Department of Mathematics

National Central University

Chung-Li, Taiwan 32054

E-mail: rthuang AT math.ncu.edu.tw

Education:

Ph.D. 2007 under the supervision of Maxim Braverman at the Department of Mathematics of the Northeastern University

Experience:

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

Teaching

2019 Fall: Calculus I, Topology

2019 Spring: Calculus II

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

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 boundary, arXiv:1711.05537

Journal papers:

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), 401-449.

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.

7.(with 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 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.

11.(with Chin-Yu Hsiao) The asymptotics of the analytic torsion on CR manifolds with S^1 action, Communications in Contemporary Mathematics, Vol. 21, No. 4, (2019), 1750094, (35 pages).

12.(with Guokuan Shao) Morse inequalities for Fourier components of Kohn-Rossi cohomology of CR covering manifolds with S^1-action, arXiv:1809.06243, to appear in Pacific Journal of Mathematics.

Conference Proceedings:

(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.