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: 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

TBA

Hardness and Algorithms for Packing Steiner Trees in Digraphs

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

A Square-freeness Condition for Graphs Determined by Their Generalized Spectra

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.

Card Shuffling with Adjacent Swaps and Fill's Gap Problem

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.

Partial Difference Sets: Broadening the Scope of the Denniston Family

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).

Counting sum-free sets

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.

Halpern-Läuchli theorem and Reverse Mathematics

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.