Date/Time : 28 Jan 2026 16:00
Venue : S17 #05-11 (Seminar Room 5)
Speaker : Swee Hong Chan, Rutgers University

Consider the set of positive integers representing the number of spanning trees in simple graphs with n vertices. How quickly can this set grow as a function of n? In this talk, we discuss a proof of the exponential growth of this set, which resolves an open problem of Sedlacek from 1966. The proof uses a connection with continued fractions and advances towards Zaremba’s conjecture in number theory. This is joint work with Alex Kontorovich and Igor Pak. This talk is intended for general audience.

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Date/Time : 16 Jan 2026 16:00
Venue : S17 #04-06 (Seminar Room 1)
Speaker : Seog-Jin Kim, Konkuk University, Korea

The square of a graph G, denoted G^2, has the same vertex set as G and has an edge between two vertices if the distance between them in G is at most 2. Thomassen (2018) showed that \chi(G^2)<=7 if G is a subcubic planar graph. A natural question is whether \chi_l(G^2)<=7 or not if G is a subcubic planar graph. Recently Kim and Lian (2024) showed that \chi_l(G^2)<=7 if G is a subcubic planar graph of girth at least 6. And Jin, Kang, and Kim (2025) showed that \chi_l(G^2)<=7 if G is a subcubic planar graph without 4-cycles and 5-cycles. In this talk, we show that the square of a subcubic planar graph without 5-cycles is 7-choosable, which improves the previous results.

This is joint work with Xiaopan Lian, Atsuhiro Nakamoto, and Kenta Ozeki.

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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.

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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.

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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.

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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.

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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.)

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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).

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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).

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