The Center for Mathematics at Notre Dame will run a program on topology from May 21 to June 9 of 2009, including an undergraduate summer school on "Topological invariants in low dimensions" and a graduate summer school and conference on "Topology and field theories". The program will begin with a one week undergraduate summer school from May 21 to May 26th, which will consist of lectures and group problem solving sessions led by Margaret Doig, Matthew Hedden, and Joshua Greene. We plan to have approximately 20 students from a range of undergraduate institutions. The program will continue with a second week, which will be a graduate student level summer school in "Topology and Field Theories", which will consist of lectures given by Sergei Gukov, Andre Henriques, Jacob Lurie, and Chris Schommer-Pries. We expect to bring 40 or 50 graduate students and postdoctoral researchers for the graduate summer school. The final week of the program will be an international conference on "Topology and Field Theories", with speakers including David Ayala, Ulrich Bunke, Kevin Costello, Sergei Gukov, Andre Henriques, Jacob Lurie, Chris Schommer-Priess, Dennis Sullivan, and others.
The aim of this program is to help students learn about research in exciting and important areas of topology. For undergraduates, we aim to give students an introduction to knot theory and its variants, which combines different areas of mathematics, but also has close connections to physics and to biology, through folding properties of DNA molecules. The program will help the undergraduates make choices about graduate study. The speakers are strong young mathematicians, and have been chosen for their ability in teaching. For graduate students, the program will provide many opportunities to interact with leading researchers in an area of topology with close interactions with physics. This area has been important in a number of major advances in mathematics. The program will help graduate students transition into research, and advance their research program. The conference will provide further opportunities in a less structured environment. The speakers are all strong researchers, and excellent lecturers. For all levels, we plan to bring in students from a wide variety of institutions.
Information on the programs is available at the following website: http://centerformath.nd.edu/scientific-events-and-programs/
This grant provided funds to support summer schools in mathematics for undergraduates and for graduate students at the University of Notre Dame in May-June 2012. The subject of the undergraduate summer school was topological invariants, and in particular, studied the question of when two knots are equivalent, or can be deformed into one another. 26 students from a wide range of universities in the United States attended the summer school, including Ivy league schools and the University of Michigan, in addition to insitutions like University of Northern Arizona, Boston College, and Richard Stockton college of New Jersey. The students attended lectures and worked on problems in small groups. The survey results indicated that the students found the experience to be quite positive, and inspired further interest in topology, and in mathematics in general. A major goal of the program is to introduce undergraduates to exciting topics in mathematics, and inspire them to pursue a career in mathematics, and from the evidence, this goal was achieved. The subject of the graduate summer school was "Topology and Field Theoreis", and a major focus was on interactions between topology and physics. There was considerable emphasis on categorical ideas, which is a cutting edge area of research. The summer school consisted of four lecture series given by leading researchers. The lectures were well-attended, and again reviews were quite positive. More than 50 people attended the lectures, and there was considerable discussion aside from the lectures. The video from the lectures is available online, and we are planning a volume with detailed lecture notes with the American Mathematical Society, which will make the content of the lectures available to a wider audience. A number of women attended the lectures and participated in the program, and we hope this will encourage women towards careers in mathematics.
