The Mathematics Department has hosted a wide diversity of Undergraduate Research Opportunities Program (UROP) experiences. Every year the Department hosts around 70 different UROP projects.
Here are some recent titles:
- "Modeling Droplet Dispersion to understand Disease transmission"
- "Quantum Groups and Hecke Algebras"
- "Modular Representations of Cherednik Algebras"
- "Combinatorics of the Bruhat Order"
- "Eigenvalues and Eigenfunctions of the Laplacian and Schrodinger Operators"
Faculty UROP Coordinators:
More of these projects arose from conversations between the student and the advisor than as a project or idea proposed by the advisor. In almost every case the project represents individual research carried out by the student under the guidance of the advisor.
Quadratic forms, K-theory, algebraic topology
Project supervisor: Kyle Ormsby
Title: The homogeneous prime spectrum of Milnor-Witt K-theory
The Milnor-Witt K-theory of a field k is a Z-graded enhancement of a classical object from the study of quadratic forms: the Grothendieck-Witt ring, GW(k). The prime ideals in GW(k) are classified by the rank homomorphism and the orderings of k. The goal of this project is to study the homogeneous prime ideals in Milnor-Witt K-theory from an algebraic viewpoint. Such a classification has applications in motivic homotopy theory.
Qualifications: Strong background in abstract algebra (rings, modules, prime ideals) required, exposure to (graded) commutative algebra, algebraic geometry and number theory might be helpful.
Project supervisor: Romain Lagrange
Projects will deal with the geometry-induced buckling in mechanical engineering (e.g. buckling of a curved beam).
Qualifications: Willing to program in Matlab extensively (knowing Matlab is not necessary but could be very useful); Has to know what is an ODE; Has to know the concepts of Nonlinear dynamics: 18.354.
Combinatorics or Representation Theory
Project supervisor: Vidya Venkateswaran
Spreadsheets, Big Tables, and the Abstract Algebra of Associative Arrays
Spreadsheets are used by nearly 100M people every day. Triple store databases (e.g., Google Big Table, Amazon Dynamo, and Hadoop HBase) store a large fraction of the analyzed data in the world and are the backbone of modern web companies. Both spreadsheets and big tables can hold diverse data (e.g., strings, dates, integers, and reals) and lend themselves to diverse representations (e.g., matrices, functions, hash tables, and databases). D4M (Dynamic Distributed Dimensional Data Model) has been developed to provide a mathematically rich interface to triple stores. The spreadsheets, triple stores, sparse linear algebra, and fuzzy algebra. This projects seeks to strengthen the abstract algebraic foundations of associative arrays. The student will work with the faculty advisor to develop the basic theorems of associative arrays by building on existing work on fuzzy algebra and linear algebra. Participants will be paid.
Qualifications: Strong mathematical background (the student should have completed 18.701 and 18.702). Experience with Matlab is helpful, but not a requirement.
Projects in the Imaging and Computing Group
Project supervisor: Prof. Laurent Demanet
Application deadline: First Friday of each term. Summer UROPs may also be possible.
For information please see the attached PDF file.
Project supervisor: Prof. John Bush
See Prof. Bush's webpage for information on his current research projects and interests.
Please note that UROP opportunities are not limited to those advertised above. Students are encouraged to speak to faculty to find out about possible projects.