Principal Investigator: Alan W. Reid, Robert E. Gompf, Cameron M. Gordon, John E. Luecke
This RTG proposal is focused on training in low-dimensional topology and its applications. The study of low-dimensional manifolds has become one of the central areas of research activity in mathematics. The PI's have an established track-record of research accomplishments in several different areas of low-dimensional topology; for example knot theory, 3 and 4-manifold topology, hyperbolic manifolds and symplectic topology. The project will also allow the PI's to continue their training of postdocs and students. The subject of this RTG Proposal interacts with several other branches of mathematics as well as the applied sciences. It therefore provides fertile ground for research, education and training experiences at all levels.
One of the main features of the proposal is to build, and elevate, the successful structure for training and education currently in place in the Department of Mathematics. However, an important new component of our proposal is training for interdisciplinary research. This will afford postdocs, graduate and undergraduate students educational and training experiences different from the traditional ones available at present. We therefore aim to provide a framework that supports education and training by instruction in the traditional sense, and also provide opportunity for training experiences in applications of topology in the physical and biological sciences. As part of this latter effort the project will promote interactions with scientists studying knotting phenomena in DNA and biomedical mathematics. As part of our outreach efforts, we will instigate a public lecture series that will raise the profile and level of awareness of the role of topology in other sciences in the University and local community.
. The study of low-dimensional manifolds has become one of the central areas of research activity in mathematics. The subject interacts with several other branches of mathematics as well as the applied sciences. This interaction was visbile in the training of students (both graduate and undergraduate) as well as postdocs. Without question, the aims of the proposal to enhance, extend and enrich at all levels, education and training in low-dimensional topology and its applications at the Department of Mathematics at The University of Texas at Austin were met. Some highlights of the last five years include: 1. The ability to recruit high quality postdocs and graduate students and allow for support of continuing graduate students during their time here. For example, one of our first RTG Postdocs Henry Segerman is now an Assistant Professor at Oklahoma State University, and one of our last RTG Postdocs Marion Moore Campisi will take up a position at Stanford University in Fall of 2013. Regarding graduate students supported, Andrew Gillette went on to do a Ph.D on aspects of Computational Topology (with Prof C. Bajaj, UT Computer Science and ICES) and will take up an Assistant Professor Position at Univerity of Arizona in Fall 2013. Gillette also helped organize a conference: "Mathematical Aspects of Imaging, Modeling and Visualization in Multiscale Biology" 2. One of our first RTG Postdocs developed a course which was an applied topology course, featuring topics such as, the geometry & topology of proteins, RNA and DNA, introductory knot theory and tangle analysis, mathematical models of recombination and topoisomerase mechanism; 3. A series of Outreach Lectures were given with the aim of exposing the local community to aspects of low dimensional topology. Lectures were given by Professor J. Weeks and Professor C. Adams. 4. A workshop on a highly topical subject at the cutting edge of research in low-dimensional topology was hosted here at UT Austin and funded in part by the award. The workshop was aimed at graduate students and young researhers in the field. 5. A constant stream of visitors were funded over the course of the grant. As well as giving lectures, the visitors interacted with graduate students and postdocs. 6. Many of the postdocs and grauate students funded by the grant gave lectures in the undergraduate UT Math Club and Saturday Morning Math Club (for High School students, teachers and parents). 7. Many of the postdocs and graduate students funded by the grant also helped out in local high schools. For example Laura Starkston volunteered at a public high school in Austin, tutoring math after school through "STEM tutoring".
