Abstract: In this talk, we first present some elementary new proofs (using Cayley digraphs and spectral graph theory) for Waring's problem over finite fields, and explain how in the process […]
The mean of a random quantity is supposed to confirm our expectations. What happens when it defies them? We will look at a few famous expected values; some old, some […]
I will begin by describing a number of important examples of isometric actions of circles in Euclidean space and their restrictions to subspaces of Euclidean space. The goal of the talk will […]
Abstract: Bats in North America have been dying off due to the invasion of a fungal disease (White Nose Syndrome). In this talk, I'll present a very simple linear algebraic […]
Abstract: In 1960 Rudolph Kalman published what is arguably the first paper to develop a systematic, principled approach to the use of data to improve the predictive capability of mathematical models. As our […]
Growth regulation and pattern formation are two main problems in developmental biol- ogy. How cells know when to stop growing at certain tissue size with specic shape is an important […]
Convolutional sparse representation is an efficient tool for computing sparse representations for entire signals in terms of sums of a set of convolutions with dictionary filters. Unlike representations that are based on overlapping image patches, the convolutional representation optimizes over the entire image, yielding representations that are very sparse both spatially and across the filters. […]
Abstract: The kissing number problem asks for the maximal number k(n) of equal size nonoverlapping spheres in n-dimensional space that can touch another sphere of the same size. This problem […]
Abstract: Augusta Ada, Countess of Lovelace, is today viewed as the rst person to recognize the power of algorithmic machines and a pioneer in computer programming. Her biographers have often disagreed on her mathematical talents, her mathematical contributions, and her legacy. In this talk I explore the various approaches taken towards her, focusing explicitly on […]
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 […]
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 […]
