UROP Research Mentor Project Submission Portal: Submission #571 | Center for Undergraduate Research and Academic Engagement

Submission information

Submission Number: 571

Submission ID: 9126

Submission UUID: 4eb264cb-bd16-4228-b65b-cbdfe56730aa

Submission URI: /urop-research-mentor-project-submission-portal

Submission Update: /urop-research-mentor-project-submission-portal?token=BBXZZrZzus0bQWAt-2B47asynY290iZkq81K8oxF_0g

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

Webform: UROP Project Proposal Portal

Submitted to: UROP Research Mentor Project Submission Portal

Research Mentor Information

Primary Research Mentor Name Alexander Reznikov

Research Mentor Preferred Pronouns {Empty}

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) {Empty}

Additional Research Mentor(s)

Research Assistant Supervisor (if different from above) {Empty}

Research Assistant Supervisor Preferred Pronouns {Empty}

Research Assistant Supervisor Preferred Honorific? {Empty}

Contact Email (FSU Email if affiliated) {Empty}

Name of Other Faculty/Collaborator(s) (if applicable) {Empty}

Other Faculty/Collaborator(s) Preferred Pronouns {Empty}

Other Faculty/Collaborator(s) Preferred Honorific? {Empty}

Contact Email (FSU Email if affiliated) {Empty}

Overall Project Details

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? {Empty}

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): {Empty}

UROP Program Elements

Mentor Handbook, FAQs, and Communication Yes

UROP Performance Evaluation Yes

Materials Grant Yes

UROP Poster Presentation Yes

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Year 2023

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