Probability is a now-classic tool in combinatorics, especially graph theory. Some applications of probabilistic techniques are: (1) describing the typical/expected properties of a class of objects, (2) uncovering phase transitions […]
In this talk, I will describe an approach to finding upper bounds for the number of arithmetic operations necessary for doing harmonic analysis on permutation modules of finite groups. The […]
Several conditions are known for a self-inversive polynomial that ascertain the location of its roots, and we present a framework for comparison of those conditions. We associate a parametric family […]
Let K be a field and S = K be the polynomial ring in n variables over K. For a graded S-module M with minimal free resolution the Castelnuovo-Mumford regularity […]
Let S be a set of k > n points in n-dimensional Euclidean space. How many parallel hyperplanes are needed to cover it? In fact, it is easy to prove […]
Quandle coloring quivers categorify the quandle counting invariant. In this talk we enhance the quandle coloring quiver invariant with quandle modules, generalizing both the quiver invariant and the quandle module […]
It is well known that a real number is badly approximable if and only if the partial quotients in its continued fraction expansion are bounded. Motivated by a recent wonderful paper by Ngoc Ai Van Nguyen, Anthony Poels and Damien Roy (where the authors give a simple alternative solution of Schmidt-Summerer's problem) we found an […]
The talk will concentrate on open questions related to the optimal bounds for the discrepancy of an $N$-point set in the $d$-dimensional unit cube. The so-called star-discrepancy measures the difference between the actual and expected number of points in axis-parallel rectangles, and thus measures the equidistribution of the set. This notion has been explored by H. Weyl, K. Roth, and many others, […]
For k >= 2, the k-coloring graph C(G) of a base graph G has a vertex set consisting of the proper k-colorings of G with edges connecting two vertices corresponding to two different colorings of G if those two colorings differ in the color assigned to a single vertex of G. A base graph whose […]
The orthosymplectic Lie superalgebra $\mathfrak{osp}(1|2n)$ is rich in representation theory: while the finite dimensional $\mathfrak{osp}(1|2n)$-module category is semisimple, the study of infinite dimensional representations of $\mathfrak{osp}(1|2n)$ is wide open. In […]
