There are two (limited) Math Department funds for graduate students travelling to conferences, the AMSC fund and the Levermore fund. Each fund can be used at most once a year. The AMSC fund covers expenses for up to  600, and is available to students giving a talk or presenting a poster, or else students who have some additional funding from other sourses (advisor, conference organizers, etc.). The Levermore fund covers smaller emounts. The two funds cannot be combined.  For either fund, please  limit the amount requested for meals to $ 25/day.

The printing of posters can be covered by the department, as a separate expense.

In addition, there is the University Goldhaber fund which provides matching funds for students presenting posters or giving talks.

Students planning to travel to conferences should see the Associate Chair for Graduate Studies  for preliminary approval, and then fill out a travel form al least two weeks before departure day, listing the graduate chair as PI.

(Under construction)


Recent UMD PhD theses can be found here.  You can search for an individual author, or all Math dissertations. You may also be interested in the Math Genealogy Project.

  • Aziz Osborn Gold Medal in Teaching Excellence 2016-2017

Kristin Carfora

Liam Fowl

Nicholas Paskal

Tengfei Su

Adil Virani

Nathan Yu

  • Aziz Osborn Gold Medal in Teaching Excellence 2015-2016

Sean Ballentine

Chae Clark

Stefan Doboszczak

Rebecca Black

Oliver Rourke

Nakhila Mistry

  • Aziz Osborn Gold Medal in Teaching Excellence 2014-2015

Xia Hu

Siming He

Lucia Simonelli

Richard Rast

Ryan Hunter

Patrick Daniels

  • Aziz Osborn Gold Medal in Teaching Excellence 2013-2014

Robert Maschal

Matthew Whiteway

Oliver Lum

Ryan Kirk

Jinhang Xue

Sam Bloom

  • Gold Medal in Teaching Excellence for Graduate Students 2012-2013

Matthew Becker

Colleen Stock

James Murphy

Matt Begue

Jacob Ralston

  • Gold Medal in Teaching Excellence for Graduate Students 2011-2012

Adam Lizzi

Kanna Nakamura

Geoffrey Clapp

Maxx Cho

Jong Jun Lee

  • Gold Medal in Teaching Excellence for Graduate Students 2010-2011

Hana Ueda

Catherine Ochalek

Stephen Balady

Alexander Cloninger

Each year the Mathematics Department hosts a competition for graduate students called Spotlight on Research, with cash prizes. The competition is run and judged by current studnets in the MATH, AMSC, and STAT programs.

Previous winners are at this link: Spotlight on Graduate Research Awards

The requirements below are for students in pure mathematics, not in statistics. For students in Statistics: Qualifying Exams must be passed in Statistics, Probability, and Applied Statistics.

1. Students must pass 2 qualifying exams from the following list:

Algebra (Math 600, 601)
Analysis (Math 630, 660)
Geometry (Math 730, 740)
Probability (Stat 600, 601)
Statistics (Stat 700, 701)

A student in pure mathematics can use at most one of Probability and Statistics to satisfy the exam requirement.

2. Students must take four additional semesters of courses from the following list, with a grade point average of 3.3 or better for the four courses used to satisfy this requirement. Courses with grades less than B cannot be included (for example, B− is not allowed).

Math 600, 601 (Algebra)
Math 630, 660 (Analysis)
Math 730, 740 (Geometry)
Stat 600, 601 (Probability)
Stat 700, 701 (Statistics)
Math 634 (Harmonic Analysis)
Math 642 (Dynamical Systems I)
Math 712, Math 713 (Logic)
Math 734 (Algebraic Topology)
AMSC 666, AMSC 667 (Numerical Analysis)
Math 631 (Real Analysis)
Math 670 (ODE)
Math 673, Math 674 (PDE)

The four semesters are not required to be in the same sequence of courses. For example, Math 730, Math 670, AMSC 666, and AMSC 667 would be acceptable. These four semester-long courses must be distinct from the ones supporting the qualifying exams passed in Part 1.

A student may take and pass a third (and possibly, a fourth) qualifying exam in place of taking the actual courses. For example, passing the written exams
in Algebra, Analysis, and Geometry would count as 2 exams plus 2 semesters.

One qualifying exam must be passed by January of the second year, and all requirements must be finished by January of the third year.

Students who have taken courses from the second list elsewhere may petition the graduate chair to have such courses satisfy up to two semesters of the four-semester requirement (although generally students should instead use these courses as preparation for qualifying exams).

Each course on the lists should have serious assessment methods (graded homework, projects, exams, and/or similar). There should be some significant assessment that is guaranteed to be done solely by the student (that is, an exam, not only homework).


Archives: 2011 | 2012 | 2013 | 2014 | 2015 | 2016 | 2017

  • Waves in viscoelastic media

    Speaker: Francisco-Javier Sayas (Department of Mathematical Sciences, University of Delaware) -

    When: Tue, September 5, 2017 - 3:30pm
    Where: Kirwan Hall 3206

    View Abstract

    Abstract: I will explain ongoing work with my team (Tom Brown, Shukai Du, and Hasan Eruslu) on Finite Element simulation of elastic wave propagation in media that are modeled using a strain-to-stress relation that keeps track of the past evolution of the solid. The family of models I will discuss includes the classical (Zener) differential viscoelastic model, a fractional derivative version thereof, and combinations of the above with pure elastic behavior. The analysis will be presented using transfer function techniques, but I will explain how in some cases refined results can be found using techniques of semigroup theory.
  • Finite element approximation of nonconvex uniformly elliptic fully nonlinear equations

    Speaker: Abner J. Salgado (University of Tennessee, Knoxville) -

    When: Tue, September 12, 2017 - 3:30pm
    Where: Kirwan Hall 3206

    View Abstract

    Abstract: We propose and analyze a two-scale finite element method for the Isaacs equation. By showing the consistency of the approximation and that the method satisfies the discrete maximum principle we establish convergence to the viscosity solution. By properly choosing each of the scales, and using the recently derived discrete Alexandrov Bakelman Pucci estimate we can deduce rates of convergence.
  • An angular momentum method for approximating wave maps into the sphere

    Speaker: Franziska Weber (Department of Mathematics, University of Maryland, College Park) -

    When: Tue, September 19, 2017 - 3:30pm
    Where: Kirwan Hall 3206

    View Abstract

    Abstract: We present a convergent finite difference method for approximating wave maps into the sphere. The method is based on a reformulation of the second order wave map equation as a first order system by using the angular momentum as an auxiliary variable. This enables us to preserve the length constraint as well as the energy inherit in the system of equations at the discrete level. The method is shown to converge to a weak solution of the wave map equation as the discretization parameters go to zero. Moreover, it is fast in the sense that O(N log N) operations are required in each time step (where N is the number of grid cells) and a linear CFL-condition is sufficient for stability and convergence. The performance of the method is illustrated by numerical experiments.

    The method can be extended to a convergent scheme for the damped wave map equation and the heat map flow. If time permits, I will also discuss possible extensions of the method to applications for liquid crystal dynamics.
  • An optimal adaptive Fictitious Domain Method

    Speaker: Rob Stevenson (University of Amsterdam) -

    When: Thu, October 5, 2017 - 3:30pm
    Where: Kirwan Hall 3206

    View Abstract

    Abstract: We consider a Fictitious Domain formulation of an elliptic PDE, and solve the arising saddle-point problem by an inexact preconditioned Uzawa iteration.
    Solving the arising `inner' elliptic problems with an adaptive finite element method, we prove that the overall method converges with the best possible rate.
    So far our results apply to two-dimensional domains and lowest order finite elements (continuous piecewise linears on the fictitious domain, and piecewise constants on the boundary of the physical domain).

    Joint work with S. Berrone (Torino), A. Bonito (Texas A&M), and M. Verani (Milano).
  • Adaptive Higher-Order Finite Element Simulations for the Time-Harmonic Maxwell Equations

    Speaker: Matthias Maier (University of Minnesota) -

    When: Tue, October 10, 2017 - 3:30pm
    Where: Kirwan Hall 3206

    View Abstract

    Abstract: In the terahertz frequency range, the effective (complex-valued) surface conductivity of atomically thick 2D materials such as graphene has a positive imaginary part that is considerably larger than the real part. This feature allows for the propagation of slowly decaying electromagnetic waves, called surface plasmon-polaritons (SPPs), that are confined near the material interface with wavelengths much shorter than the wavelength of the free-space radiation. SPPs are promising ingredients in the design of novel optical applications promising "subwavelength optics" beyond the diffraction limit. There is a compelling need for controllable numerical schemes which, placed on firm mathematical grounds, can reliably describe SPPs in a variety of geometries.

    In this talk we present a higher-order finite element approach for the simulation of SPP structures on a conducting sheet, excited by a plane-wave or electric Hertzian dipole sources. Aspects of the numerical treatment such as absorbing, perfectly matched layers, local refinement and a-posteriori error control are discussed. Corresponding analytical results are briefly presented as well.
  • TBA

    Speaker: Shawn Walker (Louisiana State University) -

    When: Tue, October 17, 2017 - 3:30pm
    Where: Kirwan Hall 3206
  • TBA

    Speaker: Jie Shen (Purdue University) -

    When: Tue, October 24, 2017 - 3:30pm
    Where: Kirwan Hall 3206
  • Adaptive FEM for the fractional Laplacian: a priori and a posteriori error estimates, efficient implementation and multigrid solver

    Speaker: Christian Glusa (Sandia National Laboratories) -

    When: Tue, October 31, 2017 - 3:30pm
    Where: Kirwan Hall 3206

    View Abstract

    Abstract: We explore the connection between fractional order partial differential
    equations in two or more spatial dimensions with boundary integral
    operators to develop techniques that enable one to efficiently tackle
    the integral fractional Laplacian. We develop all of the components
    needed to construct an adaptive finite element code that can be used to
    approximate fractional partial differential equations, on non-trivial
    domains in \(d\geq 1\) dimensions. Our main approach consists of taking
    tools that have been shown to be effective for adaptive boundary element
    methods and, where necessary, modifying them so that they can be applied
    to the fractional PDE case. Improved a priori error estimates are
    derived for the case of quasi-uniform meshes which are seen to deliver
    sub-optimal rates of convergence owing to the presence of singularities.
    Attention is then turned to the development of an a posteriori error
    estimate and error indicators which are suitable for driving an adaptive
    refinement procedure. We assume that the resulting refined meshes are
    locally quasi-uniform and develop efficient methods for the assembly of
    the resulting linear algebraic systems and their solution using
    iterative methods, including the multigrid method. The storage of the
    dense matrices along with efficient techniques for computing the dense
    matrix vector products needed for the iterative solution is also
    considered. Importantly, the approximation does not make any strong
    assumptions on the shape of the underlying domain and does not rely on
    any special structure of the matrix that could be exploited by fast
    transforms. The performance and efficiency of the resulting algorithm is
    illustrated for a variety of examples.

    This is joint work with Mark Ainsworth, Brown University.
  • TBA

    Speaker: Simon Foucart (Texas A&M University) -

    When: Tue, November 7, 2017 - 3:30pm
    Where: Kirwan Hall 3206
  • TBA

    Speaker: Alex Townsend (Cornell University) -

    When: Tue, November 14, 2017 - 3:30pm
    Where: Kirwan Hall 3206
  • TBA

    Speaker: Mert Gurbuzbalaban (Rutgers University) -

    When: Tue, November 28, 2017 - 3:30pm
    Where: Kirwan Hall 3206