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; […]
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 […]
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 […]
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 […]
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 […]
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 […]
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 […]
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 […]
