Spectral Theory Of Differential Operators (STODO)
An undergraduate research program
Organizer: Wencai Liu
Description: I am running ongoing research projects (two semesters + summer sessions). I have some projects about (inverse) spectral problems of (discrete)differential operators at hand, which are suitable to high school and undergraduate students. Each project ranges from one semester to 1 year. It is expected to have graduate students and/or postdocs to work with me on projects.
Structure of each project: The project has two weekly meetings. In the first meeting (1-2 hours), we do lectures and student presentations. In the second meeting (1-2 hours), students study and work together on the project.
Acknowledgment: Currently, STODO is partially funded by a grant from College of Arts and Sciences Undergraduate Research Program
Announcement: The registration for this Fall (2023) is closed. We will recruit students to form a team to work on a project after finishing the current one. If you are interested in participating in a future project, please feel free to contact me.
Current project
Project 5
Inverse spectral problems with mixed data
Date: August 2023-present
Participated Students: Ethan Luo
Four Past Projects
I have run four projects about spectral problems of differential operators in 2022-2023.
Project 4
Floquet isospectrality for periodic Schrodinger operators
Assistants: Rodrigo Matos and Matthew Faust
Date: August 2022-present
Participated Students: Jenna Plute, Jonah Robinson (student leader), Yichen Tao, Ethan Tran, Cindy Zhuang
Outcome: A research paper, Floquet isospectrality of the zero potential for discrete periodic Schrodinger operators. arXiv version
Blocker 628, Dec 7, 2022
Jenna Plute, Yichen Tao, Ethan Tran and Cindy Zhuang gave slide and poster presentations in the 6th annual TX-LA undergraduate mathematics conference, LSU, March 25-26 2023. Below are some pictures.
Project 3
Embedded eigenvalues of perturbed Dirac operators
Assistant: Kang Lyu
Date: January 2022-July 2022
Participated high school and undergraduate students: Vishwam Khapre and Andrew Yu
Outcome: A research paper, Sharp bound for embedded eigenvalues of Dirac operators with decaying potentials. New York J. Math. 28 (2022) 1317–1328.
The following two projects are part of inverse spectral problem of discrete Schrodinger operators.
Project 2
Ambarzumian type problems with mixed data.
Assistant: Burak Hatinoglu
Date: April 2020-August 2020
Participated undergraduate students. Alejandra Puente, Sithija Manage, Jerik Eakins, Lucille Lamb, William Frendreiss
Outcome: A research paper, Ambarzumian-type problems for discrete Schrödinger operators. Complex Anal. Oper. Theory 15 (2021), no. 8, Paper No. 118, 13 pp. Arxiv version
Project 1
Ambarzumian type problems of long range operators.
Assistants: Burak Hatinoglu and Rodrigo Matos
Date: August 2020-April 2021
Weekly Tentative Schedule in Spring 2021 (including all notes)
Weekly Tentative Schedule in Fall 2020 (including all notes)
Participated undergraduate students: Alejandra Puente, Sithija Manage, Lucille Lamb, William Frendreiss