Date: Jan. 9
Time: 2:30pm-4:30pm UTC
Speaker: Wenjun Yu (Ben-Gurion University of the Negev)
Title: Repair Schemes and Properties of Linear Codes
Abstract: There are two major factors that influence the speed of repairing a single failed node in distributed storage systems. The first is the number of blocks required to recover the failed
node, and the second is the proportion of sequential reads and writes, which can be quantified using the skip cost introduced by Yeow Meng Chee et al. They proposed repair schemes with zero skip cost for
Zigzag Codes and distributed storage systems based on certain $(3,4,v)$ designs. In this talk, we present repair schemes with zero skip cost for distributed storage systems based on $(t,k,v)$ covering designs.
Another topic addresses the relationship between the generalized cover radii (with applications to PIR) $R_t$ and the generalized Hamming weights of a linear code (related to security performance) $d_t$. Dor and Moshe
conjectured that $R_t \geq \floor{\frac{d_t-1}{2}}$ for all linear codes. We demonstrate that this conjecture holds for specific classes of linear codes.
Date: Mar. 6
Time: 9:30am-11:30am UTC
Speaker: Jinxin Zhou (Beijing Jiaotong University)
Location: Online (Tencent Meeting: 760-114-864)
Title: On the symmetry of token graphs
Abstract: Let G be a graph with n vertices. For 1< k < n, the k-token graph of G is a graph with vertices the k-subsets of V(G) such that two k-subsets are adjacent whenever their symmetric difference
is an edge of G. In this talk, we shall introduce some of our recent work on the symmetry of token graphs.
Date: Mar. 13
Time: 9:30am-11:30am UTC
Speaker: Hong Liu (Institute for Basic Science, Korea)
Location: Online (Tencent Meeting: 690-971-088)
Title: Chromatic, homomorphism and blowup thresholds
Abstract: I will talk about the classical chromatic/homomorphism thresholds problems which studies density conditions that guarantee an H-free graph to have bounded complexity.
I will survey some recent developments, including an unexpected connection to the theory of VC dimension and also discrete geometry, a novel asymmetric version that we introduce to interpolate
the two problems. If time permits, I will discuss two related problems, blowup and VC thresholds.
Date: Mar. 20
Time: 9:30am-11:30am UTC
Speaker: Yuejian Peng (Hunan University)
Location: Online (Tencent Meeting: 948-2462-3387)
Title: Chromatic profile of $C_{2k+1}$-free graphs
Abstract: Erd\H{o}s and Simonovits asked the following question: For an integer $r\geq 2$ and a family of non-bipartite graphs $\mathcal{H}$, what is the tight bound of $\alpha$ such
that any $\mathcal{H}$-free $n$-vertex graph with minimum degree at least $\alpha n$ has chromatic number at most $r$? We answer this question for $\mathcal{H}=\{C_{2k+1}\}$, $r\ge 2$ and $k\ge 3r+4$.
This is a joint work with Yan Zilong and Yuan Xiaoli.
Date: Apr. 3
Time: 9:30am-11:30am UTC
Speaker: Xujin Chen (Academy of Mathematics and Systems Science)
Location: Online (Tencent Meeting: 948-2462-3387)
Title:Network Topologies Immune to the Strong Braess Paradox
Abstract: The Strong Braess Paradox (SBP) describes a counterintuitive scenario where providing additional roadway options to some self-interested travelers can paradoxically increase their
travel times. SBP extends the classical Braess paradox by introducing stricter conditions, requiring that travel latency strictly increases for travelers who gain access to more road options.. In this talk,
we discuss the conditions under which SBP does not occur in networks with selfish routing behavior. In particular, we present a complete characterization of network topologies that are immune to a
particular case of SBP—the Informational Braess Paradox—thereby resolving an open question posed by Acemoglu et al. (2018).
Date: Apr. 10
Time: 9:30am-11:30am UTC
Speaker: Yongtang Shi (Nankai University)
Location: Online (Tencent Meeting: 948-2462-3387)
Title:Extremal results on the sum of degree powers of graphs
Abstract: Let $G$ be a simple graph with the degree sequence $(d_1, d_2, \ldots,d_n)$. Given a positive integer $p$, denote the \textit{degree power} of $G$ by $e_p(G)=\sum_{i=1}^nd_i^p$.
The degree power has extensive applications not only in the study of graph structures but also is closely related to graph spectra. In this talk, we show some extremal results on the sum of degree powers
of graphs.
Date: Apr. 24
Time: 9:00am-11:00am UTC
Speaker: Qing Xiang (Southern University of Science and Technology)
Location: Online (Tencent Meeting: 212-489-675)
Title:Linear Representations of Finite Geometries and Associated LDPC Codes
Abstract: 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.
Date: May 6
Time: 2:00pm-4:00pm UTC
Speaker: Ben Lund (Institute for Basic Science, Korea)
Location: Cybersecurity Innovation Building A-1236（网络安全创新大楼12楼A-1236）, Tencent Meeting: 529-195-633
Title: Embedding distance graphs into subsets of finite vector spaces
Abstract: Iosevich and Rudnev showed that every sufficiently large subset of a finite vector space determines every (algebraically defined) distance. I will talk about how to use their result,
in combination with techniques developed in the study of pseudorandom graphs, to embed large classes of nearly spanning graphs of distances in arbitrary subsets of finite vector spaces. I will mention
results from two recent papers, one joint with Debsoumya Chakraborti and the other with Chuandong Xu.
Date: May 15
Speaker: Yue Zhou (National University of Defense Technology)
Location: Online (Tencent Meeting: 948-2462-3387)
Title:New maximal additive d-codes on symmetric matrices over finite fields
Abstract: Let $q$ be an odd prime power and let $X(n, q)$ denote the set of symmetric matrices over $\mathbb{F}_q$. A subset $\mathcal{C}$ of $X(n,q)$ is called a \emph{$d$-code} if the rank
of $A-B$ is at least $d$ for any distinct $A$ and $B$ in $\mathcal{C}$. It has been proved by Schmidt that if $\mathcal{C}$ is additive, then
\[
|\mathcal{C}|\leq
\begin{cases}
q^{n(n-d+2)/2}, &2\mid n-d;\\\
q^{(n+1)(n-d+1)/2}, &2\nmid n-d.
\end{cases}
\]
Additive $d$-codes meeting the bounds above are called \emph{maximal}. When $d=n$, they are equivalent to commutative finite semifields which have been investigated for around 120 years, and many
constructions are known. When d\le n-1, there are very few known constructions of maximal additive $d$-codes in X(n,q)
In this talk, we present a new family of maximal additive $(n-2)$-codes for odd $q$ and $n=6,8$ and $10$.
Date: May 29
Speaker: Jian Wang (Taiyuan University of Technology)
Location: Online (Tencent Meeting: 948-2462-3387)
Title:On r-wise t-intersecting uniform families
Abstract: Let $\mathcal{F}$ be a family of $k$-subsets of an $n$-set. For integers $r\geq 2$, $t\geq 1$, $\mathcal{F}$ is called $r$-wise $t$-intersecting if any $r$ of its members have at least
$t$ elements in common. The most natural construction of such a family is the full $t$-star, consisting of all $k$-sets containing a fixed $t$-set. In the case $r=2$ the Exact Erd\H{o}s-Ko-Rado Theorem
shows that the full $t$-star is largest if $n\geq (t+1)(k-t+1)$. In this talk, we show that for $n\geq (2.5t)^{1/(r-1)}(k-t)+k$, the full $t$-star is largest in case of $r\geq 3$. Examples show that the
exponent $\frac{1}{r-1}$ is best possible. This represents a considerable improvement on a recent result of Balogh and Linz. Joint work with Peter Frankl.
Date: Jun. 3
Time: 2:30pm-4:30pm UTC
Speaker: Thang Pham (Vietnam National University Hanoi)
Location: Cybersecurity Innovation Building A-1236（网络安全创新大楼12楼A-1236）
Title:The Erdős and Falconer distance conjectures: connections and applications
Abstract: In this talk, I present recent results on the Erdős and Falconer distance conjectures, highlighting the interplay between these two problems. I also discuss applications to intersection
patterns, in particular addressing the prime‐field version of a question posed by Pertti Mattila. These results are based on joint work with Murphy, Petridis, Rudnev, and Steven (2022) and with Yoo (2023).
Date: Jun. 19
Speaker: Achill Schürmann (University of Rostock)
Location: Cybersecurity Innovation Building A-1236（网络安全创新大楼12楼A-1236）
Title:Computing Certificates for Complete Positivity
Abstract: A key problem in computer proofs based on solutions from copositive optimization, is checking whether or not a given
quadratic form is completely positive or not. In this talk we describe the first known algorithm for arbitrary rational input. It is based
on a suitable adaption of Voronoi's Algorithm and the underlying theory from positive definite to copositive quadratic forms. We observe
several similarities with the classical theory, but also some differences, in particular for three and more variables. A key element and
currently the main bottleneck in our algorithm is an adapted shortest vector computation, asking for all nonnegative integer vectors that
are short with respect to a given copositive quadratic form.
(based on joint work with Valentin Dannenberg, Alexander Oertel, Mathieu Dutour Sikirić and Frank Vallentin)