Organizers
The SUSTech Discrete Mathematics Seminar is organized by Ferdinand Ihringer, Caiheng Li, Qing Xiang, and Ziqing Xiang.
You can contact us under discretemath@sustech.edu.cn.
Talks
Speaker: Elizaveta Iarovikova (Moscow Institute of Physics and Technology)
Room: College of Science M1001
Time: 2026/09/10, Thursday, 10:00 - 11:00
Tencent Meeting: 175 945 501
We consider intersecting families of $k$-dimensional subspaces of $\mathbb{F}_q^{n}$. It is known that for n>2k the largest families with these properties are point-pencils, i.e. families of all subspaces that contain a fixed line. For n = 2k any extremal example is either a point-pencil, or its dual.
We are interested in a Hilton—Milner type of problem: what are the size and structure of largest families that are not contained in a point-pencil or its dual? This problem was previously solved for n > 2k+1. During the talk we will solve it for n=2k and sufficiently large q, using the spread approximation technique and association schemes.
Speaker: Yuval Filmus (Technion - Israel Institute of Technology)
Room: College of Science M1001
Time: 2026/09/17, Thursday, 10:00 - 11:00
Tencent Meeting: 864 241 067
If a Boolean function $f\colon {0,1}^n \to {0,1}$ satisfies $f(x \oplus y) = f(x) \oplus f(y)$ w.p. $1–\epsilon$, then it is close to a function satisfying this condition for all $x,y$, a classical result in theoretical computer science known as “linearity testing”.
We prove a general theorem which includes as special cases linearity testing and other related results such as AND testing, Kalai’s quantitative Arrow’s theorem, and Friedgut and Regev’s result on almost intersecting families.
Joint work with Yaroslav Alekseev appearing in FOCS 2026 (under the title “Approximate Polymorphisms”).
Speaker: Yuefang Sun (Ningbo University)
Room: College of Science M1001
Time: 2026/10/15, Thursday, 10:00 - 11:00
Tencent Meeting: 267 575 018
Packing combinatorial objects—such as graphs, digraphs, and hypergraphs—by smaller ones is one of the central problems in graph theory and combinatorial optimization. Among these, the Steiner tree packing problem stands out not only for its theoretical significance but also for its practical relevance, particularly in VLSI circuit design. Over the past decades, it has attracted much attention from researchers across graph theory, combinatorial optimization, and theoretical computer science, and has matured into a well-established area. In this talk, we survey known hardness and algorithmic results for the directed Steiner tree packing problem, along with several related topics. This presentation is based on joint work with Anders Yeo, Shanshan Yu, and Xiaoyan Zhang.
Recent Talks
Speaker: Wei Wang (Xi'an Jiaotong University)
Room: College of Science M1001
Time: 2026/06/11, Thursday, 10:00 - 11:00
Tencent Meeting: 430 886 351
A graph $G$ is said to be
determined by the generalized spectrum (DGS), if for any graph $H$, whenever
$H$ and $G$ are cospectral and their complements are also cospectral, then $H$
is isomorphic to $G$. Previously, we show a graph $G$ is DGS provided $2^{-\lfloor
n/2\rfloor}\det W(G)$ is odd and square-free, where $W(G)$ denotes the
walk-matrix of $G$. In this talk, we show that the oddness assumption can actually
be removed, thereby confirming a two-decades conjecture of the second author. Joint work with Quanyu Tang and Hao Zhang.
Speaker: Gary R. W. Greaves (Nanyang Technological University)
Room: College of Science M1001
Time: 2026/04/23, Thursday, 10:00 - 11:00
Tencent Meeting: 637 218 483
Certain biased card shuffles, which have been extensively studied in probability and combinatorics, can be modelled by a natural Markov chain on the symmetric group in which neighbouring elements are swapped according to prescribed probabilities. The spectral gap of the transition matrix determines how quickly the Markov chain converges to equilibrium.
In this talk, I will present a sharp lower bound on the spectral gap for abroad class of such Markov chains and explain how this resolves a longstanding conjecture of Fill. The key idea is to decompose the transition matrix into an average of elementary transition matrices that can be interpreted as orthogonal projections in a suitable inner-product space. Finally, I will discuss results on the multiplicity of the second-largest eigenvalue in the extremal case where the spectral gap is minimised.
Speaker: Shuxing Li (University of Delaware)
Room: College of Science M1001
Time: 2026/03/24, Tuesday, 11:00 - 12:00
Tencent Meeting: 689 341 002
In 1969, Denniston introduced a family of maximal arcs in Desarguesian
planes of even order, a construction that gave rise to a classical family of
partial difference sets with deep connections to finite geometry. These partial
difference sets, later named after him, are defined within the additive group of
a finite field of characteristic 2.
This naturally raises the question: Do Denniston partial difference sets
exist in fields of odd characteristic? For over five decades, no progress was
made on this problem—until recent breakthroughs by multiple research groups
established the construction of Denniston partial difference sets in elementary
abelian groups.
Building on this momentum, we extend Denniston partial difference sets to
a significantly broader class of elementary abelian groups. Our construction
employs character theory and relies critically on meticulous manipulation of
Gauss sums over finite fields.
This is joint work with James Davis (University of Richmond), Sophie
Huczynska (University of St Andrews), Laura Johnson (University of Bristol),
and John Polhill (Commonwealth University of Pennsylvania).
Speaker: Hong Liu (Institute for Basic Science, Daejeon, Korea)
Room: College of Science M1001
Time: 2026/03/24, Tuesday, 10:00 - 11:00
Tencent Meeting: 689 341 002
Enumeration problems occupy a central place in Extremal Combinatorics. In this talk, I will survey classical results of this sort and go over some recent developments. In particular, I will discuss the problem of estimating the number of maximal sum-free sets in both integers {1,..,n} and finite abelian groups. Here, a set is called sum-free if it does not contain any solution to the equation x+y=z.
Speaker: Yue Yang (National University of Singapore)
Room: College of Science M1001
Time: 2025/12/11, Thursday, 10:00 - 11:00
Tencent Meeting: 116 415 990
Halpern-Läuchli Theorem (HL) is one instance of Ram-seyan theorems, with deep connections to mathematical logic. In this talk, I will report some recent results related to HL, jointly obtained with Chitat Chong and Wei Li from National University of Singapore. I will also spend some time introducing Reverse Mathematics to the general audience, including some history, main motivation and basic terminologies.
