The beauty of mathematics is often encountered when one discovers that two apparently very different phenomena actually share a common origin. I will discuss such a surprising connection between two apparently unrelated mathematical objects. One is purely combinatorial: the number of ways one can drive from USC to the Claremont Colleges. The other one is […]
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 be tweaked to give most characteristic classes in differential and complex geometry).
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 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 to encode many invariants of a metric space such as volume, dimension, and capacity. When studying a metric space in topological data analysis using persistent […]
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 how one can prove a generalization that counts roots of two bivariate polynomials (with few monomial terms), using nothing more than basic calculus. In other […]
In 2007, Dr. Maria D'Orsogna learned of proposed oil activities in her home region of Abruzzo, Italy. Century-old wineries were to be uprooted to build clusters of oil wells, refineries and pipelines, turning scenic Abruzzo into an oil district. Although based in California, 6,000 miles away, Dr. D'Orsogna took it upon herself to raise awareness […]
A fascinating fact on mathematics is that there are many interesting connections between seemingly different mathematical disciplines. In this talk, I will present a surprising formula counting integral points on polygons and sketch its proof. We will see a delightful interaction between algebra, combinatorics, and geometry. This talk aims primarily for undergraduate students. No prerequisite […]
Silica-based glasses are increasingly becoming vital components in our current technology, from optical data transmission lines, to electronics, to optical lenses, to smartphone screens. These materials are inherently brittle and subject to failure under shock, non-equilibrium stress states, or corrosive environments. Identifying new compositions and processing conditions that result in improved fracture resistance (i.e. a […]
UNAIDS has proposed an ambitious strategy for ending the HIV pandemic. Their strategy depends upon achieving a treatment coverage goal of 90% by 2030. However, distance to healthcare and lack of transportation are major barriers to accessing HIV treatment in SSA. I will use data-based geospatial modeling to determine their potential impact as barriers to […]
In today's environment of universal connection and media updates, we are constantly informed about infectious diseases and the ramifications. We can combat infectious diseases using mathematics to gain insight into diseases dynamics and outbreaks. I will focus primarily on Ebola Virus Disease, exploring different models focused on capturing various dynamics. First, I will present a […]
In general terms, a Tauberian theorem deals with the relationship between the properties of one transform of a measure with those of another transform. We will introduce the notion of a Tauberian theorm, and present our own recent theorem in this direction. Our theorem provides a uniform theory for the construction of certain localized kernels […]
In this talk, we'll discuss the problem of constructing meaningful distances between probability distributions given only finite samples from each distribution. We approach this through the use of data-adaptive and localized kernels, and in a variety of contexts. First, we construct locally adaptive kernels to define fast pairwise distances between distributions, with applications to unsupervised […]
