California Research Training Program in Computational and Applied Mathematics (2011 – Present)
The thrust of this Computational and Applied Mathematics program is engaging students starting and finishing the critical transition point from undergraduate to PhD student in high quality university level research. Students experience both the development of independent research projects and the milestones needed to get admitted to and succeed in a top PhD program. They participate in summer research modules on topics such as crime modeling, fluid dynamics experiments and modeling, robotics and control, medical imaging, cancer stem cells, bone growth, remote sensing applications, alcohol biosensors, photovoltaic cells, and algorithm design for microscopy. The program involves faculty from Mathematics in collaboration with faculty in Medicine, Anthropology, Engineering, Chemistry, and other disciplines. The project includes a training program for postdocs and junior faculty to learn how to involve pre-PhD students in publication-level research. The training program is based at UCLA and includes undergraduate and masters student participation from nearby colleges and universities. The program goal is to directly address diversity and access to top level PhD programs in computational and applied mathematics. This program is funded by National Science Foundation Grant DMS-1045536.
Logic (2011 – 2016)
This Research and Training Group (RTG) award for the Logic group at Caltech/UC-Irvine/UCLA supports a variety of initiatives designed to increase the number of US citizens and permanent residents who pursue careers in mathematical logic and mathematics as a whole, and to tighten the connection between training, studies, research, and professional skills. These initiatives will enhance training, increase participation, and increase the visibility of mathematical logic and mathematics as a whole, at a wide spectrum of training stages, both locally and nationally.
Algebra and Number Theory (2009 – 2014)
This is a joint program of the UCLA Algebra and Number Theory groups. Research programs of faculty of the RTG concern the theory of essential dimension, geometric and modular representation theory, categorification, tensor triangular geometry, K-theory of schemes (motives), Hodge theory and topology of algebraic varieties, mock theta functions and their generalizations, p-adic families of automorphic forms, Iwasawa theory, congruence, Langlands program, cryptography and algebra geometry related to mathematic physics, among other topics. The main goal of the RTG grant itself is to increase the number of gifted researchers and teachers in these areas who are US citizens or permanent residents. The main funding of the RTG is therefore directed to stipend support of graduate students with an interest in Algebra and related fields. However, postdoctoral researchers are also supported. The RTG faculty have also organized a number of successful conferences and instructional workshops attended by many US students and postdocs.
Analysis and Applications (2009 – 2014)
The analysis group at UCLA has wide research interests ranging from operator algebras and free probability to harmonic analysis, combinatorics, mathematical physics and number theory. The RTG analysis grant has its main goal to increase the number of US citizens and residents who study analysis and related areas as UCLA graduate students or postdoctoral scholars who go on to have successful careers as university teachers and research mathematicians.
Applied Differential Equations and Scientific Computing (2006 – 2010)
This program is run with the philosophy that there a number of ways to effectively involve undergraduates in research that gives them a meaningful experience beyond the classroom. Bringing students from four year colleges to UCLA allows them to have an experience working alongside PhD students and postdocs that they would not obtain in their college environment. In addition to providing a valuable research experience for undergraduates, we try to heavily involve young faculty, postdocs, and advanced PhD students in the mentoring process, while maintaining oversight by senior faculty. These interactions provide the REU students with a viewport into the steps needed to develop a research career. Moreover, it provides invaluable mentoring experience for our junior researchers, often enabling them to advance their careers through broader access to tenure track positions and through additional research publications and products brought about by projects involving the undergraduate researchers.
The VIGRE Program of the National Science Foundation at UCLA (2000 – 2010)
The UCLA Mathematics Department held an NSF VIGRE grant for ten years from the year 2000 until 2010. VIGRE grants were five year grants with a possible renewal for an additional five years. The general idea of the VIGRE program (VIGRE= vertical integration of research and education) was to give a large long-term grant to the whole department for the over-all purpose of moving the "culture" of departments towards a more integrated form of mathematics education, in which undergraduate and graduate students would have earlier and deeper exposure to research environments, to mathematics research as it is actually practiced, rather than only a prolonged series of lecture courses. There was also a component of attracting larger numbers of US nationals into mathematics research.
UCLA's two approved VIGRE proposals were a departmental effort, with Tony Chan and Robert Greene as PIs(Principal Investigators) in 2000 and with Andrea Bertozzi and Robert Greene in 2005(Greene directed the day to day operation of the program through-out). Specific program features included research -introductory courses (Math 290s, instituted by David Gieseker as Chair), an expanded summer REU (research experiences for undergraduates) program to which Bertozzi made a particularly major contribution , a mentored post-doctoral program, and a large expansion of the number of graduate students (the number of graduate students increased by more than 60% from 1999 to the mid 2000's). VIGRE support was large-scaled-the grant amount was close to a million dollars a yearly, much of it going to graduate student support-relief time for TAing in particular-and post-doctoral support. While the VIGRE program at UCLA ended in 2010, being replaced in good part by several different RTGs(research training grants), the impacts of the VIGRE program have been permanent and very positive.