Research Training Groups

The Group Theory and Dynamics Research Group at UT Austin consists of 7 core faculty, Daniel Allcock, Lewis Bowen, Jeff Danciger, Cameron Gordon, Kate Juschenko, John Luecke and Lorenzo Sadun with interests in Coxeter groups, ergodic theory of group actions, geometric structures on manifolds, low-dimensional topology, knot theory, amenability, operator algebras, tiling dynamics and more.

This award will facilitate a variety of new activities by the University of Texas at Austin Groups and Dynamics (UTGD) research group. These activities are designed to foster a rich educational environment for undergraduates, graduate students, and postdocs at UT by increasing introductory research opportunities for undergraduates and research-level training for graduate students. The overall goals of this initiative are to increase the number of math majors going to top-tier graduate schools, increase the number of Ph.D.s obtaining top-tier postdocs, improve the career placement of postdoctoral fellows after their time at UT, and increase the number of women and minorities pursuing advanced degrees and careers in mathematics research and education.

The UTGD is led by seven faculty members at UT Austin. The group brings a wealth of different viewpoints and motivations together, from low-dimensional topology and geometry, to amenability, representation theory, random walks and ergodic theory. Building on a departmental Group Theory and Dynamics Seminar that has run for the past five years, the emphasis and resources of the grant will bring together expertise in the many areas represented by the research group while providing an arena for new mathematics and for the training of new mathematicians. 

To increase the number of graduate students entering into fields involving higher mathematics, UTGD will provide a summer Directed Reading Program (DRP) designed to prepare undergraduates for graduate school. UTGD will create a course, Experimental Mathematics, and enhance another, Discrete Math, to help prepare students for research. To improve the placement of graduating UT Ph.D.s, this award will enhance the UT graduate program by providing graduate fellowships/traineeships and travel funds and support for graduate mini-Schools and a Groups and Dynamics junior seminar. To build the departmental activity centered around Groups and Dynamics, this award will add four postdoctoral positions and provide visitors to work with postdocs, graduate students, and faculty. In the use of these resources, the management team will actively seek to increase the proportion of members of underrepresented groups in mathematics. 

The grant also proposes a number of ways to impact mathematics outside the department. The materials resulting from any of the projects will be made available through a dedicated website. The mini-Schools will draw from graduate students nationwide; the undergraduate conference, and the summer DRP will draw broadly from Texas schools. The Julia Robinson Math Festival will bring engaging and new mathematical experiences to K-12 students in the Austin area. The activities with the Math Teachers' Circle will create a stronger working relationship between the faculty and students of the math department and local K-12 teachers.
 

• Francesco Maggi (Principal Investigator)
• Natasa Pavlovic (Co-Principal Investigator)
• Alexis Vasseur (Co-Principal Investigator)
• Arie Israel (Co-Principal Investigator)
• Stefania Patrizi (Co-Principal Investigator)
• Luis Caffarelli
• William Beckner
• Thomas Chen
• Matias Delgadino
• Irene Gamba
• Maria Gualdani
   

The Research Training Grant in Analysis aims at fostering interactions between undergraduate students, graduate students, and postdoctoral associates and the group of faculty at the Department of Mathematics, constituted by Luis Caffarelli, William Beckner, Thomas Chen, Matias Delgadino, Irene Gamba, Maria Gualdani, Arie Israel, Francesco Maggi, Natasa Pavlovic, Stefania Patrizi and Alexis Vasseur, who are active in a broad array of topics in Analysis.

The goal of this project is enhancing in several directions the research-training activities in the area of the Analysis of partial differential equations (PDE) at the University of Texas (UT) at Austin. The Analysis of PDE is an area of Mathematics that is central to the development of Natural Sciences. Indeed, PDE are used in the modeling of many phenomena, like the atomic properties of matter, the dynamics of celestial bodies, the mechanics of fluids and gases (used for example in weather forecast), and the study of electromagnetic phenomena (fundamental to modern communications). This variety of applications is reflected in the complexity of a field rich in open problems and fruitful research directions. The training of graduate and undergraduate students in Analysis is thus crucial to the scientific and economic competitiveness of the US, and so is any effort to attract students to the area. At the same time, leading students to achieve a view of the subject that is not merely technical and overly specialized, but also succeeds in emphasizing the versatility and depth of the field, requires the coordinated work of a group.

The five co-PIs (Israel, Maggi, Patrizi, Pavlovic, Vasseur), together with the larger group of PDE experts at UT Austin (including Beckner, Caffarelli, Chen, Delgadino, Gamba and Gualdani ), are strongly committed to research training, with a combined research activity that covers a vast area of interconnected topics in PDE, and has received international recognition. This project will include 5 postdoctoral fellowships and 20 annual graduate fellowships, thus increasing the number of US citizens trained in the Analysis of PDE at UT Austin; and a comprehensive series of actions aimed at increasing the visibility of our activities among undergraduate students, both internally and externally to UT Austin, and with particular emphasis on students from universities in Central Texas serving large minority populations. The educational activities of the group (seminars, courses, informal lectures, reading courses, etc.) will be carefully revisited and enhanced, to expose trainees to new ideas, and to multiply the opportunities for mentoring, teaching, professional development, and interactions at all levels. An annual Summer Program and a professionally designed and maintained website will increase the national visibility of our program and help dispersing its most successful practices. The ultimate expected outcome is creating positive lasting changes in the research training culture at our department and beyond.