Orbifold is the space with simplest kind of singularity where it is locally modeled on the quotient of a smooth manifold by a finite group. They appear naturally in many subjects of mathematics and physics. A classical theory due to Satake has been existed for half of century. But it fails to capture the true nature of orbifolds. In this proposal, the principal investigator proposes to systematically study "stringy" geometry and topology of orbifolds, i.e., stringy properties of orbifolds arisen from string theory.
The principal investigator, Yongbin Ruan, proposes to systematically study what is called the stringy geometry and topology of orbifolds. These are important geometric objects arisen from geometry in mathematics and from string theory in physics, and involve with many branches of mathematics. This proposal seeks to develop close and fruitful interactions among those fields. The project is interdisciplinary in its conception. Both physical and mathematical ideas are used in an essential way. Through research seminar, organizing and participating at national and international conference this proposal will also enhance the training of undergraduate and graduate students, as well as postdoctoral fellows.
