This award supports a workshop at the University of North Carolina at Chapel Hill, held from October 31st to November 2nd, 2014. The talks cover a range of topics spanning algebra, combinatorics, geometry, and topology. The goal of the workshop is to give predominantly upcoming junior researchers an opportunity to present their work and to interact with more senior researchers, thereby encouraging new research collaborations. The grant also supports the attendance of graduate students and postdoctoral researchers at the workshop, and hence will contribute to the the training of younger mathematicians in some of the most active areas of mathematical research. Participation of students from nearby universities is encouraged, to strengthen ties with regional peer institutions, and diversity among the speakers and the participants is a priority.
The general themes of the workshop are moduli spaces, derived geometry, and geometric representation theory. Moduli spaces are spaces that parametrize geometric objects of some kind, and are ubiquitous in algebraic geometry. Representation theory is a powerful method of reducing problems in abstract algebra to simpler problems in linear algebra. Similarly, derived geometry is a way of reducing geometric problems to problems in homological algebra. There have been significant recent advances in these areas. Moreover, new connections between these different areas have been discovered. Derived categories and wall-crossing formulas have revealed new ways of studying the geometry of moduli spaces. Methods and ideas from derived geometry and geometric representation theory are also starting to converge. The workshop brings together experts working on these topics, and will serve to promote interaction and foster new collaborations. More details can be found at the conference website www.unc.edu/~sawon/UNCworkshop14.html.
