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 […]