Ya-Lun
Tsai ½²¨ÈÛ 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

**Submitted papers:**

l Studying
some symmetrical classes of Dziobek configurations and their bifurcation
surface

**Published papers: **

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. 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