Algebra / Number Theory / Combinatorics Seminar

If $F$ is a finite field and $d$ is a positive integer relatively prime to $|F^\times|$, then the power map $x \mapsto x^d$ is a permutation of $F$, and so is called […]

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 […]

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 […]

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 that every such set can be covered by k-n+1 parallel hyperplanes, but do there exist sets that cannot be covered by fewer parallel hyperplanes? We […]

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 polynomial invariant. This is joint work with Karma Istanbouli (Scripps College).

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 […]