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Some Mathematical Problems in Quantum Communication and Perfect Codes in Circulant Graphs

  date:2017-7-17  hits:58


School of Mathematical SciencesJuly 15, 2017 at 3:30p.m. A series of reports of some mathematical problems in quantum communication and perfect codes in circulant graphs were successfully held in the school of mathematical sciences H306. The report invited the professor Keqin Feng from the department of mathematics at Tsinghua university and professor Rongquan Feng from the school of mathematical sciences at Peking University. Our dean Yizheng Fan, vice president of the professor Xiangfeng Pan, the associate professor Huazhang Wu, the associate professor Minjia Shi, the associate professor of Yanhong Bao, Dr. Bo Wu, the postdoctoral Lin Sok, as well as a number of young teachers and, graduate students attended the series reports.

                              

Our dean Yizheng Fan chaired this report and introduced two well-known professors in detail.  

                                            

First, the professor Keqin Feng made a report titledLinear algebra in quantum communication. He introduced some mathematical problems in quantum communication and the relationship between spherical t-design and number theory in detail. He specifically emphasized two linear algebraic problems in quantum communication (MUB and SIC-POVM), MUB and SIC-POVM have important applications in quantum communication. For example, quantum measurement, quantum cryptography, etc., in fact, they belong to a special kind of spherical 2-design. In the end, the concept of Optimal Codebooks is introduced, and the Optimal codes constructed are obtained by the difference of the group. He also introduced more research value in some mathematical problems in quantum communication in the future, enrich the research of quantum communication in the field of mathematics, to provided a wider research direction for the vast number of teachers and students.

                               

 

      Finallythe professor Rongquan Feng made a report titledPerfect Codes in Circulant Graphs. He first introduced the history of the perfect codes, the background of the study, the Hamming bound and the binary Golay code. Then, the perfect codes and the dominating set in the graph are introduced in detail, as well as the application of the dominating set and the definition of the total perfect codes. He emphasized the Cayley graph, and the ciculant graph of the special situation in Cayley graph, with particular emphasized on the main conclusions of the ciculant graph. In particular, he give the main results of the perfect codes in ciculant graphs of degree 3 and 4 and the main conclusion is proved by using the cyclotomic polynomials. At last, he introduced the relevant tools and references.

Introduction of reporterKeqin Feng, born in 1941 in Ninghe, Tianjin. He is now a professor department of mathematics at Tsinghua universit. His supervisor is Mr.  Luogeng Hua, a famous mathematician in our coutry. He has published over 80 academic papers and more than 10 books and textbooks, and undertaken the national natural science fund's key mathematics project. He participated in international conferences and visits abroad. Mainly engaged in combinatorics, number theory and algebra in coding theory and information security application.

Rongquan Feng, he is a professor and doctoral tutor of the school of mathematics sciences of Peking University, a member of the mathematics curriculum teaching steering committee of the university of education and a secretary of the mathematics discipline evaluation group of the state council. Now he is the secretary-general of the Beijing mathematics society, the director of the Chinese cipher society, the cipher mathematics professional committee of the Chinese cipher society and the member of the academic working committee, and the director of the Chinese association of mathematics and graph theory. In 1994, he received doctor's degree in institute of systematic sciences, Chinese academy of sciences.The main research direction is cryptography and information security and algebraic combination theory. He published more than 90 papers in core journals or conferences at home and abroad.

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