PROGRAM
11:00 (GMT+3)
| Alexander Guterman | Moscow State University |
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Bio: Alexander Guterman obtained his PhD from Lomonosov Moscow State University, Department of Mathematics and Mechanics, in 2001. In 2009 he defended the Doctoral Dissertation and in 2010 became a full professor at MSU. He mainly works in Linear Algebra and its Applications and in Ring Theory and has made several important contributions in that areas. He was distinguished by scientific prizes including the Gold Medal of European Academy and several other grants and awards for perspective scientists. Professor Guterman was a plenary speaker at many professional conferences and workshops. He is an author of more than 120 scientific papers in well reputed algebraic journals. |
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Values of permanent and positive solution of Wang-Krauter problem.
The talk is based on the joint work with M.V. Budrevich. The class of $(-1,1)$-matrices is very important in algebra and combinatorics and in various their applications. For example, well-known Hadamard matrices are of this type.
An important matrix function is the permanent. While the computation of the determinant can be done in a polynomial time, it is still an open question, if there are such algorithms to compute the permanent.
In this talk we discuss the permanents of $ \pm 1$-matrices. In 1974 Wang posed a problem to find a decent upper bound for the absolute value of the permanent of a square $\pm 1$-matrix of given rank. In 1985 Krauter conjectured some concrete upper bound. We prove the Krauter's conjecture and thus obtain the complete answer to the Wang's question. In particular, we characterized matrices with the maximal possible permanent for each value of the rank.
12:00 (GMT+3)
| Chuanming Zong | Tianjin University |
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Bio: Chuanming Zong obtained his PhD from Vienna University of Technology in 1993. He was a professor at the Chinese Academy of Sciences and Peking University. Currently, he is a distinguished professor at Tianjin University. He mainly works in number theory. He has made important contribution in Hilbert’s 18th problem and tiling theory. He has been awarded a Conant Prize by Amer Math Soc in 2015, a National Science Prize by the Chinese government in 2009, and a S. S. Chern Prize by the Chinese Math Soc in 2007. He was a plenary speaker at Asiacrypt2012, a author of two solicited papers in Bull AMS and three books at Springer and Cambridge University Press. |
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From Sphere Packings to Post-Quantum Cryptography
In 1611, Kepler made the following conjecture: In three dimensions, the density of the densest sphere packing is $\pi/\sqrt{18}$. Through the works of Newton, Gauss, Hilbert, Minkowski and others, sphere packings has been developed into an important mathematical discipline between number theory and geometry. In 1940s, the methods and results of sphere packings had been applied into information theory by Shannon, Hamming and others. Around 2000, lattice sphere packings surprisingly found applications in modern cryptography. In particular, Shor, Ajtai, Pipher and others applied it into post-quantum cryptography. In this talk, we will briefly introduce this dramatic development.
The meeting will be held in the form of a webinar on the Zoom platform.
Pre-registration for the event is not required.
To join Zoom meeting（You can join in the meeting without a phone number):
https://zoom.com.cn/j/64563211865?pwd=Njd2M3NzSFcvWmlONTlJOUd5bmRjdz09
Meeting ID : 645 6321 1865
Passcode：341825
Instructions for installing and using the Zoom platform are available here:
https://support.zoom.us/hc/ru/articles/201362033-Начало-работы-на-ПК-и-Mac