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Abstract
Symmetry is widespread in the physical world. Lie groups and their representations are mathematical descriptions of symmetry. Typical Lie groups, including orthogonal groups, symplectic groups, unitary groups and quaternion groups are the most common Lie groups in mathematical and physical research. Finite-dimensional representation theory of typical Lie Group's was established and developed by the outstanding mathematician Weyl and others in the 20th century. Two of the outstanding achievements are classical invariant theory and classical bifurcation law. The infinite-dimensional representation theory of typical Lie groups originated from the study of quantum mechanics and has become an important tool for the study of number theory. We will introduce the basic theory of Lie group representation, and give examples to introduce the classical invariant theory, classical bifurcation law and their development to infinite dimension representation.
About the Speaker
Binyong Sun, professor of Academy of Mathematics and Systems Sciences, Chinese Academy of Sciences, received the bachelor's degree from Zhejiang University in 1999 and PhD from Hong Kong University of Science and Technology in 2004. He has made a series of important achievements in the study of Lie group representation theory. He has won the Chen Jiageng Youth Science Award (2014), China Outstanding Young Scientists and Talents Award (2016), the Chinese Academy of Sciences Young Scientist Award (2016), and the National Natural Science Award Second Prize (2018) and so on.