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Summer 2019 Undergraduate Research Programs at Cornell University These are 8 week programs and both will run from June 3, 2019 - July 26, 2019
Summer Program for Undergraduate Research - SPUR Research Experience for Undergraduates - REU
These summer programs provide the opportunity for undergraduate students of mathematics to participate in leading-edge research. This year, some projects are designated "SPUR" and others are designated "REU." The difference between SPUR and REU projects is the funding available: Student funding for SPUR projects comes from Cornell. To receive funding, you need to be a Cornell student but do not need to be a US citizen or resident.
Student funding for REU projects comes from the US National Science Foundation. For this, you need to be a US citizen or permanent resident, but do not need to be a Cornell student.
If you come with your own funding, the above restrictions do not apply, but of course you will still be subject to the same competitive selection process.
International students: International students are welcome to apply. Students accepted to the
program will be self-funded and will be registered under the umbrella of
the Provost’s International Research Internship Program (PIRIP). For
more information on the PIRIP program go to https://global.cornell.edu/provosts-international-research-internship-program and https://global.cornell.edu/sites/default/files/PIRIP_Procedures_070717.pdf.
You will be responsible for paying an administrative fee ($2,190),
which is 25% of the current summer extramural tuition rate for 6 credits
(S/U Grade – satisfactory/unsatisfactory). Summer 2019 fee = $1,460
per credit x 25% x 6 credits = $2,190. To apply you will need the following:
SPUR Program Projects Project 1: Analysis on Fractals
Students in this project will study properties of functions defined on fractals. For certain fractals, including the Sierpinski gasket, the Sierpinski carpet, and some of the classical Julia sets, there is now a theory of “differential equations.” (See my book, Differential Equations on Fractals, a tutorial, Princeton University Press, 2006.) One of the goals of this project is to obtain more information about solutions of these fractal differential equations, following up on work that has been done by past REU students. Most of the work on this project will involve both computer experimentation and theoretical study, but individual students may put more emphasis on one or the other. We expect that students will be involved in all stages of the process: planning what examples to study, doing the programming for the computations, and interpreting the results (and attempting to prove the conjectures that come out of the process). Project 2: Computations in derived algebraic geometry and equivariant cohomology This project
will focus on doing calculations in the emerging field of derived algebraic
geometry. We will focus on studying differential graded algebras and
their global avatar, differential graded schemes. An example of such a
calculation is to compute derived intersections, which capture possible
non-transversality and which have been studied in the case of smooth subvarieties
of smooth varieties; another is to find explicit presentations of derived
moduli stacks of local systems on some explicit topological surfaces. We
will investigate possible generalizations of these results to mildly singular
varieties in both local and global settings. Another question involves
studying circle-equivariant cohomology with rational coefficients and its
relationship with differential graded algebras over a certain differential
graded ring. Students
participating in this project should have some exposure to commutative rings or
algebraic topology. Programming experience may be helpful since
investigations can be done using software such as Macaulay2. REU Program Project
Project: Mechanics, Control, Robotics, and Dynamics This project will focus on the analysis of problems in mechanics, control theory, and robotics from the perspective of dynamical systems theory. Within mechanics, we will focus on the equilibrium and stability properties of thin elastic structures, and we will use these results to model the behavior of toys such as a Slinky. Within control theory, we will study problems in optimal control, inverse optimal control, and ensemble control. Within the field of robotics, we will focus on the problem of automated manipulation for deformable objects and on the problem of simultaneously controlling many robots with a limited number of signals. Finally, within dynamical systems theory, we will study the connections between stability and optimality and how optimality can be used to model collective motion. Students participating in this project should have strong backgrounds in linear algebra and ordinary differential equations. Previous experience with computer programming, optimization, classical mechanics, or control theory will be helpful, but is not required. The problems we will solve can be tailored to students' expertise, and the problems can be computational, analytical, or a mix of both. See the following link for descriptions of potential topics that students can explore during this project. Diversity and Inclusion are a part of Cornell University's heritage. We are a recognized employer and educator valuing AA/EEO, Protected Veterans, and Individuals with Disabilities. |
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