Individuals may choose to create social groups where their individual fitness and success is influenced by those around them. A group may increase an individual's success in finding food, shelter, and safety; however, if the group fails, so does the individual. In this talk, we will explore how choices of individuals influence group dynamics using both agent-based modeling […]
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 […]
Shannons sampling theorem provides a link between the continuous and thediscrete realms stating that bandlimited signals are uniquely determined by itsvalues on a discrete set. This theorem is realized in practice using so called analog to digital converters (ADCs). Unlike Shannons sampling theorem, the ADCs are limited in dynamic range. Whenever a signal exceeds some […]
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 […]
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 […]
At the turn of the twentieth century, physicist Henri Bénard heated a shallow plate of fluid from below. For temperatures above a critical value, the fluid’s evenly heated state became unstable as thermal convection took hold; heated fluid rose in localized areas while cooler fluid fell nearby. The rising and falling fluid created hexagonal convection cells, […]
We review some recent developments in the study of biquandle brackets and other quantum enhancements.
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 […]
Clustering in image analysis is a central technique that allows to classify elements of an image. We describe a simple clustering technique that uses the method of similarity matrices, and an algorithm in which a collection of image elements is treated as a dynamical system. Efficient clustering in this framework is achieved if the dynamical system admits […]
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 a power permutation of $F$. For any function $f: F \to F$, and $a, b \in F$, we define the differential multiplicity of $f$ with respect to […]
Markov chains are widely used throughout mathematics, statistics, and the sciences, often for modelling purposes or for generating random samples. In this talk I’ll discuss a different, more recent application of Markov chains, to developing distributed algorithms for programmable matter systems. Programmable matter is a material or substance that has the ability to change its […]
Counting points on algebraic curves over finite fields has numerous applications in communications and cryptology, and has led to some of the most beautiful results in 20th century arithmetic geometry. A natural generalization is to count the number of points over prime power rings, e.g., the integers modulo a prime power. However, the theory behind the latter kind of point […]
