Summer Research Opportunity @ QC
Professor Nicholas Vlamis will be running two separate undergraduate research projects during Summer 2024 for Queens College students. Each project will have two undergradautes. One of the projects will be in pure mathematics and the other in machine learning. Participants will be paid a stipend of $4400. The projects are funded by NSF Award DMS-2212922. Please see below for more details for individual projects.
If you have any questions, please feel free to contact me at nicholas.vlamis@qc.cuny.edu.
Pure Mathematics
Project Summary: Students will spend a significant amount of time learning about group theory and topology, with the goal of being able to understand and successfully work on the problem below:
We will investigate homeomorphism groups of zero-dimensional spaces (or equivalently, automorphism groups of Boolean algebras). We will likely focus on two properties: (1) the boundedness of left-invariant metrics on these groups, and (2) the existence of dense conjugacy classes (we will view these groups as topological groups). This project is a bit of a mix of topology, group theory, and descriptive set theory.
Stipend: $4400
Number of students: 2
Time period and Duration: Summer 2024, 6-8 weeks, likely June–July, but exact dates and duration have some flexibility and will be decided on as a team. Depending on the schedule, students should expect to spend 25–40 hours per week on the project.
Prerequisites: Students will need to have completed at least one of Math 301 or Math 320 (or their equivalents, i.e. a course in group theory or topology) by the start of the project. Students should be ready to do some independent reading before the project in either group theory or topology.
Application: Apply here. You will need to login using your @login.cuny.edu account. Applicants must be US citizens, US nationals, or US permanent residents.
Application Deadline: Friday, March 1, 2024.
Machine Learning
Project Summary: Students will learn the basics of neural networks as well as some standard algorithms for turning documents into vectors. These things will be learned while working on the project described below:
The arXiv is a preprint repository for academic articles in several disciplines, including mathematics. When submitting a preprint, the user is asked to classify their article into one of the given fields and subfields represented on the arXiv. The arXiv recently released an API that will attempt to automatically determine this classification. The goal of the project will be to see if we can produce a model based on neural networks that beats their in-house classification.
Stipend: $4400
Number of students: 2
Time period and Duration: Summer 2024, 6-8 weeks, likely June–July, but exact dates and duration have some flexibility and will be decided on as a team. Depending on the schedule, students should expect to spend 25–40 hours per week on the project.
Prerequisites: Math 231 and CSCI 111 (or their equivalents, i.e., linear algebra and a course in programming). It is also recommended, but not required, that students have taken Math 201 and Math 241. Experience with Python will be helpful.
Application: Apply here. You will need to login using your @login.cuny.edu account. Applicants must be US citizens, US nationals, or US permanent residents.
Application Deadline: Friday, March 1, 2024.
Troubleshooting
Several students have had issues accessing the form. As a first step, please see the following pdf showing the steps a student took to successfully login: http://qc.edu/~nvlamis/login.pdf. If this does not work, try using a different browser or device.