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Measurement error, formally defined as the difference between the measured value and the true value of a quantity of interest, is ubiquitous. When a doctor takes your blood pressure, the […]
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Job Talk: Christina Edholm, University of Tennessee "Epidemiological models examining two susceptible classes" Monday, February 25 4:00-4:50pm Balch 218, Scripps College |
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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 […] |
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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 […] |
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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). […]
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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 […]
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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 […] |
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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 […]
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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 […] |
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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 […] |
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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 […] |
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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 […] |
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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, […] |
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In 1897, Indiana physician Edwin J. Goodwin believed he had discovered a way to square the circle, and proposed a bill to Indiana Representative Taylor I. Record which would secure Indiana's the claim to fame for his discovery. About the time the debate about the bill concluded, Purdue University professor Clarence A. Waldo serendipitously came […] |
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A lot of the mathematics done at NIST supports the research on and measurement of advanced materials and technology. In this rather applied context. surprising mathematics makes an appearance. We […] |
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I will talk about a few graph-theoretic metrics then introduce the concept of refinements on a class of functions that include all metrics. As a case study, we will construct various refinements on the shortest-path distance. Consequently, we obtain a few "better" versions of the Erdos number. In the course of our investigation, we realized various construction […] |
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Abstract: As intelligent agents assume larger role in our daily lives, reasoning by humans about liability of such agents as well as reasoning by the intelligent agents themselves about liability […] |
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The traditional method of treating most human diseases is to direct a therapy against targets in the host patient, whereas conventional therapies against infectious diseases are directed against the pathogen. […] |
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A Fibonomial is what is obtained when you replace each term of the binomial coefficients $ {n \choose k}$ by the corresponding Fibonacci number. For example, the Fibonomial $${ 6\brace 3 } = \frac{F_6 \cdot F_5 \cdot \dots \cdot F_1}{(F_3\cdot F_2 \cdot F_1)(F_3\cdot F_2 \cdot F_1)} = \frac{8\cdot5\cdot3\cdot2\cdot1\cdot1}{(2\cdot1\cdot1)(2\cdot1\cdot1)} = 60$$ since the first six Fibonacci […] |
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Abstract: We overview some basic and striking facts concerning the theory of hypercyclic operators (considered to be born in 1982): 1. Hypercyclicity is a purely infinite-dimensional phenomenon: no finite dimensional […] |
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