M@TH Hub Workshop: Overcoming the Computational Complexity of Large Dynamical Systems with Parallel Computations:
Organizers: Emmanuel Fleurantin (UNC-CH, GMU), Jorge L. Gonzalez (GT), Jason Mireles-James (FAU), Wai-Ting Lam (YU), Molei Tao (GT)
Scientific Committee:
Andrey Shilnikov (GSU), Flavio Fenton (GT), Hannah Choi (GT), Gemma Huguet (UPC),
Christopher K.R.T. Jones (UNC-CH), Evelyn Sander (GMU), Thomas Wanner (GMU), Thomas Redd (NCAT), Maciej Capinski (AGH).
Prerequisites: Successful completion of one
course in Linear Algebra and ODE, and basic programming skills (experience with Python, Matlab, Julia, Fortran, or C/C++ would be sufficient), completion of introduction to computational Mathematics course preferred.
Timeline for the event - length of the event and when: The program (workshop) will tentatively run from September to December.
At the end of the workshop a small student conference will hosted by Georgia Tech.
The program consists of several discussion groups that will collaborate closely to understand complex
dynamics while working on different applications.
The program will not be comparable to a coding camp; however, the participants are expected to learn to
develop their own software. The participants will begin the workshop by enrolling in an appropriate
Udemy course focusing on parallel computing in order to learn the basics. The course enrollment fee will
be fully paid by the program. In addition, the mentors will supervise the progress of the mentees and
assign computational exercises utilizing the tools mastered during the Udemy course, building up to the
main goal of the project. The workshop will also create a GitHub repository for the participants to share
their projects at the end of the program. The program offers incentives such as recommendations and a
certificate of completion of the program. At the end of the program, participants will have the
opportunity to present their progress at a small conference at Georgia Tech. Travel and accommodations
will be fully covered by the program. Other activities and discussions involving all the participants of
the program will take place virtually. These activities will consist of hands-on presentations,
discussions, etc. The intention is that the different groups of students interact periodically.
The participants will have the opportunity to engage in group presentations with the goal of polishing
their work.
Participation will require a modest but consistent time commitment. The weekly schedule will incorporate the following elements (in person or virtually):
- Weekly meetings with the group mentor (1 hour)
- Weekly lab work + independent reading (3 hours)
- Monthly group presentations + progress report (1 hour)
- Regular seminar (1 hour), OR
- Monthly invited speakers (1 hour):
Calendar
The projects will focus on the following themes:
Neuroscience : Large-scale simulation of neural networks in the presence of noise.
An exploratory study of invariants of large population of neurons using different models. We will explore questions such as: What is the relationship between network dynamics and network topology?
Climate Dynamics : Working on problems involving the Atlantic Meridional Overturning Circulation (AMOC), polar vortex, and atmospheric blocking.
Starting with conceptual models then evolving into large-scale simulations with rigorous computations of invariant sets whenever possible. Introduction to rate-induced tipping and the study of different possible regime transitions in low (or high dimensional) climate models.
Celestial Mechanics : Connecting orbits between invariant sets play a fundamental role in the design of low energy transfer missions in the solar system. The James Webb telescope’s halo orbit near L2 is a timely example. Students will learn to apply ideas from dynamical systems theory to problems in space mission planning.