SIAM Student Chapter Seminar/Fall2019
- When: Every other Friday at 1:30 pm
- Where: B333 Van Vleck Hall
- Organizers: Xiao Shen
- Faculty advisers: Jean-Luc Thiffeault, Steve Wright
- To join the SIAM Chapter mailing list: email [email@example.com].
|Jan 31||Lorenzo Najt (Math)||Ensemble methods for measuring gerrymandering: Algorithmic problems and inferential challenges|
|Feb 14||Polly Yu (Math)||Algebra, Dynamics, and Chemistry with Delay Differential Equations|
|Feb 21||Gage Bonner (Physics)||Growth of history-dependent random sequences|
Jan 31, Lorenzo Najt (Math)
Ensemble methods for measuring gerrymandering: Algorithmic problems and inferential challenges
We will review some recent work regarding measuring gerrymandering by sampling from the space of maps, including two methods used in a recent amicus brief to the supreme court. This discussion will highlight some of the computational challenges of this approach, including some complexity-theory lower bounds and bottlenecks in Markov chains. We will examine the robustness of these statistical methods through their connection to phase transitions in the self-avoiding walk model, as well as their dependence on artifacts of discretization. This talk is largely based on https://arxiv.org/abs/1908.08881
Feb 14, Polly Yu (Math)
Algebra, Dynamics, and Chemistry with Delay Differential Equations
Delay differential equations (DDEs) can exhibit more complicated behavior than their ODE counterparts. What is stable in the ODE setting could exhibit oscillation in DDE. Where do delay equations show up anyway? In this talk, we’ll introduce DDEs, and how (sort-of-)linear algebra gives information about the stability of DDEs.
Feb 21, Gage Bonner (Physics)
Growth of history-dependent random sequences
Unlike discrete Markov chains, history-dependent random sequences are sequences of random variables whose "next" term depends on all others seen previously. For this reason, they can be difficult to analyze. I will discuss some simple and fun cases where the long-term behavior of the sequence can be computed explicitly in expectation.