Theory of dynamical systems and its connections with number theory, geometry and representation theory.
My current research topic is studies of Nilflow. Nilflow is an example of parabolic dynamics which exhibits polynomial divergence of orbits.
The flow enjoys ergodicity (uniquely) under assumption that Diophantine condition on its projected flow on base torus is irrational. It is quite natural question to ask the speed (rate) of convergence in quantitative sense, and it is requires Harmonic analysis and representation theory on nilmanifold.
According to the studies of Cohomological equations on nilflows developed by L. Flaminio and G. Forni, we estimate the ergodic average as a distribution on Sobolev space under certain rescaling its the size of vector fields.
Compared to horocycle flow, another example of Parabolic flow which admits Renormalization technique, it fails on Nilflow due to the absence of recurrence (except Heisenberg case.)
For this reason, we expect to find nice way of rescaling the unitary operator to optimize the speed under choice of scaling factors.
We expect this result will be applicable to prove statistical properties on nilflows and be generalized to other parabolic flows which do not admit renormalization flow such as ASL(2,R).
I am a Ph.D graduate student under supervision of Giovanni Forni.
Education and Experience
Visiting student, Institut de Mathematiques de Jussieu - Paris Rive Gauche (IMJ-PRG), University Paris Diderot, 2017-18, Spring 19
M.S in Mathematics, North Carolina State University, 2013
B.S in Mathematics Education, Pusan National University, 2011
Exchange student, Mathematics, University of Hawaii at Hilo, 2009-10
- Effective equidistribution for generalized higher step nilflows.
- Calculus III (MATH 241), UMD, Fall 2018
- Calculus for Life Sciences II (MATH 131), UMD, Spring 2017
- Differential Equations for Scientists and Engineers (MATH 246), UMD, Spring 2016
안녕! Hello! Aloha! ¡Hola! Ciao! 你好! Bonjour! ආයුබෝවන්! வணக்கம்! السلام عليكم! Здравствуйте!