REU Program

Research Experience for Undergraduates (REU) Program

The NSF Research Experience for Undergraduates (REU) program in applied mathematics at IUPUI offers students an opportunity to conduct mathematical research with applications in the medical sciences, fluid mechanics, neuroscience, and physics. Each year, we invite eight undergraduate students from across the United States to participate in this competitive, eight-week summer program. Students will work in pairs under the guidance of a faculty research mentor from the IUPUI Departments of Mathematical Sciences and Physics. Students will make specific research contributions that often lead to publications and/or conference presentations.

The program will be held in-person in Summer 2024. Each participant will receive a $4,800 research stipend, housing/food accommodations, and $500 for travel expenses.

The 2024 REU Program will run June 3 – July 26, 2024. Complete applications are due February 5, 2024. Please see project descriptions and the application below.

For additional information about the 2024 REU Program, please contact Dr. Julia Arciero at

Projects for the 2024 REU Program

  1. Mathematical modeling of retinal oxygenation (Advisor: Dr. Julia Arciero)
  2. Incorporating subcellular structures into cellular models (Advisor: Dr. Jared Barber)
  3. Mathematical modeling in addictions (Advisor: Dr. Alexey Kuznetsov)
  4. Modelling cellular and membrane dynamics (Advisor: Dr. Horia Petrache)

Additional project details

REU Advisor: Dr. Julia Arciero, Mathematics

Primary open angle glaucoma is the second-leading cause of blindness worldwide and is characterized by progressive retinal ganglion cell death and irreversible vision loss. Previous experimental studies have established aspects of the relationship between retinal structure and function, while others have demonstrated correlations between vascular health and glaucoma. However, a unified theory of the structural and hemodynamic factors that combine within tissue to cause visual impairment in glaucoma is missing. Students working on this REU project will collaborate with a mathematician and ophthalmologists to simulate the effects of vascular heterogeneity, tissue layer, capillary density, and venous collapsibility on retinal tissue oxygenation. Students will gain experience coding in MATLAB and building and analyzing mathematical models of the vasculature.

REU Advisor: Dr. Jared Barber, Mathematics

We seek to better understand cell migration (e.g., wound healing, cancer metastasis, immune response) and flow sensing by cells (e.g., blood flow, kidney filtration, urinary tract) by including subcellular structures in our current set of cell models. Using experimental images from our collaborators, we will work together to incorporate subcellular features such as focal adhesions and contractile actomyosin fibers (cell migration) and primary cilia (flow sensing) into those cell models. This will help us answer questions about the relative roles of subcellular components in such scenarios. Students will work with a mathematician including collaboration with an experimental physicist. They will also learn about fluid and solid mechanics and cellular biology and gain valuable experience in modeling using tools such as MATLAB.

REU Advisor: Dr. Alexey Kuznetsov, Mathematics

Several projects are available within the greater theme of research on addictions, particularly alcohol use disorders. Generally, these disorders are associated with abnormal impulse control, decision-making, and compulsivity. We investigate the functions of the brain regions responsible for these behaviors. To do this, we develop computational models that replicate the functions of these brain regions and the behaviors of the healthy and addicted agents (humans or animals).

Commonly implicated in this context are the brain's dopamine system for motivation signals, the prefrontal cortex for the assessment of rewards, and the basal ganglia as a center for their interaction that determines the choice of actions. We extend this list to include the Insula as a center of compulsivity and the amygdala as an emotional center. The projects aim to model interactions among some of these regions to reproduce behaviors in experiments testing impulsivity, such as the delay discounting task, and compulsivity, such as aversion-resistant actions. A project may begin with the physiology and build on the known anatomy of the brain. Alternatively, it could commence with behavior first and construct an abstract agent who engages in the delay discounting task, drinking, gambling, or becomes involved in any other form of addictive behavior.

REU Advisor: Dr. Horia Petrache, Physics

In order to survive and grow, biological cells need nutrients such as glucose. We will use the CompuCell3D platform to analyze the diffusion of glucose in cellular aggregates with the goal of finding optimum geometries and cell growth rates. Since uptake of glucose is through cellular membranes, we will also analyze membrane transport using Molecular Dynamics simulations of lipid bilyers.