NSF Summer Research Experiences for Undergraduates

REU Site: Research Training for Undergraduates in Mathematical Analysis with Applications in Allied Fields


Program Dates: June 10August 4, 2019

This REU Site is supported by the National Science Foundation, and this support is gratefully acknowledged. Our 2019 REU Summer Program provides an intensive eight-week summer research experience that prepares undergraduates for the rigors of graduate level research in mathematics. Advanced undergraduates are invited to Chattanooga to participate in collaborative research projects with experienced faculty mentors. Our Special Summer Colloquium Series, augmented by other group activities, presents opportunities for REU participants to interact with world-class mathematicians and scientists who are actively pursuing theoretical, computational, and methodological research at the frontiers of mathematical analysis and its applications.

Research Areas

  • Multiplicative number theory
  • Fourier analysis
  • Uniform distribution modulo one
  • Random polynomials
  • Resolvent identities and spectral shift functions
  • Dynamical systems and biological applications
  • Optimal control simulation

Research Groups

My mind rebels at stagnation. Give me problems, give me work, give me the most abstruse cryptogram, or the most intricate analysis, and I am in my own proper atmosphere. But I abhor the dull routine of existence. I crave for mental exaltation.

      Sherlock Holmes, in Arthur Conan Doyle’s The Sign of the Four

We are excited to have eleven talented and energetic undergraduate researchers participate in our 2019 REU Summer Program. We have formed three research groups.

Dr. Andrew Ledoans research group will study the L1 mean of the exponential sum whose coefficients are values of the Möbius function:

  • Emily Eckels, Emory University
  • Steven Jin, University of Maryland at College Park
  • Brian Tobin, Harvard University

Dr. Jin Wangs research group will investigate cholera transmission dynamics under the impact of disease control measures and develop and analyze a new multi-scale model for cholera that links the between-host and within-host dynamics and their interaction with the environment:

  • Margaret Brown, University of Maryland at College Park
  • Shan (Miko) Jiang, Mount Holyoke College
  • Nafisa Tabassum, York College of City University of New York
  • Carolyn Valenti, Bucknell University

Dr. Roger Nichols’s research group will study Krein-type resolvent identities for singular Sturm–Liouville operators and their connection to the spectral shift function:

  • Blake Allan, Baylor University
  • Justin Kim, Vanderbilt University
  • Gregory Michajlyszyn, University of Rochester
  • Donald Rung, Sewanee: The University of the South 

Group Events and Photos

  • Wednesday, June 12, 2019: Our first group dinner with REU mentors and students at Big River Grille & Brewing Works in Downtown Chattanooga. Our group photo at the dinner.
  • Thursday, June 20, 2019: Undergraduate researchers from the Mathematics REU Program get together with those from the UTChattSat, ICompBIO, and URaCE REU Programs in Benwood Auditorium (room EMCS 230, 6:30 PM) for a screening of The Most Unkown, an epic documentary film that sends nine scientists to extraordinary parts of the world to uncover the answers to some of humanitys biggest questions.

Special Summer Colloquium Series

This series is presented in conjunction with the NSF-funded 2019 REU Summer Program. The talks are intended to be accessible to advanced undergraduate and beginning graduate mathematics majors. These talks will be given at 2:00 PM in EMCS 422 on their scheduled dates.



Title and Abstract




Dr. Scott Alexander AtkinsonVanderbilt University


The Hardy–Littlewood Circle Method and Applications

The Hardy–Littlewood circle method, also known as the exponential sum method, is a central tool in analytic number theory. I will describe what this classical and important method is, and how it applies to various problems in additive number theory, including Vinogradov’s three primes theorem (the ternary version of the Goldbach conjecture) and Roth’s theorem in combinatorics. I will also discuss the limitation of the circle method, and the modern development in the past decade to overcome this.

Dr. Fernando Xuancheng Shao, University of Kentucky



Dr. Judy D. DayThe University of Tennessee, Knoxville






Dr. Carmeliza Navasca, University of Alabama at Birmingham





  • Undergraduate status with minimum grade point average of 3.0
  • Rising senior—outstanding rising juniors or sophomores who meet the other selection criteria will be considered
  • Majoring in mathematics, statistitics, or related fields
  • Have completed linear algebra, differential equations, and at least two upper level courses such as abstract algebra, matrix theory, analysis, complex variables, elementary number theory, probability, and numerical analysis

Women, minorities from underrepresented groups, first-generation college students, and students from predominantly undergraduate institutions with limited research programs are especially encouraged to apply.


  • U.S. citizens and permanent resident students will receive airfare and transportation (up to $400) to Chattanooga, room and board, and a $4,000 stipend.
  • Accepted students will be notified of awards by March 25, 2019.

Application Deadline

  • All application materials must be submitted by March 15, 2019.
  • Late materials will not be accepted.
  • Incomplete applications will not be accepted.

Application Requirements

  • Completed Application: Please visit MathPrograms.Org to apply.
  • Curriculum Vitae: Please indicate clearly U.S. citizenship or permanent residency.
  • Personal Statement: In approximately 500 words, please answer the following questions: 
    • Why are you applying to this UTC REU program?
    • What are your research interests?
    • What are your future career goals?
    • What have you achieved toward these goals?
  • College or University Transcript: A copy of your college or university transcript is required. Unofficial transcripts will be accepted.
  • Faculty Letter of Recommendation: Two faculty letters of recommendation are required. Each letter should be written on university letterhead and submitted to MathPrograms.Org by the reference writers.

             Apply Now

Faculty Mentors

Evaluation of this UTC REU program will be performed annually throughout the duration of the program by Dr. Sherry Marlow Ormsby, Interim Executive Director, Office of Panning, Evaluation, and Institutional Research. Ms. Heather Shirley Heinlein will provide additional administrative support.

More Information

UTC is a national model for regional metropolitan universities and has a history of excellence in undergraduate education and research. The campus is at the heart of Downtown Chattanooga and within walking distance of such attractions as

Chattanooga is a gorgeous and thriving city located on the Southeastern corner of Tennessee. Nestled between the majestic mountainscapes of Missionary Ridge, Lookout Mountain, and Signal Mountain, the city is situated perfectly between Atlanta, Knoxville, Nashville, and Birmingham. It has the fastest Internet speed in the nation, with its community-wide fiber optic network that can turbocharge Internet speed up to 1,000 megabits per second. Chattanooga is an ideal location that offers many avenues for the development of collegial relationships and interactions between REU participants.


Please write to Andrew-Ledoan@utc.edu with any questions.