6 papers
A Computational Obstruction to Swapping Area and Dinv: An Automata-Theoretic View of the -Catalan Symmetry
Jineon Baek, Byung-Hak Hwang, Joonhyun La +1
Algebraic combinatorics often seeks bijections that explain identities between distributions object by object. Encoding combinatorial objects as words lets automata theory study su…
A review on the kinetic theory of oscillator chains
Pierre Germain, Joonhyun La, Angeliki Menegaki
We review the kinetic theory of one-dimensional nonlinear oscillator chains, of which the most famous example is the Fermi-Pasta-Ulam-Tsingou equation. We provide detailed, though…
Entropy maximizers for kinetic wave equations set on tori
Miguel Escobedo, Pierre Germain, Joonhyun La +1
We consider the kinetic wave equation, or phonon Boltzmann equation, set on the torus (physical system set on the lattice). We describe entropy maximizers for fixed mass and energy…
Stability of Rayleigh-Jeans equilibria in the kinetic FPU equation
Pierre Germain, Joonhyun La, Angeliki Menegaki
We study the nonlinear dynamics of the kinetic wave equation associated to the FPU problem and prove stability of the non-singular Rayleigh-Jeans equilibria. The lack of a spectral…
Local Well-posedness for the Kinetic MMT Model
Pierre Germain, Joonhyun La, Katherine Zhiyuan Zhang
The MMT equation was proposed by Majda, McLaughlin and Tabak as a model to study wave turbulence. We focus on the kinetic equation associated to this Hamiltonian system, which is b…
Graph 4-braid groups and Massey products
Ki Hyoung Ko, Joon Hyun La, Hyo Won Park
We first show that the braid group over a graph topologically containing no -shape subgraph has a presentation related only by commutators. Then using discrete Morse theory and…