Reed College Science Research Fellowship for Faculty-Student Collaborative Research
Funding is available from the Reed College Science Research Fellowship (RCSRF) to facilitate and financially support summer research by teams of Reed College faculty and students. The Reed College Science Research Fellowship was created through the generosity and thoughtfulness of Reed alumni who were elected members of the National Academy of Sciences in recognition of their distinguished and continuing achievements in original scientific research. Application is open to faculty/student research teams proposing to work on problems of substantial scientific merit. Awards are not intended for curriculum development.
These funds are available to students and faculty who will be returning to Reed for the academic year following the summer grant period. Student applicants must be in good academic standing.
The student-driven project proposal should introduce the research area in adequate detail to make the explicitly stated hypothesis unambiguous. Methodology must be outlined, but need not be minutely detailed. Of considerable importance in the evaluation process will be a discussion of the significance to the central hypothesis of alternative outcomes to the proposed experiments. A complete application will consist of:
- Student-driven proposal: single spaced description of the project, not to exceed 5 pages including references and includes:
- Abstract: Describe the salient features of the proposal in terms easily understood by an educated, but not scientifically trained reader. See examples at the bottom of this page.
- Background and rationale
- Specific aim and hypothesis
- Design and procedure
- Predicted outcomes and alternative outcomes
- Role of the student
- Role of the faculty member
- Benefit to the student (written by faculty member)
- Research Supply Budget
The RCSRF Awards are limited to $6,800. Of this total, $5,300 is specified as stipend for the student intern for 10 weeks. The remaining $1,500 is available for research supplies. These should be listed on a separate budget page and accompanied by a justification for any item(s) that are not routine and obvious for the sort of study proposed.
The completed proposal should be uploaded online. Link to online grant application. Applications are due March 4, 2020 at 12:00 pm.
For more information on eligibility or any questions about the application process, applicants are strongly encouraged to contact Anne Ha, URC Administrator at email@example.com.
Project abstract examples that were returned for revision.
Original: This research project will answer whether correlated-hopping processes in a perturbative solution to the Hubbard model stabilize a novel state of matter known as orbital antiferromag-netism.
Revised: This research project is a theoretical investigation into what physical mechanisms potentially lead to the formation of microscopic current patterns inside materials. The existence of these current patterns, called orbital antiferromagnetism, is potentially related to high-temperature superconductivity, one of the great unsolved problems in physics. Our work will build upon that of Punjari and Henley  and Reed physics senior Indy Liu (’16); we will apply the high-order approximation method developed by Liu to the systems studied by Punjari and Henley, which are directly relevenat to the high-temperature superconductors. This investigation will answer whether a physical process known as cor-related hopping, which involves the simultaneous rearrangement of a number of electrons, can explain the formation of these current patterns.
Original: Algebraic Geometry attempts to characterize questions about geometric objects (such as curves through space) using computationally-oriented algebraic machinery. Core to many areas of math are the concept of invariants, or properties that are preserved via some transformation. Elementary examples of invariants include the shape of a polygon under translation, or the ratio of the circumference to the diameter of any circle (which is the familiar constant π). Classiﬁcation of invariants is instrumental in attempting to fully classify various kinds of mathematical objects. A module is a mathematical space that allows you to take linear combinations of elements within it. A free module in addition has a basis, i.e., it has a generating set that makes the coeﬃcients in their linear combinations uniquely determined. A resolution is a sequence of functions between modules that fulﬁlls certain properties. Graded modules over polynomial rings decompose as direct sums of subspaces called graded components, and the multiplication by homogeneous polynomials is compatible with the labels on the components. The gradings are used in the resolutions to keep track of the maps on the typically ﬁnite-dimensional graded components. Then many questions on resolutions can be translated into more tractable linear algebra. Within a subﬁeld of Algebraic Geometry known as Commutative Algebra, it is desirable to classify the resolutions of free graded modules via their graded Betti numbers, which are a numerical invariant of the resolutions. In my project, I will examine the graded Betti numbers of various well-behaved graded free modules and see if they admit a classiﬁcation.
Revised: Algebraic Geometry attempts to characterize geometric objects, such as curves through space, using computationally-oriented algebraic tools. One main form of characterization is known as classiﬁcation, which attempts to group together objects that are have similar properties. This can be immensely useful, as it can allow one to study a single object, and from it understand how a whole class of objects behave. Curves in space have certain characteristics it can be desirable to compute. One of these is known as the minimal free resolution, which can be used to classify curves. In general, it can be extremely diﬃcult to compute this, yet highly desirable to. While algorithms exist for this purpose, applying them to a general case is a computationally diﬃcult prospect (it is an exponential time algorithm, which can be interpreted as “very slow”). In recent years, analytic methods have been successful in computing minimal free resolutions of certain simple curves  . In this project, we will examine curves in four-dimensional space via their free resolutions, extending the work of Roy and Gimenez to new curves. The main goal is to classify these curves and provide their Boij-S¨oderberg decomposition, a new technique within Commutative Algebra that can give better insight on how the minimal free resolution of a curve is structured .