Theory of dynamical systems and its connections with number theory, geometry and representation theory.
My current research topic is studies of Nilflows. Nilflow is an example of parabolic dynamics which exhibits polynomial divergence of orbits.
The nilflows enjoys ergodicity (uniquely) under Diophantine condition on its projected flow on base torus. It is quite natural question to ask the speed (rate) of convergence in quantitative sense.
We adopt the method of Cohomological equations developed by L. Flaminio and G. Forni, which estimate the ergodic averages in distribution sense by renormalization.
Compared to horocycle flow, another example of Parabolic flow which admits renormalization, it fails on nilflow due to the absence of recurrence (except Heisenberg case.)
For this reason, we introduce techniques of rescaling the vector fields in the way of optimize to approximate the averages under the certain choice.
We also expect this result will be applicable to prove other properties on nilflows and can be generalized to other parabolic flows which do not admit renormalization.
About me
I am a Ph.D graduate student under supervision of Giovanni Forni.
[C.V (PDF)]
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
Publication
Preprint
- Effective equidistribution for generalized higher step nilflows.
Minsung Kim
Teaching (Recent)
- 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
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