Research Training Group in Groups and Dynamics

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This award will facilitate a variety of new activities by the University of Texas at Austin Groups and Dynamics (UTGD) research group. These activities are designed to foster a rich educational environment for undergraduates, graduate students, and postdocs at UT by increasing introductory research opportunities for undergraduates and research-level training for graduate students. The overall goals of this initiative are to increase the number of math majors going to top-tier graduate schools, increase the number of Ph.D.s obtaining top-tier postdocs, improve the career placement of postdoctoral fellows after their time at UT, and increase the number of women and minorities pursuing advanced degrees and careers in mathematics research and education.The UTGD is led by seven faculty members at UT Austin. The group brings a wealth of different viewpoints and motivations together, from low-dimensional topology and geometry, to amenability, representation theory, random walks and ergodic theory. Building on a departmental Group Theory and Dynamics Seminar that has run for the past five years, the emphasis and resources of the grant will bring together expertise in the many areas represented by the research group while providing an arena for new mathematics and for the training of new mathematicians. To increase the number of graduate students entering into fields involving higher mathematics, UTGD will provide a summer Directed Reading Program (DRP) designed to prepare undergraduates for graduate school. UTGD will create a course, Experimental Mathematics, and enhance another, Discrete Math, to help prepare students for research. To improve the placement of graduating UT Ph.D.s, this award will enhance the UT graduate program by providing graduate fellowships/traineeships and travel funds and support for graduate mini-Schools and a Groups and Dynamics junior seminar. To build the departmental activity centered around Groups and Dynamics, this award will add four postdoctoral positions and provide visitors to work with postdocs, graduate students, and faculty. In the use of these resources, the management team will actively seek to increase the proportion of members of underrepresented groups in mathematics. The grant also proposes a number of ways to impact mathematics outside the department. The materials resulting from any of the projects will be made available through a dedicated website. The mini-Schools will draw from graduate students nationwide; the undergraduate conference, and the summer DRP will draw broadly from Texas schools. The Julia Robinson Math Festival will bring engaging and new mathematical experiences to K-12 students in the Austin area. The activities with the Math Teachers' Circle will create a stronger working relationship between the faculty and students of the math department and local K-12 teachers.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.