UROP

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.

For information, please contact Anna Ferrigno at the MAS office or visit the MIT UROP website.

Advertised Opportunities:

Please see the attached PDF file for a list of possible projects and research areas.

Quadratic forms, K-theory, algebraic topology

Project supervisor: Kyle Ormsby

Title: The homogeneous prime spectrum of Milnor-Witt K-theory

Project description

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.

Contact: Kyle Ormsby, ormsby@math.mit.edu

Elasticity

Project supervisor: Romain Lagrange

Project description

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.

Contact: Romain Lagrange, lagrangr@math.mit.edu

Combinatorics or Representation Theory

Project supervisor: Vidya Venkateswaran

Contact: Vidya Venkateswaran, vidyav@math.mit.edu

Spreadsheets, Big Tables, and the Abstract Algebra of Associative Arrays

Project supervisors: Dr. Jeremy Kepner and Prof. Alan Edelman

Project description

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.

Website: www.mit.edu/~kepner/

Qualifications: Strong mathematical background (the student should have completed 18.701 and 18.702). Experience with Matlab is helpful, but not a requirement.

Contact: Dr. Jeremy Kepner, kepner@ll.mit.edu

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.

Project description

For information please see the attached PDF file.

Contact: Apply directly with Prof. Laurent Demanet, laurent@math.mit.edu. State your interest and qualifications in the application.

Fluid Dynamics

Project supervisor: Prof. John Bush

Project description

See Prof. Bush's webpage for information on his current research projects and interests.

Contact: Prof. John Bush, bush@math.mit.edu

 

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.