This is a very brief introduction to oriented matroids based on personal recollection, with hope that the theory gets wider attention from younger generation of mathematics in Korea.
The Maximum Independent Set (MIS) problem is NP-complete and remains so for every minor-closed graph class that includes all planar graphs (Garey and Johnson [SIAM J. Appl. Math.'77]). On the other hand, due to the Grid Theorem of Robertson and Seymour [JCTB'95], every minor-closed graph class that excludes a planar graph has bounded treewidth, and MIS can be solved in polynomial time on such...
In this talk, I’ll share a few of these thoughts, from research focus to future planning, in the hope that they resonate with others in similar stages. There won’t be any magic answers, but maybe a few ideas that help make the uncertainty a bit more manageable.
We introduce a linear-time algorithm for computing the Frobenius normal form (FNF) of symmetric Toeplitz matrices by utilizing their inherent structural properties through a graph-theoretic approach. Previous results of the authors established that the FNF of a symmetric Toeplitz matrix is explicitly represented as a direct sum of symmetric irreducible Toeplitz matrices, each corresponding to...
The Gowers uniformity norm has played a significant role in additive combinatorics as a measure of randomness associated with solution sets of certain linear configurations. In this talk, I introduce the notion of Gowers uniformity norms and demonstrate how they capture additive structures in a given set of integers. Gowers norms capture additive structures both through k-term arithmetic...
