Are you tall?: An Introduction to the Sorites Paradox and Fuzzy Logic
In this talk, we will introduce fuzzy logic, a non-classical logic that provides a mathematically rigorous way of dealing with vagueness. We will motivate the development of fuzzy logic using a philosophical paradox known as the Sorites paradox, or the paradox of the heap. We will explore a particular type of fuzzy logic called Lukasiewicz fuzzy logic. Finally, we will return to the Sorites paradox and see how it can be resolved using this fuzzy logic.
Fictional Mathematics: A Brief Glimpse into Math in Fantasy and Science Fiction
Mathematics pops up all over the place in storytelling, from evaluating limits in the background of Mean Girls to an episode of Futurama that spawned its own theorem. Science fiction writers have been inspired by mathematical breakthroughs for generations (and quite a few more fantasy authors than you might think!) In this talk I will highlight some of the many ways mathematics has been used in speculative fiction, with the goal of emphasizing the inherent creativity of math and all the weird and wacky ways it can be used in storytelling.
Data Assimilation via Hayden-Olson-Titi: Approximating Solutions of Differential Equations Using Sparse Data
How could one model something as complicated as the weather while only measuring how the air is moving at a few points? Data Assimilation describes a broad class of methods which aim to approximate the solution of some differential equation by integrating sparse observed data into the solution in some way. In this talk, we explore the data assimilation method of Hayden, Olson, and Titi (HOT for short) for several different ordinary differential equations. We will explore when the method provides accurate approximations, when the approximations break down, and discuss how one could apply this method to many other models of interest.
Code Design for Data Storage in Synthetic DNA
Storing data in synthetic DNA is an emerging data storage technology. Nanopore sequencers are devices that allow for the quick and cheap, if currently error-prone, retrieval and decoding of information stored in synthetic DNA. In this talk we will discuss the DNA code design problem for nanopore sequencers and provide a graph construction of a code that accommodates the three primary combinatorial restrictions imposed by nanopore sequencers. Moreover, we show that our code can quickly detect erroneous insertions, deletions, and substitutions that can be introduced during the DNA storage process.