UROP Project
Gradient descent on the unit sphere
Calculus, potential energy, optimization, gradient descent
Research Mentor: None; just write "Hello Alexander" Alexander Reznikov,
Department, College, Affiliation: Mathematics, Arts and Sciences
Contact Email: areznikov@fsu.edu
Research Assistant Supervisor (if different from mentor):
Research Assistant Supervisor Email:
Faculty Collaborators:
Faculty Collaborators Email:
Department, College, Affiliation: Mathematics, Arts and Sciences
Contact Email: areznikov@fsu.edu
Research Assistant Supervisor (if different from mentor):
Research Assistant Supervisor Email:
Faculty Collaborators:
Faculty Collaborators Email:
Looking for Research Assistants: Yes
Number of Research Assistants: 1
Relevant Majors: Preferably mathematics or computer science, but open to all majors
Project Location: On FSU Main Campus
Research Assistant Transportation Required: Remote or In-person: Partially Remote
Approximate Weekly Hours: 7, Flexible schedule (Combination of business and outside of business. TBD between student and research mentor.)
Roundtable Times and Zoom Link: Not participating in the Roundtable
Number of Research Assistants: 1
Relevant Majors: Preferably mathematics or computer science, but open to all majors
Project Location: On FSU Main Campus
Research Assistant Transportation Required: Remote or In-person: Partially Remote
Approximate Weekly Hours: 7, Flexible schedule (Combination of business and outside of business. TBD between student and research mentor.)
Roundtable Times and Zoom Link: Not participating in the Roundtable
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.