RTG Analysis

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The goal of this project is to increase the number of US citizens and permanent residents who are able to employ advanced mathematical ideas for independent research or applications in other fields. The major emphasis of the project will be the education of graduate students who want to obtain a PhD in mathematics, and the promotion of the careers of postdoctoral researchers who are affiliated with the analysis group at the University of California, Los Angeles. A variety of measures involving members of the analysis group is intended to attract students on all levels to mathematics and possibly to the area of analysis. The goal is to secure a "pipeline" of suitable candidates who want to learn advanced mathematical concepts and help them to be successful with this quest. For elementary, middle, and high school students these initiatives include the cooperation with the Los Angeles Math Circle that has regular meetings on Sundays and offers expository lectures, problem-solving sessions, and study groups. For undergraduates there will be summer review sessions with a view towards preparation for the GRE subject test in mathematics. Incoming graduate students will benefit from the "Boot Camp", an intensive six-week long review session on central topics in mathematics that is intended to facilitate the transition between undergraduate and graduate training. These additional activities will be "vertically integrated" to ensure interactions between students and researchers on all levels with a twofold goal in mind: improving the communication and presentation skills of the research trainees and raising the awareness of students, in particular among underrepresented groups, for mathematics as an interesting and exciting field of study.Since the times of Leibniz and Newton, analysis has been one of the core subjects of mathematics. It has led to many spectacular applications in science and engineering. By now analytic tools are ubiquitous in all areas of investigation based on quantitative reasoning. Many of the more prominent recent advances within mathematics itself rely heavily on sophisticated analytic methods. Examples are Perelman's solution of Thurston's geometrization conjecture for 3-manifolds, the work by Lawler-Schramm-Werner on the stochastic Loewner equation and its applications for random processes, or the investigations by Tao-Vu on universality laws in random matrix theory. Today analysis is a vibrant area of mathematical investigation with a wide range of applications. The analysis group in the Department of Mathematics at UCLA includes many distinguished researchers and has a high standing in comparative rankings. Its members have a broad range of research interests including operator algebras, partial differential equations, complex analysis, harmonic analysis, mathematical physics, probability, and analytic number theory. In addition to the strength of its researchers, the analysis group has a long and successful history of training mathematicians. With the diversity of interests within the group and its strong past record, it has the unique expertise to impart a broad vision of the field to its students and to train the next generation of experts in analysis.