Previous Undergraduate Research Projects 

Name: Sydney Kohn
Class: Undergraduate, Honors College  

 

  • Faculty: Brooke Max, Lecturer, Deparment of Mathematics
  • Project: Fall 2020 semester, began working with the research process and created coding for the project that investigates the intersection of geometry and children's thinking in mathematics textbooks designed for future elementary school teachers. This project will hopefully lead to a presentation or published paper.

 

Name: Zijie (Jerry) Zhou
Class: Senior; Mathematics Honor major  


  • Project: RIPS REU
  • Jun 2019 to Aug 2019
  • Institute for Pure and Applied Mathematics(IPAM) at UCLA
  • Online Learning and Matching for Resource Allocation Problems
  • We presented at the end of the REU program and at JMM conference. Also, we submitted the paper to the journal SIAM Undergraduate Research Online (SIURO) and was accepted January 2021.
  • Arxiv link: https://arxiv.org/abs/1911.07409

  • Project: Polymath REU
  • Jun 2020 to Aug 2020
  • University of Michigan-Dearborn
  • Director:Professor Yunus Zeytuncu 
  • Weak-time (1,1) Estimates for Riesz Transforms
  • Due to the pandemic, this REU is online. We presented at the end of the REU program and I applied to present on Undergraduate Mathematics Symposium at University of Illinois at Chicago this November. We are currently writing the paper. Polymath Presentation

 

Name: Juliet Aygun
Class: Undergraduated Mathematics major  

  • Project: REU
  • Summer 2020
  • University of California, Santa Barbara
  • Conducted research concerning the Riemannian and symplectic geometry on almost Abelian Lie Groups. presented at three virtual conferences, namely SURMC at Stanford University, Young Mathematicians Conference at the Ohio State University, and the Southern California Math REU Conference at Occidental College. The paper is expected to be published in 2021.

 

 

Name: Victor Hughes
Class: Junior, Mathematics and Applied Mathematics major (Graduated in 2020).


More Research Projects 

 REU Projects under Professor Jonathon Peterson:

Mike Cinkoske (Purdue), Joe Jackson (Swarthmore College), Claire Plunkett (Case Western Reserve)

    • 8 week REU at Purdue University in the summer of 2017. Part of an NSF funded REU grant: Purdue Research in Mathematics Experience (PRiME)
    • "On the speed of an excited asymmetric random walk"
    • Presented at 2017 Indiana Undergraduate Math Research Conference, 2017 Mathfest, and 2018 Joint Mathematics Meetings
    • Published in Rose Hulman Undergraduate Mathematics Journal. https://scholar.rose-hulman.edu/rhumj/vol19/iss1/6/
    • Poster presentation.pdf

Jacob Menix (Western Kentucky), Paige Schoonover (Tennessee)

    • 8 week REU at Purdue University in the summer of 2017. Part of an NSF funded REU grant: Purdue Research in Mathematics Experience (PRiME)
    • "Statistical tests for convergence of some random walks to perturbed Brownian motion"
    • Presented at 2017 Indiana Undergraduate Math Research Conference and 2017 Mathfest.
    • Poster presentation.pdf

 

REU Projects under Professor Birgit Kaufmann:

  • Name: Justin Copenhaver and Raunaq Kumaran
  • DURI project about quantum computing in quantum chemistry
  • Jan 20--Sep 20
  • Funded by a DURI grant and Kaufmann’s CAREER grant. 
  • Publication: J.Copenhaver, A.Wasserman and B. Wehefritz-Kaufmann,  Using quantum annealers to calculate ground state properties of molecules, J. Chem. Phys. 154 (2021) 034105
  • Name: Kyler Overton
  • Class: Undergraduate Student and Ascarelli Fellow
  • Project: Worked on graph Hamiltonians as an REU
  • Jan 19--May 19
  • Name: Tibor D’ome
  • Class: Undergraduate visiting from ETH Zurich
  • Project: Wrote term paper "The Periodic Zero-Field Six-Vertex-Model"
  • Jan 18--Apr 18
  • Name: Brant Coburn
  • Class: Undergraduate
  • Project: Worked on Hecke algebras and quantum spin chains as an REU; presented a poster at the Purdue Undergraduate Poster Symposium
  • Aug 14--May 15
  • Name: Nolan Teasdale
  • Class: Undergraduate REU student
  • Project: Worked on Monte{Carlo simulations of reaction-difussion models
  • Jan 10--May 10

 

Name: Tong Ding
Faculty: Professor Jingwei Hu  

  • Project: Particle method for the Landau equation
  • This project was presented by the student at the 2019 Purdue Undergraduate Research Conference.
  • Summer 2018 to Spring 2019

 

Name: Logan J. Cross
Faculty: Professor Xiangxiong Zhang  

  • Project: On the monotonicity of high order discrete Laplacian.  A very challenging project, resulted in a high-quality paper, currently under review in a top numerical analysis journal.
  • Publication: https://arxiv.org/abs/2010.07282
  • 2019-2020

 

Name: Fernando Davis, Grant Bowman, Truman Bennet
Faculty: Professor Greg Buzzard  

  • Project: Hyperparameter optimization for Deep Learning
  • Support:  NSF CCF-1763896, Purdue SURF Program
  • June-August 2019

 

Name: Trevor Crupi
Faculty: Professor Greg Buzzard  

  • Project: Foundations of Deep Learning
  • January-May 2020

 

Name: Yuzhang Wu
Faculty: Distinguished Professor Laszlo Lempert  

  • Project: Hyperbolic geometry in the Poincare model, that is, in the unit disc in the complex plane, where the motions are the Moebius maps of the disc. The purpose was to rediscover what had already been discovered, and accordingly no publication resulted.
  • September 2019- December 2019
  •  

Working with Professor Jim McClure, sophomore Alec McGail read David Bressoud’s book, A Radical Introduction to Real Analysis. Alec also worked on a project to reconstruct all of the standard properties of sin and cos by using only facts about their power series. Since Alec had a special interest in philosophy, Professor McClure asked him to write a philosophical reflection on whether the sin and cos he creates this way are “the same” as the ones he knew in high school.

In independent discussions with Professor Uli Walther, senior Kathryn Marsh investigated various topics in mathematics, touching on subjects in group theory, topology, knot theory, and prime numbers. Weekly meetings supplemented and guided individual reading. Between students, communication was in the form of editing a class Rhea page on topics they were individually researching.

In a project with Professor Jon Peterson, junior Lirong Yuan and senior Jingdan Liu focused on studying the probabilistic properties of eigenvalues of random matrices and roots of random polynomials. While the statements of the problems they were interested in were very basic, the research brought up a variety of topics not often encountered by undergraduates: Rouche’s theorem, Cardano’s formula, weak convergence of probability distributions, and the change of variables formula for n-dimensional integrals. In addition to learning some more advanced mathematics, Lirong and Jingdan were able to experience how research in mathematics works. In particular, they were able to see that hard problems are attacked by first solving smaller simplifications of the problem, and that sometimes one needs to try several different approaches to a problem before finding one that works. Lirong likened mathematical research to climbing a mountain:  when standing at the base of the mountain there are many possible routes to the top, but it might take several attempts to find the best route to the summit; moreover, the joy when reaching the summit makes all the previous failed attempts worthwhile.

Other summer math REUs were seniors Brett Ernst, Sean Fancher and junior Abi Komanduru, who worked with former Golomb Assistant Professors. Seniors Ronald Archer, Benito Martinez, junior Han Liu, and sophomore Steve Mussmann engaged in projects under the guidance of former Professor Edray Goins.