Job Talk – Scripps Candidate for Assistant Professor in Mathematics
Job Talk: Christina Edholm, University of Tennessee "Epidemiological models examining two susceptible classes" Monday, February 25 4:00-4:50pm Balch 218, Scripps College
Job Talk: Christina Edholm, University of Tennessee "Epidemiological models examining two susceptible classes" Monday, February 25 4:00-4:50pm Balch 218, Scripps College
Modular forms are ubiquitous in modern number theory. For instance, showing that elliptic curves are secretly modular forms was the key to the proof of Fermat's Last Theorem. In addition to number theory, modular forms show up in diverse areas such as coding theory and particle physics. Roughly speaking, a modular form is a complex-valued […]
Abstract: Whether enjoying the lucid prose of a favorite author or slogging through some other writer's cumbersome, heavy-set prattle (full of parentheses, em-dashes, compound adjectives, and Oxford commas), readers will notice stylistic signatures not only in word choice and grammar, but also in punctuation itself. Indeed, visual sequences of punctuation from different authors produce marvelously […]
One foundational pillar of low dimensional topology is the connection between link invariants and 3-manifold invariants. One generalization of this has been given by Reshetikhin and Turaev to a surgery theory for colored ribbon graphs. Then to complete the analogy rather than 3-manifold invariants we now have a 2+1 dimensional topology quantum field theory (TQFT). […]
Candidate for Assistant Professor in Mathematics Howard Levinson, University of Michigan Seeing Clearly Through a Microscope The goal of microscope imaging is to obtain high-resolution images of cells. However, due to the underlying physics involved, the resulting images are often blurred. In this talk, I will develop the mathematical framework to describe this blurring, which […]
One very important concept in understanding a dynamical system is coherent structure. Such structure segments the domain into different regions with similar behavior according to a quantity. When we try to partition space-time into regions according to a Lagrangian quantity advected along with passive tracers, such class of coherent structure is called the Lagrangian coherent […]
TOPIC: Graph Theory, Part II On the surface, graphs seem to be some of the simplest objects you might encounter in mathematics. After all, they are made up of just two kinds of parts, vertices and edges, and those parts fit together in simple ways. But appearances can be deceiving! In this series of two […]
I will present mathematical and computational methods used to model interactions between a viscous fluid and elastic structures in biological processes. For example, microfluidic devices carry very small volumes of liquid through channels and may be used to gain insight into many biological applications including drug delivery and development, but mixing and pumping at this […]
Chebotarev's theorem on roots of unity says that every minor of a discrete Fourier transform matrix of prime order is nonzero. We present a generalization of this result that includes analogues for discrete cosine and discrete sine transform matrices as special cases. This leads to a generalization of the Biro-Meshulam-Tao uncertainty principle to functions with […]
Abstract: Growing up, I always loved learning about world-changing scientific breakthroughs that were discovered by accident. Penicillin, artificial sweeteners, X-rays, and synthetic dyes are just a few of the discoveries that were stumbled upon by scientists who had other goals in mind. More recently, I have come to wonder why anecdotes about accidental discoveries in […]
For two genus $g$ handlebody-knots $H_{1}$ and $H_{2}$, we denote $H_{1} \geq H_{2}$ if there exists an epimorphism from the fundamental group of the handlebody-knot complement of $H_{1}$ onto the one of $H_{2}$. In the case of $g = 1$, this order is a partial order on the set of prime knots and has been […]
We study the problems of clustering covariance stationary ergodic processes and locally asymptotically self-similar stochastic processes, when the true number of clusters is priorly known. A new covariance-based dissimilarity measure is introduced, from which efficient consistent clustering algorithms are obtained. As examples of application, clustering fractional Brownian motions and clustering multifractional Brownian motions are respectively performed to illustrate the asymptotic consistency of […]