If you are an undergraduate student who wants to do a research-oriented project such as a capstone course or a Jr./Sr. thesis, then you may want to look for a consultant or advisor in the area that you are interested in. On this page you can learn more about some of the math research interests of our faculty. Also, if you are interested in learning more about a specific subject, you can discuss this with a faculty expert or you can do a directed research.

Below is a list of the research interests of some of the Northeastern mathematics faculty. Click on the names to find more information about these faculty members.This list is not complete. Many faculty members list their research interests on their own web pages. For a list of people in the mathematics department, follow the link (and scroll down):

People in the Mathematics Department

Chris Beasley |
My research involves geometric aspects of quantum field theory and string theory, both of which extend quantum mechanics. Many different flavors of mathematics are relevant to questions about string theory, but I am especially interested in areas where differential geometry and topology play a role. |

Harm Derksen |
My research includes invariant theory, representation theory of quivers, tensors and applications. Invariant theory is an area of commutative algebra where one studies multivariate polynomials that remain unchanged after spacial symmetries. For example, the polynomial x^{2}+y^{2}+z^{2} does not change after an orthogonal transformation. A quiver is just a direct graph. If you attach vector spaces to the vertices and linear maps to the arrows, then you get a representation of a quiver. Quiver representations are studied to understand general problems in linear algebra, the modules of a finite dimensional associative algebra, or the combinatorics of cluster algebra. Tensors are multi-dimensional arrays. There are interesting applications to algebraic complexity theory (how fast can we multiply two matrices?), data science and machine learning. I am particularly interested in applications in health care such as heart arrhythmia detection from ECG using machine learning. |

Evan Dummit |
My research is in number theory, broadly construed, and algebraic combinatorics. Most modern projects in number theory require either comfort with real and complex analysis (for problems in analytic number theory) or with abstract algebra (for problems in algebraic number theory). A number of my projects have computational components involving Mathematica or Sage, and many of these would be very good starting points for an undergraduate project. I also do some work in algebraic combinatorics on problems involving point-line configurations over finite fields and local rings. |

Anthony Iarrobino |
Commutative algebra, combinatorics, algebraic geometry. Recent work concerns pairs of nilpotent commuting n by n matrices: that is AB=BA, and A^{n}=B^{n}=0. For a nilpotent matrix, the Jordan block decomposition is just a partition of n giving the dimensions of the Jordan blocks; the question is, what pairs of partitions can occur for a pair of commuting non matrices. Other recent work has pertained to Artinian algebras — finite vector spaces having an algebra (addition, multiplication) structure). Multiplication by a non-unit (no inverse) element is nilpotent, and is linear so determines a nilpotent matrix. The Jordan type of the matrix – a partition – is information about the algebra. Each of these areas allows space for a dedicated student to participate, and, in fact in each of the two areas, there has been published paper with an undergrad student, or recent-undergrad as coauthor. I also have taught Math 4020, a fall undergrad research capstone. Students match with a consultant in a pure or applied or even teaching-focus area, and write an original paper (original to you, maybe not to mathematics) and also practice presenting and explaining there work on the board and in writing.; There is a lot of feedback, discussion of presenting math, of ethics other topics students choose. Happy to discuss options for undergrad research. I have supervised several junior-senior honors undergraduate theses, most recently by Xiaoying He, on Braid group Presentations. The theses require two courses, often Math 4020, followed by Math 4971 and must be approved by the undergraduate research committee (see website with information). |

Ben Knudsen |
I’m an algebraic topologist working primarily on the homology of configuration spaces. Configuration spaces are connected to many areas of mathematics, as well as to physics and robotics, and their study features an appealing blend of geometric and pictorial reasoning, algebraic and homotopical structure, and computation. |

Alex Martsinkovsky |
My research interests are in Homological Algebra and related topics with special emphasis on categories of finitely presented functors. Such functors behave similar to abelian groups but have a lot of additional structure, which has interesting applications to the study of general rings and modules. In the last couple of years it also became clear that one can use software for computations in such categories and, most surprising, such computations can be viewed as theorem proving. |

David Massey |
I study singularities, places where abstract spaces in any number of dimensions are not smooth. The goal is to describe properties of the spaces near such points. |

Robert McOwen |
I study partial differential equations (PDEs) and their applications in geometry and fluid dynamics, especially on nonimpact or singular domains. Most of my work has involved elliptic PDEs, but recently I have worked with some parabolic PDEs. |

Alex Suciu |
My research interests are in Topology, and how it relates to Algebra, Geometry, and Combinatorics. I currently investigate cohomology jumping loci, and their applications to algebraic varieties, low-dimensional topology, and toric topology, such as the study of hyperplane arrangements, Milnor fibrations, moment angle complexes, configuration spaces, and various classes of knots, links, and manifolds, as well as the homology and lower central series of discrete groups. |

He Wang |
My research interests are in algebraic topology and its applications. More specifically, in rational homotopy theory, cohomology jumping loci, braid groups, etc. I am also interested in topological data analysis, which is an application of algebraic topology to data analysis and machine learning. |

Milen Yakimov |
Classical mathematical areas and physical theories deal with objects for which the product operation is commutative, for instance, multiplications of real numbers, multiplications of functions of several variables and others. However, in many other important settings, such as quantum mechanics, we have to deal with objects with a noncommutative multiplication. The simplest example is the product of square matrices. I employ geometric and algebraic techniques to study the properties of these objects. Furthermore, I also study their symmetries, which play a crucial role since they allow us to decrease the degrees of freedom of objects and thus to better understand them. I study dynamical systems on such objects which are of non-chaotic nature (integrable systems) and the explicit description of these objects via combinatorial techinques called cluster algebras. |

Xuwen Zhu |
My research interests are in analysis, geometry and their relation to mathematical physics. Broadly speaking, this includes the study of shapes of lines, surfaces and (in general) manifolds. For example, you cannot wrap a piece of paper over a sphere without creating creases (because of curvature), on the other hand you can wrap a piece of paper on a cylinder (still because of curvature); what if we puncture one, two, three or even more holes on a sphere and still want it to look as uniform as possible (uniformization). These can be studied using differential equations which model these geometric phenomena and give rigorous explanations for the intuitive pictures. A lot of the (more complicated) geometry phenomena arise from theoretical physics, however we can still learn from simple models and many tools would still work! |