Each summer, 12 undergraduate students will participate in an 8 week research program in the Cornell University Mathematics Department directed by 3 faculty members (the Principal Investigator, R. Strichartz, and 2 others chosen from among current and former department members) and assisted by graduate students and postdocs. The students will work on research projects that are within their grasp, and which present real opportunities for new discoveries that will be of value to the mathematical community. It is expected that some, but not all, of the research will lead to published papers. Two types of projects will be emphasized: 1) computer related research, with students writing programs, or using existing software, to work out examples, generate conjectures, and perform experiments in areas such as analysis on fractals, free probability, dynamics of differential equations, and probabilistic models in genetics; 2) problems in combinatorics and other areas that do not require a great deal of background knowledge. In addition, the students will gain experience in communicating mathematics by presenting talks to each other and to the public.
Website: www.math.cornell.edu/Undergraduate/REU/
The purpose of the program was to introduce undergraduates to serious mathematical research under the supervision of a faculty mentor assisted by a graduate student. Research problems were carefully chosen to be within the grasp of undergraduate students, yet also to be of interest to the mathematical research community. Successful projects typically led to joint papers that have been submitted to respectable mathematics journals. Because of the challenging nature of the problems, not all projects were successful, and those that were involved long term commitments of time by the students in the process of writing papers. Many of the students also presented talks on their research at mathematical conferences. Thus the students were exposed to the full spectrum of activities of a research mathematician, with all its joys and frustrations. Over a period of 5 summers (2007 – 2011), there were 61 student participants. Of these, 42 were male and 19 were female, 5 were from Cornell and 46 from other schools, and 3 were underrepresented minorities. Each summer there were 3 faculty mentors leading research groups. The research ranged over many areas of mathematics: analysis, algebra, topology, combinatorics, logic, and differential geometry. During all five summers the P.I. led research projects in analysis on fractals, an emerging area of interest to both mathematicians and physicists, that attempts to create a theory of "differential equations" on fractal spaces where the usual theory of calculus does not apply. It is notable that the contributions of REU students over a period of 16 years has had a substantial impact on the development of this area. During three of the summers, Collin Bleak directed research projects on Thompson’s groups, an area that lies between algebra and Topology. The other projects that were offered for one summer were: 1.) A problem in combinatorics that arises in the new area of free probability (Todd Kemp). 2.) A project in linear orders and logic (Francois Dorias). 3.) A project on automata and games on the borderline of theoretical computer science and logic (Sasha Rubin). 4.) Geometric differential equations, related to the Ricci flow theory of Hamilton and Perelman that led to the recent celebrated proof of the Poincaré conjecture and Thurston’s geometrization conjecture (Xiaodong Cao). 5.) Optimal control problems (Alexander Vladimirsky). 6.) The structure of generating sequences for finite groups (Keith Dennis). 7.) Combinatorial problems relating to simplicial complexes in topology (Ed Swartz). At this time, the research has yielded 7 papers that have been published or accepted for publication, 6 papers submitted for publication and 14 papers in preparation. Most of the students are now in graduate school or are applying to graduate school in the mathematical sciences, computer science, or physics. Several have been awarded NSF graduate fellowships.
