Facets 2022: Schedule

The definition of a matroid is easily stated and understood. So is that of log-concavity. Mason's log-concavity conjectures for matroids (which too are easily stated) have been in the news of late: they find mention in the 2022 Fields Medal award citation of June Huh. The talk will be an introductory exposition aimed at college students of these conjectures and their proofs.

We will familiarize ourselves with a multiplicity automaton - this is a kind of finite graph that represents functions from (an infinite set of) words to integers. We will see some examples/exercises of designing such automata for some functions. We will see an algorithm to determine if two such automata represent the same function.

Every time you move your head you are rotating the space around you. And you do this constantly, every day, every minute, while you're awake and even while you're asleep. But how well do you really know the collection of rotations of three dimensional space? With the help of a spherical puppet we'll count the dimensions of the space of rotations, and then try to understand the shape of this rather perplexing and counter-intuitive space: if you wear a belt or have a long plait of hair it'll come in handy here! To build your intuition for this space, you will construct a spherical puppet of your own, which you will send on a journey through some very strange loops. So come prepared to move your body! Finally, we'll enlist the aid of the Quaternion numbers to definitively know our place in the space of rotations.

This talk will be about some of the algorithms used to solve combinatorial games, like sudoku, and combinatorial optimization problems, like scheduling, routing, etc. These algorithms are "dumb" in the sense that they only use random numbers and require very little prior insight to the specific problem. However they are very interesting as they draw inspiration from real physical and biological processes, which seem to naturally use these algorithms. The talk will also make connections between combinatorial optimization problems and others like spin glasses, protein folding etc.

Numbers have been an integral part of human evolution. Mathematics was born from our curiosity to understand the mystery of numbers and it still continues to baffle us. In this talk, we will discuss some elementary problems in number theory, some methods to approach them and a few questions which remain unsolved.

I present a personal perspective of my crossover journeys between mathematics and music with computing as a go-between pathway. I draw inspiration from a number of sources using which I've dispelled myths about each for myself, and how that added joy to the pursuit of both. We'll talk about similarities between the cultures of musicians and mathematicians and take lessons from masters to (hopefully) bring some of that joy into our own lives. We'll explore "mathematicking" in the same spirit as "musicking" -- with our bodies -- and share stories of how children relate to both, and how we forget that. My hope is in part to demystify these abstract arts enough so we all feel encouraged to experience them in whatever measure comes to us ... and perhaps contribute some of that joy back to our world.