It was organized by one of our newest hires in topology, Dr. Mike Usher. The focus was on symplectic topology, Floer theory, and related topics. The conference drew an excellent and diverse crowd ranging from graduate students and new Ph.D.s up to superstars like the Institute for Advanced Study's recent permanent member, Helmut Hofer.
We also mention that the proceedings of the 2009 Georgia Topology conference, Low-dimensional and Symplectic Topology, edited by Michael Usher and dedicated to Clint McCrory, has been published by the American Mathematics Society. Although this conference is an annual event, every eight years it is expanded to a major international event. 2009 was one of those years and this text contains survey and research articles that were presented at that conference.
Arithmetic Dynamics Summer School
May 16-27, 2011
The 2011 VIGRE Summer School Program concerned arithmetic dynamics: the study of iterates of rational maps defined over number fields. It was held in the Boyd Graduate Studies Building from Monday, May 16 through Friday, May 27, and was funded by UGA’s VIGRE grant. There were 15 guest speakers and 28 graduate and post-doctoral participants, including 7 students from UGA who had taken part in a year-long VIGRE seminar on arithmetic dynamics leading up to the SSP. The Summer School was organized by Dr. Rumely, with assistance from Tamara Haag.
The program was designed to be "by young people, for young people", allowing young researchers to present their work in more detail than was possible at a usual conference, and encouraging interaction between researchers and students. It was organized in AIM style, with lectures by invited speakers in the mornings, and group research sessions in the afternoons. Invited speakers included Matt Baker, Xander Faber, Ben Hutz, Patrick Ingram, Rafe Jones, Sarah Koch, Joey Lee, Aaron Levin, Alon Levy, Michelle Manes, Alice Medvedev, Clay Petsche, Mike Tepper, and Tom Tucker. Students participants came from as far as Hawaii, Vancouver, and Massachusetts.
Topics covered in the program spanned the full breadth of the field. Patrick Ingram, Rafe Jones, and Michelle Manes gave a series of introductory talks about dynamical heights, galois properties of periodic points, and special families of maps. Xander Faber lectured about Berkovich spaces and described his work on the Berkovich ramication locus. Tom Tucker discussed the dynamical Manin-Mumford and Mordell-Lang conjectures. Alice Medvedev presented results proved using mathematical logic and model theory. Ben Hutz, Alon Levy, and Joey Lee spoke about moduli space approaches. Sarah Koch discussed connections with classical complex dynamics, and Aaron Levin spoke about transcendence theory. In addition there were several student presentations. Jacob Hicks, a second year UGA graduate student, presented data he had gathered during the VIGRE group which brought the dynamical Lang’s conjecture into question, and John Doyle, a third year UGA graduate student, discussed algorithms that his VIGRE group had developed for rigorously computing points of small dynamical height over number fields. Several of the speakers posed unsolved problems arising from their work, and lead afternoon research sessions about them.
Feedback from the program was extremely positive. Many participants expressed hope that such a conference could be an annual event.