Rung-Tzung Huang (黃榮宗)
Department of Mathematics
National Central University
Chung-Li, Taiwan 32054
E-mail: rthuang AT math.ncu.edu.tw
Ph.D. 2007 under the supervision of Maxim Braverman at the Department of Mathematics of the Northeastern University
2007/7/1~2009/8/7 Research fellow, School of Mathematics, Korea Institute for Advanced Study(KIAS)
2009/8/10~2011/7/31 Postdoctor, Institute of Mathmatics, Academia Sinica
2011/8/1 ~ 2015/7/31 Assistant Professor, Department of Mathematics, National Central University
2015/8/1 ~ Associate Professor, Department of Mathematics, National Central University
2018 Fall: Calculus I
2018 Spring: Calculus II, Liner Algebra II
2017 Fall: Calculus I, Liner Algebra I
2017 Spring: CalculusII, Geometry I
2016 Fall: Calculus I, Algebraic Topology
2016 Spring: Calculus II
2015 Fall: Calculus I
2015 Spring: Geometry I, Calculus II
2014 Fall: Complex Variables I, Calculus I
2014 Spring: Differential Geometry II, Calculus II
2013 Fall: Differential Geometry I, Calculus I
2013 Spring: Linear Algebra II
2012 Fall: Linear Algebra I
2012 Spring: Calculus II
2011 Fall: Calculus I
Research Interests: Analysis on manifolds, Complex and CR geometry. In
particular, Analytic torsion, Eta invariant, Index theorem, Szego kernel
Publications and Preprints
1.(with Chin-Yu Hsiao) G-invariant Szegö kernel asymptotics and CR reduction, arXiv:1702.05021.
2.(with Chin-Yu Hsiao, Xiaoshan Li, Guokuan Shao) S^1-equivariant
index theorems and Morse inequalities on complex manifolds with
3.(with Guokuan Shao) Morse inequalities for Fourier components of
Kohn-Rossi cohomology of CR covering manifolds with S^1-action, arXiv:1809.06243
1.Refined Analytic Torsion: Comparison Theorems and Examples, Illinois
Journal of Mathematics, Vol. 51, No. 4, (2007), 1309-1327.
2.Cappell-Miller analytic torsion for manifolds with boundary,
Proceedings of the American Mathematical Society, Vol. 138, No. 10,
Oct. (2010), 3733-3747.
3.Twisted Cappell-Miller holomorphic and analytic torsions, Pacific
Journal of Mathematics, Vol. 251, No. 1, May. (2011), 81-107.
4.Refined analytic torsion for twisted de Rham complexes,
Communications in Analysis and Geometry, Vol. 19, No. 2, (2011),
5.(with Yoonweon Lee) The gluing formula of the refined analytic
torsion for an acyclic Hermitian connection, Manuscripta Mathematica,
Vol. 139, (2012), No. 1-2, 91-122.
6.(with Yoonweon Lee) The comparison of two constructions of the refined
analytic torsion on compact manifolds with boundary, Journal of Geometry and Physics, Vol. 76, Feb. (2014), 79-96.
Yoonweon Lee) The gluing formula of the zeta-determinants of Dirac
Laplacians for certain boundary conditions, Illinois
Journal of Mathematics, Vol. 58, No. 2, Summer (2014), 537-560.
8.(with Yoonweon Lee) Lefschetz fixed point formula on a compact
Riemannian manifold with boundary for some boundary conditions, Geometriae Dedicata, Vol. 181, Issue 1, April (2016), 43-59.
9.The anomaly formula of the analytic torsion on CR manifolds with S^1 action, Bull. Inst. Math. Acad. Sin. (N.S.) Vol. 12, (2017), No. 2, 153-203.
10.(with Chin-Yu Hsiao) The asymptotics of the analytic torsion on CR manifolds with S^1 action, arXiv:1605.07507. accepted by Communications in Contemporary Mathematics.
11.(with Yoonweon Lee) The refined analytic torsion and a well-posed
boundary condition for the odd signature operator, Journal of Geometry and Physics, Vol 126, Mar. (2018), 68-92.
(with Yoonweon Lee) Boundary problem for the refined analytic torsion on compact manifolds with boundary,
Proceedings of the 15th International Workshop on Differential Geometry
and the 4th KNUGRG-OCAMI Differential Geometry Workshop Vol. 15,
109–119, Natl. Inst. Math. Sci. (NIMS), Daejeon, 2011.