This grants provides support for a number of new training activities in Algebraic Geometry and Topology hosted by the Department of Mathematics of the University of Utah. The funding will be used to support undergraduate students, graduate students, and postdoctoral fellows. There will be vertical integration in the activities among faculty, postdocs and students. This research training is designed to provide students and postdocs a high level of mathematical training. The program will impact young mathematical scientists at the undergraduate, graduate, and postdoctoral levels, and will provide an environment which will stimulate collaboration across levels and across fields. The program will have a deep impact also in the training of our senior graduate students and postdocs into becoming effective, motivated teachers and mentors. As they grow into mature mathematicians, this will have a long-lasting effect well beyond our local environment and the duration of the grant.