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 paper:**

Bifurcation of point vortex equilibria: four-vortex translating
configurations and five-vortex stationary configurations

**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, Journal
of Mathematical Physics **53**, 072902 (2012)

2. Counting
central configurations at the bifurcation points. Acta Applicandae Mathematicae, **144**, 99¡V120 (2016)

3. Some
enumeration problems on central configurations at the bifurcation points. Acta Applicandae Mathematicae, **155**, 99¡V112 (2018)

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, Nonlinearity, **24**, 3299¡V3321** **(2011)

2. Maxwell's
conjecture on three point charges with equal magnitudes. Physica D, **309,** 86¡V98, (2015)

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:** **Some Special Cases,
Journal of Nonlinear Science, **27**, 775¡V815, (2017).

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

Estimating
the number of tetrahedra determined by volume, circumradius and four face areas
using Groebner basis,
Journal of Symbolic
computation, **77**, 162-174,
(2016)