Undergraduate Research

I really enjoy working with undergraduate students on research projects. These projects tend to be large, multi-semester long or summer research experiences during which we tackle a problem which has not yet been solved. Sometimes we make significant progress and can fully or partially answer the question we were interested in. Other times we make very little progress or we change the question in order to prove a milder statement of the theorem or result we are interested in. The process of discovering new mathematics is challenging and rewarding. Remember, it's the journey not the destination that matters.

Projects usually begin by reading some graduate level mathematics (articles or books) in order to understand the background material. We then pose some conjectures which we attempt to prove, or we learn a new technique in order to apply it in a novel way to an existing result. I am interested in working on a variety of project topics, including topics related to partial differential equations, real and complex analysis, numerical simulations, and financial mathematics.

I ask a lot of my undergraduate students. A completed project tends to be 50-100 pages in length, which includes a summary of the advanced mathematical background material, pictures, code, proofs, and a summary of results. Sometimes this completed work can be turned into a publication. We meet at least once per week and often more, so it's important that students have the time and interest to commit to a project before we begin. Students who are interested usually have already decided that they want to earn a Ph.D. after graduation, though this is not required.

Click here to find other opportunities for undergraduate research at OSU. The Young Mathematicians Conference is an excellent place to showcase your results.

Below are some projects recently completed by undergraduate students.

Isaias Vasquez

Isaias studied optimal portfolio theory, constrained maximization problems, and trading strategies in the 2024 summer through the OHIO-5 REU program.

Caroline Borrillo

Caroline learned advanced mathematical techniques probability and optimal control and applied them to Merton's investment problem.

William Carvalho

William learned advanced mathematical techniques probability and optimal control and applied them to Merton's investment problem.

Sean-Paul Billups

Sean-Paul worked on the optimal use of risk-measures in the context of portfolio management.

Suhas Beeravelli

Suhas studied constrained maximization problems related to real-world optimal trading and investment strategies.

Nicole Hao

Nicole learned advanced mathematical techniques from analysis and differential equations and applied them to a novel problem in finance in a summer REU experience at OSU.

Diep Luong Le

Diep is working on a financial mathematics problem during her summer 2023 REU program at OSU.

Echo Li

Echo is working on an analysis problem arising from financial mathematics during his summer 2023 REU program at OSU.

James Sun

James Sun worked on pricing options using stochastic calculus. His project became an honors thesis jointly mentored by Frank Moore.

Silvia Liu

Silvia Liu worked on a project pricing American options using stochastic calculus and PDEs. She is now pursuing a Ph.D. at UCSD in applied mathematics.

Brandon Hauser

Brandon Hauser worked on the nonlinear Schrodinger equation with a delta potential and proved a new result. He intends to earn a Ph.D. in economics.

Eoghan O'Keefe

Eoghan O'keefe worked on the nonlinear Schrodinger equation using numerical techniques. He is now pursuing a Ph.D. in applied mathematics at Tufts.

Lily Wang

Lily Wang worked on optimizing the use of call and put options in a portfolio. She is now at Harvard earning a graduate degree in data science.

Charlie Yu

Charlie Yu worked on a summer project which turned into a paper studying the nonlinear Schrodinger equation. He is currently a graduate student at Wake Forest University.

Scott Crowley

Scott Crowley worked on pricing exotic options using numerical techniques and PDEs. He now works as an analyst at Jane Street Capital. Here is his thesis.

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