Colloquium

A normally functioning menstrual cycle requires significant crosstalk between hormones originating in ovarian and brain tissues. Reproductive hormone dysregulation may disrupt function and can lead to infertility, as occurs in the common endocrine disorder polycystic ovarian syndrome (PCOS). In this talk, I will discuss a mathematical model of the ovulatory cycle that accounts for mechanisms […]

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 of re-proving these results, we obtain an original result that provides an analogue of Sarkozy's theorem in the finite field setting (showing that any subset […]

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 ability to gather data grows at an enormous rate,  the importance of this work continues to grow too. The lecture will describe this paper, and developments that […]

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 question in both developmental biology and regenerative medicine, and it is still an unsolved mystery in many systems. During the growth, tissues and organs always […]

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 […]