EMSW21-RTG in Algebra and related fields at UCLA: innovations in a successful program

该奖项是根据2009年美国复苏和再投资法案（公法111-5）资助的。这个RTG将支持和培训，为研究和教育事业，20-25高度有天赋的博士生，和至少4个有才华的博士后。此外，在扩大加州大学洛杉矶分校的成功夏季靴子营为即将到来的毕业生的愿景，它将从事多达60名顶尖的本科生超过5个夏天在格拉德生院的准备活动和数学研究（REU）。转移到代数由加州大学洛杉矶分校分析组成功使用的模型，四个激烈的为期一周的夏季研究务虚会，由教师在培训和研究高度活跃，将从事选定的研究准备格拉德生在当前研究的关键领域。扩大视野的VIGRE II暑期研究实习计划，为学生提供与他们感兴趣的领域相关的强烈指导的应用研究经验，将扩大到包括代数和数论的更多应用，例如从密码学到编码理论，到代数和数论发挥新兴作用的物理领域。三个重点教学研讨会服务35-50毕业生和博士后每个将暴露学生当前研究的关键领域，如p-adic模块化形式，动机和组合学的当前研究。RTG计划强调对教师和导师以及研究人员的培训。因此，博士后将在上述活动中发挥关键作用。这RTG将使加州大学洛杉矶分校代数继续其积极的师生协同作用。加州大学洛杉矶分校在过去的几年里非常幸运地招聘了大量优秀的人才。我们的能力，继续吸引学生和博士后有足够的人才，成为真实的数学家是非常重要的教师满意度与加州大学洛杉矶分校作为一个工作环境。本科生靴子营/REU应显着提高其参与者的实力和毕业前景。由于它将开放给有才华的学生从当地机构，如加州州立大学校园，和克莱蒙学院（如哈维穆德学院），该计划可能有助于服务于一个区域/国家的需要，以及帮助我们找到合适的多样性候选人的研究生院。相关的本科课程，将涉及RTG人员将加强招聘和保留学生的数学。研究实习计划将使加州大学洛杉矶分校继续从数论到密码学的管道服务于国家利益。 在国家一级，RTG将服务于EMSW 21的关键目标，即在理论和应用领域以及工业（如密码学）中加强研究和教学的劳动力。 有这么多有才华的年轻教师在代数，数论和组合学，加州大学洛杉矶分校可以产生至少8至10个博士学位？每年在这个领域的补助金。最后，这个RTG和加州大学洛杉矶分校计划的其他努力，特别是那些受到EMSW 21启发的努力，强调在培训和研究中的团队合作，这种方式可以成为或提供元素，研究生培训的国家模式。

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.