Title: Cobordism Categories and Spaces of Manifolds. Abstract: Cobordisms have been one of the central objects in topology since the pioneering work of Rene Thom, which provided the first link between manifolds and homotopy theory. In more recent years, there has been much focus on cobordism categories. These play a fundamental role in the study […]
I plan to explain how a purely algebraic technique involving Lie Algebra Cohomology can be used to construct standard characteristic classes of vector bundles and foliations (in fact, it could […]
We develop two new pricing formulae for European options. The purpose of these formulae is to better understand the impact of each term of the model, as well as improve […]
A classic and fundamental result in number theory is due to Mordell who proved that the set of points on an elliptic curve defined over a number field forms a […]
Speaker: Kate Meyer, Cornell University Abstract: Biodiversity underpins ecosystem functioning but continues to decline on a global scale. Among human activities driving this trend, habitat destruction is a leading culprit in local and global extinctions. Simple mathematical models can address important questions surrounding habitat-driven extinctions---for example, which species are at highest risk, how delayed might […]
The hypothalamic-pituitary-adrenal (HPA) axis is a neuroendocrine system that regulates numerous physiological processes. Disruptions are correlated with stress-related diseases such as PTSD and major depression. We characterize "normal" and "diseased" […]
The magnitude is an isometric invariant of metric spaces that was introduced by Tom Leinster in 2010, and is currently the object of intense research, as it has been shown […]
Counting points on algebraic curves over finite fields has numerous applications in communications and cryptology, and has led to some of the most beautiful results in 20th century arithmetic geometry. A natural generalization […]
We review a beautiful 17th century result by the philosopher Rene Descartes: a univariate real polynomial with t monomial terms has no more than t-1 positive roots. We then see […]
TOPIC: The Mathematics of Information We are surrounded by information. Words in books, ones and zeros in computers, mathematical equations, and DNA sequences are all examples of information, but can […]
Markov chains are widely used throughout mathematics, statistics, and the sciences, often for modelling purposes or for generating random samples. In this talk I’ll discuss a different, more recent application […]
If $F$ is a finite field and $d$ is a positive integer relatively prime to $|F^\times|$, then the power map $x \mapsto x^d$ is a permutation of $F$, and so is called […]
