Ya-Lun Tsai 蔡亞倫

Associate Professor

Department of Applied Mathematics

National Chung Hsing University

Room 614, Information Science Building,

145 Xingda Rd., South Dist., Taichung City 402,

Taiwan

 

Email: yltsai@nchu.edu.tw

http://web.nchu.edu.tw/~yltsai/

 

Education:

Ph.D. in Mathematics, April 2011, University of Minnesota.

Advisor: Richard Moeckel

Dissertation: Real root counting for parametric polynomial systems and Applications


Research experiences: 

l   Central configurations from the study of celestial mechanics are described as roots of a parametric polynomial system. Studying its zeros can help to solve the Newtonian N-body problems.

1.      Dziobek configurations of the restricted (N+1)-body problem with equal masses,

2.      Counting central configurations at the bifurcation points.

3.  Mathematica Notebook: Some enumeration problems on central configurations at the bifurcation points.

l   Given some point charges in the space, they generate an electrostatic field. The numbers of equivalent points of the electrostatic field is conjectured by Maxwell. This problem of Maxwell’s conjecture can also be reduced to solving a parametric polynomial system.

1.      Special cases of three point charges,

2.      Maxwell's conjecture on three point charges with equal magnitudes.

l   The n-vortex problem of fluid mechanics is the study of the dynamics of n point vortices moving in an inviscid and incompressible fluid. The notion of relative equilibria in the n-vortex problem is the same as that in the n -body problem. For such solutions, n point vortices rotate around the center of vorticity uniformly.

1. Numbers of relative equilibria in the planar four-vortex problems

l   A problem about the tetrahedron is to enumerate the numbers of tetrahedron given some metric invariants. This is a polynomial system problem.

1.   Estimating the number of tetrahedra determined by volume, circumradius and four face areas using Groebner basis