Speaker: Xiang Qing, Professor, Southern University of Science and Technology
Reporting time: 9:00-9:30 am on December 5th
Report location: Tencent Conference ID 964 425 618
Title：Linear Representations of Finite Geometries and Associated LDPC Codes
Summary：The linear representation of a subset of a finite projective space is an
incidence structure of affine points and lines determined by the subset. In this talk we use character theory to show that the rank of the incidence matrix has a direct geometric interpretation in terms of certain hyperplanes. We consider the LDPC codes defined by taking the incidence matrix and its transpose as parity-check matrices, and in the former case prove a conjecture of Vandendriessche that the code is generated by words of minimum weight called plane words. In the latter case we compute the minimum weight in
some cases and provide a few constructions of codewords.
Speaker: Ge Gennian, Professor, Capital Normal University
Reporting time: 9:30-10:00 am on December 5th
Report location: Tencent Conference ID 964 425 618
Title：Sparse Hypergraphs: from Theory to Applications
Summary：
Speaker: Zhang Jian, Professor, University of Electronic Science and Technology of China
Reporting time: 10:00-10:30 am, December 5th
Report location: Tencent Conference ID 964 425 618
Title：Variational Correlation Between Nonlinear Schrodinger Equations with Differential Potentials
Summary：This talk is concerned with several types of nonlinear Schrodinger equations with differential potentials. We first discuss the variational characteristics for the time-independent Schrodinger equations. Then we establish the sharp conditions and sufficient conditions for global existence of the Cauchy problems. Especially, we find the comparison relations between the different ground states. We also obtain the sharp conditions for global existence of two types of Gross-Pitaevskii equations in terms of the related ground states.
Speaker: Mu Chunlai, Professor of Chongqing University
Reporting time: 10:30-11:00 am on December 5th
Report location: Tencent Conference ID 964 425 618
Report topic: Global boundedness of the solution of a quasi-linear chemotaxis model with flow restriction
Abstract: Considering the initial-boundary value problem of a class of chemotaxis models with flow restrictions, by establishing a new prior estimate, under the condition of $p>q\geq1$, it is proved that the only classical solution of the model is the existence and Regarding time is uniformly bounded, it solves what Mizukami et al. proposed in (J. Differential Equations 267(2019) 5115-5164, Acta. Appl. Math. doi.org/10.1007/s10440-019-00275-z) Open issues.
Speaker: Cai Han, Postdoctoral Fellow, Ben Gurion University of the Negev
Reporting time: 11:00-11:30 am, December 5th
Report location: Tencent Conference ID 964 425 618
Title：On Optimal Locally Repairable Codes with Super-Linear Length
Summary：In this talk, on one hand, new upper bounds on the length of optimal locally repairable codes are derived. The new bounds both improve and generalize previously known bounds. On the other hand, our focus is to construct optimal codes, whose length is order-optimal with respect to the new upper bounds. Optimal codes are constructed, whose length is order-optimal with respect to the new upper bounds. Notably, the length of the codes is super-linear in the alphabet size.
