VIASM would like to present to you the article about Workshop on Birational Geometry and Stability of Moduli Stacks and Spaces of Curves, written by Prof. Ian Morrison (Fordham University, USA) during his stay at VIASM:

The “Workshop on Birational Geometry and and Stability of Moduli Spaces and Stacks of Stable Curves” began on January 5. Each week has involved three hours of lectures and, equally important, hands-on problem sessions on Tuesday and Thursday centered on a topic about moduli spaces or curves. In addition most Fridays, the visiting lecturers travel to the Institute of Mathematics to hear local mathematicians present solutions to problems and to answer questions these suggest.

The Workshop’s first week introduced basic notions and problems about birational geometry of parameter and moduli spaces. The second week was devoted to working out the details of some of these questions for some guiding examples. The third week dealt with stability conditions that lead to moduli spaces in algebraic settings, focussing on moduli of representations of quivers as an introduction to Bridgeland stability and related areas of active research.

After a break for the Tet holiday, the Workshop’s second half began with a week on foundations of geometric invariant theory and its applications to the construction of moduli spaces. The last two weeks will focus on the relations between the geometry of linear series on curves and the commutative and homological algebra of free resolutions of their ideals, before the Workshop returns to the topics of the first weeks to consider recent constructions of effective divisors.

Through the hard work of both the visiting lecturers and the local audience, the Workshop has succeeded in opening up an important area of contemporary algebraic geometry to a new Vietnamese audience. Both groups are grateful to the staff of VIASM and of the Institute for Mathematics for facilitating their tasks by providing an excellent working environment. Already, one preprint completed during the Workshop and thanking the host institutes has appeared on (http://arxiv.org/abs/1401.1613) and other work done during the Workshop will be posted in the coming months.