This award is funded under the American Recovery and Reinvestment Act of 2009 (Public Law 111-5).
This RTG will support and train, for research and educational careers, 20-25 highly gifted PhD students, and at least 4 talented post-docs. Additionally, in an expanded vision of UCLA's successful summer Boot Camp for incoming grads, it will engage up to 60 top undergraduates over 5 summers in grad school preparatory activities and in research in mathematics (REU). Transferring to Algebra a model used successfully by UCLA Analysis group, four intense week-long Summer Research Retreats, run by faculty highly active in training and research, will engage chosen research-ready grad students in key areas of current research. The horizon-expanding VIGRE II Summer Research Internship Program, which provides students with an intensely mentored applied research experience in area related to their interest, will be expanded to include more applications of algebra and number theory, e.g. from cryptography to coding theory, to areas of physics where algebra and number theory play emerging roles. Three focused Instructional Workshops serving 35-50 grads and post-docs each will expose students to key areas of current research, such as p-adic modular forms, motives, and current research in combinatorics. The RTG plan emphasizes the training of teachers and mentors, as well as researchers. Hence, post-docs will play key roles in the activities above.
This RTG will enable UCLA Algebra to continue its positive faculty-student synergy. UCLA has been greatly fortunate to make a large number of wonderful hires in the last few years. Our ability to continue to attract students and post-docs with sufficient talent to become real mathematicians is very important to faculty satisfaction with UCLA as a work environment. The Boot Camp/REU for undergraduates should significantly improve the strength and graduate prospects for its participants. Since it will be open to talented students from local institutions, such as the California State University campuses, and the Claremont Colleges (e.g. Harvey Mudd College), the program may help serve a regional/state need as well as help us to find suitable diversity candidates for graduate school. Related undergraduate programs which will involve RTG personnel will enhance recruitment and retention of students to mathematics. The Research Internship program will enable UCLA to serve the national interest by continuing a pipeline from number theory to cryptography. At the national level, the RTG will serve the key EMSW21 goal of enhancing the workforce for research and teaching, in both pure and applied areas, and in industry (as with cryptography). With so many talented young faculty in algebra, number theory and combinatorics, UCLA can produce at least 8 to 10 PhD?s per year in the areas of this grant. Finally, this RTG and the other efforts of the UCLA program, especially those inspired by EMSW21, emphasize strongly teamwork in training and research, in a way that could become, or provide elements to, a national model for graduate training.
