Title: The Jones Polynomial and Representation Theory Abstract: In this talk, I’ll briefly introduce knots and links. Then, I’ll introduce the Jones Polynomial, an invariant of knots and links. Finally, I’ll show the connection between the Jones Polynomial and the representation theory … Read more
Title: Data Assimilation with an Application to Sea Ice Modelling Abstract: The abundance of oceanic and atmospheric data presents the question of how to incorporate this data into scientific models. Data assimilation is the process by which observations are fused … Read more
381 Phillips Hall, 4:00 pm – 5:00 pm Speaker: Samuel Jeralds, UNC Chapel Hill Title: A Gentle Introduction to Affine (and other) Lie Algebras Abstract: Affine Lie algebras are certain infinite-dimensional partners to the more familiar finite-dimensional semisimple Lie algebras. … Read more
Title: Diagonalizing the Laplacian - A Tourist's Guide to Spectral Theory Abstract: This talk is aimed at first and second year grad students who are interested in analysis, or really anyone with a passing curiosity about what analysts do all … Read more
Title: Building equations one molecule at a time Abstract: I work on multiscale models of the cytoskeleton, a system of proteins that ultimately give biological cells their mechanical properties. At the molecular level, there is a bewildering amount of complexity, … Read more
Speaker: Josh Kiers Part 1: A survey of the BGG description of cohomology of flag varieties, with applications Abstract: In these lectures we will follow the original paper of Bernstein, Gel'fand, and Gel'fand (Schubert cells and cohomology of the spaces G/P) which … Read more
Part 2: A survey of the BGG description of cohomology of flag varieties, with applications Abstract: In these lectures we will follow the original paper of Bernstein, Gel'fand, and Gel'fand (Schubert cells and cohomology of the spaces G/P) which identifies the cohomology … Read more
Title: Rate-induced Tipping in Maps Abstract: The study of dynamical systems can be divided into two main categories: continuous-time (flows) and discrete-time (maps). Although these types of systems are defined differently, we look for the same kinds of features in both of … Read more
Part 3: A survey of the BGG description of cohomology of flag varieties, with applications Abstract: In these lectures we will follow the original paper of Bernstein, Gel'fand, and Gel'fand (Schubert cells and cohomology of the spaces G/P) which identifies the cohomology … Read more
Title: Categories, and Why You Shouldn't Be Afraid of Them Abstract: Developed in the early 1940s, category theory offers a powerful, universally applicable set of tools in many fields of mathematics. However, in part due to its generality and how we discuss … Read more
Title: Spectral Asymptotics and the Heat Kernel. Abstract: In this lecture series, our goal will be to prove a result known as Weyl's law, which tells us how the Laplace eigenvalues of a compact manifold are distributed. Since eigenvalues are … Read more
Part 4: A survey of the BGG description of cohomology of flag varieties, with applications Abstract: In these lectures we will follow the original paper of Bernstein, Gel'fand, and Gel'fand (Schubert cells and cohomology of the spaces G/P) which identifies the cohomology … Read more
