UROP Research Mentor Project Submission Portal: Submission #571

Submission information
Submission Number: 571
Submission ID: 9126
Submission UUID: 4eb264cb-bd16-4228-b65b-cbdfe56730aa

Created: Thu, 08/24/2023 - 06:08 PM
Completed: Thu, 08/24/2023 - 06:08 PM
Changed: Mon, 08/28/2023 - 09:39 AM

Remote IP address: 217.180.196.52
Submitted by: Anonymous
Language: English

Is draft: No
Primary Research Mentor Name Alexander Reznikov
Research Mentor Preferred Pronouns
When potential research assistants are reaching out via email, what is your preferred honorific? None; just write "Hello Alexander"
Contact Email (FSU Email if affiliated) areznikov@fsu.edu
Position Title Faculty
FSU College (if applicable) Arts and Sciences
FSU Department or Non-FSU Organization Affiliation Mathematics
Headshot (optional)
Research Assistant Supervisor (if different from above)
Research Assistant Supervisor Preferred Pronouns
Research Assistant Supervisor Preferred Honorific?
Contact Email (FSU Email if affiliated)
Name of Other Faculty/Collaborator(s) (if applicable)
Other Faculty/Collaborator(s) Preferred Pronouns
Other Faculty/Collaborator(s) Preferred Honorific?
Contact Email (FSU Email if affiliated)
Title of the Project Gradient descent on the unit sphere
Project Keywords Calculus, potential energy, optimization, gradient descent
Are you currently looking for research assistants? Yes
Number of Research Assistants Needed 1
Relevant Research Assistant Major(s) Preferably mathematics or computer science, but open to all majors
Project Location: On FSU Main Campus
If the project location is off campus, does the research assistant(s) need to provide their own transportation?
Please select the choice that most accurately describes your expectations for the research assistant(s): Partially Remote
Approximately how many hours a week would the research assistant(s) need to work? 7
Roughly what time frame do you expect research assistant(s) to work? Flexible schedule (Combination of business and outside of business. TBD between student and research mentor.)
Overall Research Project Description Imagine putting four repelling particles on the sphere. They will move around the sphere until they reach the "ground state": a position where the combined potential energy has a local minimum. If we are not too unlucky, they will actually stop at the global minimum: i.e., the regular pyramid.
The goal of this project is to figure out what does it mean to be unlucky and experimentally show that this is a very rare situation.

This is done using "gradient descent", which is technically taught in Calculus 3 (MAC 2313). We throw four random points on the sphere and move it, one little step at a time, in the direction where the energy decreases (a.k.a., in the direction of the gradient).
Research Tasks Collect specific data of initial random configurations that are "good" (i.e., end up at the global minimum) and "bad".

If time allows, do the same in higher dimensions (this is not strongly expected).
Skills that research assistant(s) may need: Required: Calculus sequence, some coding skills.
Recommended: Having C++ or Python (preferably) installed, some confidence in coding.

We will discuss the approach, and you can learn the specific tools/packages along the way, but I would strongly prefer you to be able to open Python on your own.
Mentoring Philosophy Passing a course without applying it makes the course useless in the long term because things get forgotten. I view this project as an excellent opportunity to combine your Calculus knowledge and coding skills to solve a real-world problem. The mentee will not only get a taste of real research environment, but also some understanding of how to find practical applications of what seemed to be "pure theory".
Please provide a link to your publications, a video clip, or a website for your research project (if applicable): https://scholar.google.com/citations?user=x5-srkIAAAAJ&hl=en
Please add any additional information here (if applicable):
Mentor Handbook, FAQs, and Communication Yes
UROP Performance Evaluation Yes
Materials Grant Yes
UROP Poster Presentation Yes
Year 2023
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