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Transversally biharmonic maps between foliated Riemannian manifolds

Exponential wave maps

Biharmonic maps on V-manifolds

Spectral geometry of V-manifolds and its application to harmonic maps

Harmonic maps of V-manifolds

Harmonic maps between Riemannian manifolds were first established by James Eells and Joseph H. Sampson in 1964. Wave maps are harmonic maps on Minkowski spaces and have been studied since the 1990s. Yang-Mills fields, the critical points of Yang-Mills functionals of connections whose curvature tensors are harmonic, were explored by a few physicists in the 1950s, and biharmonic maps (generalizing harmonic maps) were introduced by Guoying Jiang in 1986. The book presents an overview of the important developments made in these fields since they first came up. Furthermore, it introduces biwave maps (generalizing wave maps) which were first studied by the author in 2009, and bi-Yang-Mills fields (generalizing Yang-Mills fields) first investigated by Toshiyuki Ichiyama, Jun-Ichi Inoguchi and Hajime Urakawa in 2008. Other topics discussed are exponential harmonic maps, exponential wave maps and exponential Yang-Mills fields.

Developments of Harmonic Maps, Wave Maps and Yang-Mills Fields into Biharmonic Maps, Biwave Maps and Bi-Yang-Mills Fields (Frontiers in Mathematics)

MATH 121 – Calculus I (3 credits)

MATH 224 – Multivariable Calculus (3 credits)

MATH 471, 472 – Real Analysis I, II (3 credits, 3 credits)

Yuan-Jen Chiang specializes in global analysis and analysis on manifolds, geometry, differential equations, topology and mathematical physics. She was a recipient of a Waple Professorship in 2016-2018. She published the research book "Developments of Harmonic Maps, Wave Maps and Yang-Mills Fields into Biharmonic Maps, Biwave Maps and Bi-Yang-Mills Fields'' in the series of Frontiers in Mathematics, by Birkhauser-Springer in Europe in 2013. Her research has been published in over 40 articles in peer-reviewed journals, including, including the International Journal of Mathematics, the Journal of Geometry and Physics, the Annals of Global Analysis and Geometry, the International Journal of Mathematics and Mathematical Sciences, Proceedings of American Mathematical Society, Bulletin of Math Institute, Academia Sinica, Notices of American Mathematical Society, and Journal of Geometry. She has presented at international meetings or universities in Brazil, USA, Chile, China, France, Spain, Italy, India, Poland, Greece, Bulgaria, Taiwan, and Vietnam.

Since 1991, Dr. Chiang has been a reviewer of Mathematical Review, published monthly by the American Mathematical Society, and has written reviews for more than 120 scholarly papers on differential geometry and global analysis. Her awards include 18 UMW Research Grants, two Natural Science Foundation Grants in China, and three Jepson grants for excellence in teaching.

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