Date/Time : 05 Nov 2025 15:00
Venue : S17 #06-11 (Seminar Room 6)
Speaker : Ander Lamaison, Institute for Basic Science, South Korea

We study Turán problems for hypergraphs with an additional uniformity condition on the edge distribution. This kind of Turán problems was introduced by Erdős and Sós in the 1980s but it took more than 30 years until the first non-trivial exact results were obtained. Central to the study of the uniform Turán density of hypergraphs are palette constructions, which were implicitly introduced by Rödl in the 1980s. We prove that palette constructions always yield tight lower bounds, unconditionally confirming present empirical evidence. This results in new and simpler approaches to determining uniform turán densities, which completely bypass the use of the hypergraph regularity method.

Add to calendar :

Date/Time : 17 Oct 2025 16:00
Venue : S17 #04-04 (Seminar Room 3)
Speaker : Yibo Gao, BICMR, Peking University

A partially ordered set is called Sperner if the size of its largest antichain does not exceed the size of its largest rank. In this talk, we show that the weak Bruhat order of the symmetric group is strongly Sperner via sl2 representations, resolving an old conjecture by Björner. We will also discuss its relations with Schubert polynomials, which are polynomial representations of the Schubert classes in the cohomology ring of the flag variety.

Add to calendar :

Date/Time : 03 Oct 2025 15:00
Venue : S17 #04-04 (Seminar Room 3)
Speaker : Mihir Mittal, Indian Institute of Technology Kanpur

Zarankiewicz’s problem asks: Given a bipartite graph on n vertices without a K_{k,k} subgraph, how many edges can it have? The classical Kővári–Sós–Turán Theorem gives us the bound O(n^{2-1/k}); this remains the best possible bound for general situations. In geometric settings, however, stronger bounds can be achieved. Recent work of Basit, Chernikov, Starchenko, Tao, and Tran showed that semi-linear incidence graphs in real vector spaces admit almost-linear Zarankiewicz bounds.

In this talk I will describe a counterpart of their result for the additive group of the p-adic numbers and more generally in valued vector spaces. This is obtained through introducing a new purely combinatorial notion of laminarity. As a corollary, we get almost-linear bounds for K_{k,k}-free point–box and point–polytope incidence graphs in these settings.

Add to calendar :

Date/Time : 29 Jul 2025 14:00
Venue : S17 #06-11 (Seminar Room 6)
Speaker : Vilas Sreenivasan Winstein, University of California, Berkeley

Independent sets have long been studied as a model for gases in statistical mechanics, and Sapozhenko’s famous graph container method was developed to understand their quantity in the hypercube, where they correspond to error-detecting codes. When removing edges at random (i.e. percolating the hypercube), the number of independent sets in the resulting graph becomes the partition function of a disordered system, akin to popular models like spin glasses. I will discuss a new probabilistic framework which establishes sharp distributional characterizations of this partition function and the underlying disordered system, settling several open problems and explaining various phase transitions observed in this model. This is joint work with Mriganka Basu Roy Chowdhury and Shirshendu Ganguly.

Add to calendar :

Date/Time : 17 Apr 2025 13:00
Venue : S16 #03-06
Speaker : Abdul Basit, Monash University

The independent set sequence of a graph is the sequence whose k^th term is the number of independent sets of size k in the graph. Alavi, Malde, Schwenk and Erdős studied this sequence in 1987, and showed that it can exhibit any pattern of rises and falls. They raised the question, however, of whether the independent set sequence of a tree, or more generally a forest, is always unimodal — that is, has a single peak. This intriguing question is still very much open. I’ll survey some recent results about this question. (Some of this is joint work with David Galvin and Misha Isarev.)

Add to calendar :

Date/Time : 17 Apr 2025 14:00
Venue : S16 #03-06
Speaker : Cheng Yui To, National University of Singapore

Freiman’s theorem is a cornerstone of additive combinatorics, providing a structural description of finite sets of integers with small doubling. In this talk, I will present an extension of Freiman’s theorem to infinite subsets of the integers by replacing cardinality with density. Our main tool is the abelian Lie model theorem, which harnesses the powerful machinery of ultraproducts to pass from density—a less well-behaved notion—to Haar measures, where the classical proof strategy of Freiman’s theorem can be adapted. (Joint work with Peng Fei and Tran Chieu-Minh, part of undergrad honor project requirement).

Add to calendar :

Date/Time : 17 Apr 2025 15:00
Venue : S16 #03-06
Speaker : Kong Zuxiang, National University of Singapore

Convex sets in Euclidean space enjoy the elegant property that convexity is preserved under quotient projections. From the perspective of additive combinatorics, small doubling—a condition where a set grows slowly under addition—is a natural generalization of convexity, as illustrated by equality condition in the famous Brunn–Minkowski inequality. In this talk, I will discuss recent progress on how small doubling behaves under quotients in the setting of nonabelian locally compact groups. As part of my joint paper with Fei and Tran as well as my honors thesis, we improve on a work by An, Jing, Zhang, and Tran, by proving new bounds relating the doubling constant of a set to that of its image under a quotient map. In particular, we establish a sharp quadratic bound when the set is symmetric, a cubic bound in general, and a structural result showing that a large subset with linear doubling survives the quotient. These results offer a refined understanding of how additive structure interacts with quotient projections, and bridges geometry, analysis, and combinatorics in nonabelian settings. (Joint work with Peng Fei and Tran Chieu-Minh, part of undergrad honor project requirement).

Add to calendar :

Date/Time : 24 Mar 2025 14:00
Venue : S17 #05-11 (SR5)
Speaker : Wei-Hsuan Yu, National Central University

We address the maximum size of binary codes and binary constant weight codes with few distances. Previous works established a number of bounds for these quantities as well as the exact values for a range of small code lengths. As our main results, we determine the exact size of maximal binary codes with two distances for all lengths n≥6 as well as the exact size of maximal binary constant weight codes with 2,3, and 4 distances for several values of the weight and for all but small lengths.

Add to calendar :

Date/Time : 24 Mar 2025 15:00
Venue : S17 #05-11 (SR5)
Speaker : Chia-En Chiang, National Taiwan Normal University

An almost k-cover of the hypercube Q^n = {0,1}^n is a collection of hyperplanes that avoids the origin and covers every other vertex at least k times. When k is large with respect to the dimension n, Clifton and Huang asymptotically determined the minimum possible size of an almost k-cover. Central to their proof was an extension of the LYM inequality, concerning a weighted count of hyperplanes.

In this paper we completely characterise the hyperplanes of maximum weight, showing that there are $\binom{2n-1}{n}$ such hyperplanes. We further provide stability, bounding the weight of all hyperplanes that are not of maximum weight. These results allow us to effectively shrink the search space when using integer linear programming to construct small covers, and as a result we are able to determine the exact minimum size of an almost k-cover of Q^6 for most values of k. We further use the stability result to improve the Clifton–Huang lower bound for infinitely many choices of k in every sufficiently large dimension n.

Add to calendar :