The proposed program is the area of applied and computational analysis to be hosted by the Department of Mathematics and the Institute for Computational Engineering and Sciences (ICES) at the University of Texas at Austin. The goal is the creation of a model program in applied and computational mathematic that will include enhanced undergraduate research experience (REU), reduced time to graduation and stronger background in applicable mathematics for graduate students, and the highest level of postdoctoral mentoring, all to be achieved by curriculum and examination reform, new undergraduate concentrations, new integrated seminar and working group series, summer programs, and an active mentoring program.
The intellectual merit of the proposed work is based on applied and computational analysis as the fundamental field that links mathematics to the different areas of applications in the natural and social sciences and engineering both within and outside of the university. Focus will be on non-linear theory and computations of differential equations, which give the most fundamental of mathematical models in science and technology from an applied point of view. The need for young, well-trained mathematicians capable of connecting to diverse areas of applications has never been higher. At the local level, the proposed program will contribute towards the increase of the number of students attracted to mathematics, and, at the national level, it will serve as a model program for similar initiatives.
has placed greater emphasis on the interplay of several areas of modern mathematics with engineering, natural and social sciences. It has enriched and streamlined the core areas of Non-Linear Analysis, Probability encompassed with Applied Mathematics aspects of Partial Differential equations Stochastics and Numerical Analysis and Simulations by placing greater emphasis on applications. This RTG program not only provided young aspiring mathematicians with a firm grounding in the core of the subject but also prepared them for an ever growing multitude of career opportunities. At the local level, the program has contributed towards the increase of the number of students attracted to mathematics, and, at the national level has served as a model for similar initiatives. Our activities were all encompassed with the participation of the graduate program in Computational Engineering, Science and Mathematics (CSEM) at the Institute for Computational Engineering and Sciences (ICES) at the University of Texas at Austin. Information on the RTG Program in Applied and Computational Analysis is available at www.ma.utexas.edu/research/rtgs/acm. In particular, the most recent report posted there shows a broad range of activities developed in the last 5 years. All the PIs and core faculty of this proposed program are currently directing graduate students, and several of them are also directing postdocs. Collectively, we have experience from different public and private institutions, having worked with students of diverse backgrounds at different stages of their careers. They have also developed well-integrated regular Analysis and PDEs, Numerical Analysis/Computation, ICES, Applied Mathematics and Mathematical Physics, Probability, Stochastic and Mathematical-Finance and Statistics and Scientific Computing seminars, with external speakers. The additional working seminars in these areas allow for local members (graduate students, postdocs and faculty members of the Mathematics department, ICES and DSSC) to present their work and discuss recent progress. Current and past calendars can be found at www.ma.utexas.edu/cgi-pub/ seminar/calendar. In addition, we have several weekly discussion groups where casual open question/answer sessions take place, with graduate student, postdoc and guest visitor presentations. One of these is organized by I. M. Gamba, the Applied Mathematics Group leader at ICES, www.ices.utexas.edu/ research/centers-groups/amg/, who in collaboration with J. Haack (RTG postdoc) and the participation of RTG core faculty runs a weekly discussion on computational and analytical kinetic collisional theory that brings together ICES and Math graduate students, postdocs and faculty members (see http://users.ices.utexas.edu/~haack/Boltzmann_group.html) Two other core faculty members for this project, L. Caffarelli and A. Figalli, run a weekly discussion group in the area on non-linear PDE with focus on non-local diffusion and optimal transport theory, among many other topics. Both groups have a steady attendance of about 10 people. The funded project have also been particularly successful in recruiting junior women and minorities. The PIs have directed or are directing, combined, 3 women PhDs and 3 women postdocs in the last 5 years, as well as two Hispanic students. It funded about 8 women and 3 members of minority/underrepresented groups (see the report mentioned above for more information). In addition the core faculty of this effort, L.A. Caffarelli (coPI), B.Engquist (coPI), I.M.Gamba (PI), T. Zariphopoulou (coPI) and P. Souganideis have continue to mentor a quite ethnically and gender diverse group of graduate and postdoctoral students, including many foreign nationals. This success in graduate-student and postoc training also reflects the rise of a very strong, recently incorporated or tenured junior group in the four areas of the RTG funded program: T. Chen, A. Figalli, A. Vasseur and N. Pavlovic, in non-linear classical and applied analysis, K. Ren and R. Ward in Applied Mathematics, Numerical Analysis and Scientific Computing, M. Sirbu and G. Zitkovic, in Applied Probability. Among recent senior members are F. Baccelli in Probability and P. Muller and S. Walker in Statistics. They all add to the already established group of core faculty associated to the RTG Program in Applied and Computational Analysis that has been pivotal for the development of future planed activities, some of them already underway.
