-
23
2025/07
Оn maximal cliques in Paley graphs, generalised Paley graphs and Peisert graphs
In this talk wewill discuss maximal cliques in Paley graphs, generalized Paley graphs, andPeisert graphs. We will consider some constructions of maximal cliques andtheir geometric interpretation. We will also present some results oneigenfunctions in these graphs.
-
23
2025/07
Construction of divisible design graphs using affine designs
A $k$-regular graphwith $v$ vertices is a {\em divisible design graph with parameters}$(v,k,\lambda_1,\lambda_2,m,n)$ if its vertex set can be partitioned into $m$classes of size $n$ such that any two different vertices from the same classhave $\lambda_1$ common neighbours, and any two vertices from different classeshave $\lambda_2$ common neighbours.Divisible design graphs were introduced by H. Kharaghani and first provided byW.H. Haemers, H. Kharaghani and M. Meulenberg. In particular, the authors haveproposed several constructions of divisible design graphs using variouscombinatorial structures. Some new combinatorial constructions of divisibledesign graphs were later provided by many authors.In this talk, we present twoprolific constructions that produce infinite series of divisible design graphs.Using affine designs for these constructions develops ideas of W.D. Wallis,D.G. Fon-Der-Flaass, and M. Muzychuk.
-
23
2025/07
Complete mappings and orthogonal orthomorphisms of groups
A complete mappingof a finite group $G$ is a permutation $\phi: G\rightarrow G$ such that$x\mapsto x\phi(x)$ is also a permutation. A permutation $\theta:G\rightarrowG$ of a finite group $G$ is an orthomorphism of $G$ if the mapping $x\mapstox^{-1}\theta(x)$ is also a permutation. Two orthomorphisms $\theta$ and $\phi$of $G$ are orthogonal if the mapping $x\mapsto \theta(x)^{-1}\phi(x)$ isbijective. This talk provides a brief introduction to the existence of completemappings and orthogonal orthomorphisms of groups, focusing on their algebraicand extremal aspects. Difference matrices have a close relationship with orthogonalorthomorphisms of groups. It will also give a survey on difference matrices andtheir related topics, such as orthogonal arrays and mutually orthogonal Latinsquares.
-
23
2025/07
The Search for Rainbow 3-term arithmetic progressions: An Inspirational Journey
In this talk, wediscuss the existence of rainbow 3-term arithmetic progressions within3-colorings of various ground sets, including finite intervals, cyclic groups,and general abelian groups. This foundational question -how rainbow structuresemerge under specific density conditions on color classes- has inspired awealth of insights, problems, and generalizations within Rainbow Ramsey Theory.
-
18
2025/07
“丝绸之路”沿线国家农业科教合作概况及展望
“丝绸之路”沿线国家农业科教合作概况及展望
-
18
2025/07
LAZYs基因调控水稻分蘖角度的分子机制
LAZYs基因调控水稻分蘖角度的分子机制
-
15
2025/07
Codes, groups and designs
Theadjacency code of a rank three group contains PBIBDs by construction. When weare lucky we obtain a BIBD also known as 2-design. This is the casefor instance of the one point stabilizer of PSL(2,41) in its action onthe binary QR(41). When we are even luckyer we obtain a 3-design inthe extended code. This is the case of the XQR(41) in length 42. Byconsidering known families of rank 3 groups we obtain in that way 111 2-designand nine 3-designs. The supporting codes are constructed by modularrepresentation theory. ( joint works with Bonnecaze and with Rodrigues). Anothergroup action method applies to isodual ternary codes the automorphism group ofwhich admits two orbits on triples (joint work with Shi and Liu.) Interestingexamples are provided by Generalized Quadratic Residue codes, a family ofabelian codes discussed by van Lint and MacWilliams. Since none of thediscussed designs can be explained by the Assmus-Mattson theorem ortransitivity arguments, all of this work is based on computer calculationsin Magma. Recently a theoretical explanation of the designs in the weight10 codewords of the XQR(41) was provided by Munemasa based on harmonic weightenumerators.
-
15
2025/07
Banach Spaces with the Ball Covering Property
A Banach space is said to have the ball coveringproperty if its unit sphere can be covered by countably many open balls off theorigin. The ball covering property is a property that has close relationshipswith the topological properties and geometric properties of Banach spaces. Inthis talk, we will give a review of the historical literature and present somerecent advances on this topic. Open problems will be proposed, and approacheswill be discussed.
-
14
2025/07
Projected Sobolev gradient flows and its application to compute ground state of ultracold dipolar fermi gas
We first provide an overview of gradient flow for minimization problem. Then we note that the ground state for the ultracold fermi gas with dipole-dipole interaction is a functional minimization problem based on density functional theory (DFT). We extend the recent work on Sobolev gradient flow for the Gross-Pitaevskii eigenvalue problem, and present continuous projected Sobolev gradient flows for computing the DFT-based ground state solution of ultracold dipolar fermi gas. We prove that the gradient flows have the properties of orthonormal preserving and energy diminishing, which is desirable for the computation of the ground state solution. Many numerical technique for partial differential equation can be used to discretize the time-dependant projected Sobolev gradient flows, which may be an advantage of the method. We propose an efficient and accurate numerical scheme – semi-implicit Euler method in time and Fourier spectral method in space for discretizing these projected Sobolev gradient flows and use them to find the ground states of the fermi gas numerically. Extensive numerical examples in three dimensions for ground states are reported to demonstrate the power of the numerical methods and to discuss the physics of dipolar fermi gas at very low temperature.
-
09
2025/07
氦离子显微镜的原理与应用
氦离子显微镜的原理与应用。包括发展历史与工作原理、应用方向、总结展望。
