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: 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.
Recent Talks
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.
Speaker: Shuchao Li (Central China Normal University)
Room: College of Science M1001
Time: 2025/12/04, Thursday, 10:00 - 11:00
Tencent Meeting: 654 651 904
Turán-type problem is a fundamental problem in extremal graph theory. The spectral Turán-type problem is a newly developed one in this field. Both of these two types of extremal problems attract more and more researchers’ attention. In this talk, we first introduce the background in this field. Then we present our new results on (non-) color critical graphs along this line. Finally, we propose some further research issues in this field.
Speaker: Weicong Li (Great Bay University)
Room: College of Science M4009
Time: 2025/11/27, Thursday, 10:00 - 11:00
Tencent Meeting: 111 643 003
In this talk, I will present the complete classification of triply-transitive strongly regular graphs. This work concludes a program initiated by Herman, Maleki, and Razafimahatratra, who resolved most cases but left open the status of two infinite families from finite geometry. We prove that these remaining families are indeed triply-transitive, thereby settling the classificaition. This is joint work with Hanlin Zou.
