Harry Richman, Distinguishing graphs with tropical Weierstrass weights
2026-06-16 16:30 - 17:30 (Asia/Seoul) | Room B332, IBS (기초과학연구원)
I will introduce a new structure on finite graphs, which takes the form of a labeling of the vertices by nonnegative integers (possibly repeated). This labeling is isomorphism invariant, and seems to reflect some mix of local and global structure of the graph. I will describe an algorithm for computing these labels, which uses a form of breadth-first search, and some results on the resulting labels. This construction comes from a tropical analogue of Weierstrass weights on algebraic curves, studied in the 1800s. Finally, I will discuss some speculation on whether this may or may not be helpful for the graph isomorphism problem.
This is a joint work with Omid Amini and Lucas Gierczak.

Stefan Weltge, The relaxation complexity of the standard simplex is logarithmic
2026-06-19 16:30 - 17:30
For a set $X$ of integer points, the relaxation complexity $operatorname{rc}(X)$ is the smallest number of facets of any polyhedron P whose integer points are precisely those of X. In this paper, we focus on the case where X is the discrete standard simplex $Delta_d = {0, e_1, …, e_d}$. We show that $operatorname{rc}(Delta_d) = O(log d)$ by an explicit, elementary construction. This improves upon the previously best-known upper bound $operatorname{rc}(Delta_d) = O(d / sqrt{log d})$ due to Aprile, Averkov, Di Summa, and Hojny (2022) and matches an asymptotic lower bound by Averkov and Schymura (2020). This is joint work with Simon Keil.

Ting-Wei Chao, The Oddtown Problem Modulo a Composite Number
2026-07-10 16:30 - 17:30
A family of sets in $[n]$ is called an $ell$-Oddtown if the sizes of all sets are not divisible by $ell$, but the sizes of pairwise intersections are divisible by $ell$. The problem was completely solved when $ell$ is a prime via an elegant linear algebraic method, showing that the family has size at most $n$. However, not much was known for composite numbers. By splitting the family into families correspond to each prime factor of $ell$, one can show that the number is at most $omega n$, where $omega$ is the number of prime factors of $ell$. We used both combinatorial and Fourier analytic arguments to prove that the number of sets in any $ell$-Oddtown is at most $omega n-(2omega+varepsilon)log_2 n$ for most $n,ell$.

Stephan Kreutzer, TBA
2026-07-28 16:30 - 17:30

Tomohiro Koana, TBA
2026-08-04 16:30 - 17:30

Meike Hatzel, TBA
2026-08-05 16:30 - 17:30

Jinyoung Park (박진영), TBA
2026-08-18 16:30 - 17:30
