A global symmetry may be promoted to a gauge invariance by introducing local gauge transformations. On a non-simply connected space, there are topologically nontrivial gauge transformations which are called "large" gauge transformations. The invariance under such large gauge transformations (large gauge invariance) has surprisingly many applications in condensed matter physics such as quantum Hall effect, filling-enforced constraints, electric polarization, and general constraints on nonlinear conductivities. In this talk, I will review the background and some of the recent developments in the applications of the large gauge invariance.
Prof. Masaki Oshikawa is a theorist working in the fields of condensed matter physics and statistical physics. Prof. Oshikawa obtained his PhD from the University of Tokyo in 1995. After a short Research Associateship in the University of Tokyo and a Killam Postdoctoral Fellowship in the University of British Columbia, he joined the Tokyo Institute of Technology as an Associate Professor in 1998. In 2006, Prof. Oshikawa moved to University of Tokyo and was promoted to full Professorship, and has been there since then. He is also affiliated with the Kavli Institute for the Physics and Mathematics of the Universe as a senior scientist.
Prof. Oshikawa is well known for his highly original and fundamental work in topology, dynamics, and order in quantum many body systems and is recognized by numerous awards. He received the 7th Ryogo Kubo Memorial Award from the Inoue Foundation for Science, the SEST Award for Young Scientist from the Society of Electron Spin Science and Technology of Japan, the JSPS Prize from the Japanese Society for the Promotion of Science, and elected Fellow by the American Physical Society.

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