Mathematicians like to count things. Often in very complicated and fancy ways. In this talk I will explain how we can use quantum Airy structures -- an abstract formalism recently proposed by Kontsevich and Soibelman, underlying the Eynard-Orantin topological recursion -- to count various interesting geometric structures. Quantum Airy structures can be seen as a […]
We review some recent developments in the study of biquandle brackets and other quantum enhancements.
Domination in graphs has been an important and active topic in graph theory for over 40 years. It has immediate applications in visibility and controllability. In this talk we will discuss a generalization of domination called exponential domination. A vertex $v$ in an exponential dominating set assigns weight $2^{1−dist(v,u)}$ to vertex $u$. An exponential dominating […]
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 and sudden thresholds in the dependence of one property on another, and (3) producing examples of conjectured or unusual objects. (This last technique is sometimes […]
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 and sudden thresholds in the dependence of one property on another, and (3) producing examples of conjectured or unusual objects. (This last technique is sometimes […]
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 […]
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 […]
