Blerta Shtylla

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 new, all great.

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 be to see how isometric actions of circles and tori can be used to "recognize" the space on which they are acting.

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 model to predict the magnitude of the die-offs. By comparing these models to some data about actual bat survival, my collaborator and I also hypothesized […]

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 in dimension three was the subject of a famous discussion between Isaac Newton and David Gregory in 1694. In three dimensions the problem was finally […]

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. […]

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 […]

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 […]

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 > […]