From the view of a pure mathematician, those working in pure mathematics produce pure knowledge. Whether used or not, it has a great elegance and value in and of itself. Those in applied mathematics simply pick up what has been done and use it in designing or building things. Number theory is often used to […]
Based on geometric considerations, J. Roger and T. Yang in 2014 defined a version of the Kauffman bracket skein algebra for punctured surfaces that includes arcs going from puncture to puncture. We'll provide a brief survey of known results about this arc algebra. In particular, I'd like to mention a recent algebraic result whose […]
TOPIC: Graph Theory, Part I On the surface, graphs seem to be some of the simplest objects you might encounter in mathematics. After all, they are made up of just two kinds of parts, vertices and edges, and those parts fit together in simple ways. But appearances can be deceiving! In this series of two […]
Approximately 500 million tweets are sent everyday. Scientists monitor these tweets to predict the spread of disease, better allocate social welfare services, help first responders during natural disasters, and many other important tasks. A key step in each of these tasks is estimating the location the tweet was sent from. In this talk, I discuss how to combine machine […]
Tight frames in Euclidean spaces are widely used convenient generalizations of orthonormal bases. A particularly nice class of such frames is generated as orbits under irreducible actions of finite groups of orthogonal matrices: these are called irreducible group frames. Integer spans of rational irreducible group frames form Euclidean lattices with some very nice geometric properties, […]
In the 1970s, James O’Keefe and his team observed that certain neurons in the brain, called place cells, spike in their firing rates when the animal is in a particular physical location within its arena. If a place cell is thought of as either “active” or “silent,” then one may represent the co-firing patterns of […]
Online social networks and other networks of interest are known to exhibit community structure, where a community is defined to be a highly interconnected group of nodes with possibly shared traits or features. However, classic network models, such as the preferential attachment model, do not account for community structure. In this talk, I will present […]
Given integers $k,l$ and a graph $G$, how large can be the fraction of $k$-vertex subsets of $G$ which span exactly $l$ edges? The systematic study of this very natural question was recently initiated by Alon, Hefetz, Krivelevich and Tyomkyn who also proposed several interesting conjectures on this topic. In this talk we discuss a theorem […]
Understanding how fluid flows through heterogeneous materials, and how it can make these materials fail, are among the hardest challenges in materials science. Experiments and simulations show that flow through subsurface rock is mostly limited to a small subnetwork, or backbone, of fractures. Identifying this backbone would allow for a large speedup in flow and […]
Candidate for Assistant Professor in Mathematics, Scripps College A surprising application of mathematics: How to name a color Your brain likes patterns and categories; by grouping related ideas together, it can store and recall information quickly. Real-life continuous domains (like time and taste) are inherently composed of infinitely many points of information, which your brain […]
An agent comes to a fork in a road. There is a sign that says that one of the two roads leads to prosperity and another to death. The agent must take the fork, but she does not know which road leads where. Does the agent have a strategy to get to prosperity? On one […]
Abstract: A great deal of my research journey has involved the study of m-ary partitions. These are integer partitions wherein each part must be a power of a fixed integer m > 1. Beginning in the late 1960s, numerous mathematicians (including Churchhouse, Andrews, Gupta, and Rodseth) studied divisibility properties of m-ary partitions. In this talk, I will discuss work I completed […]
